%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV837-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:18:50 EDT 2023

% Result   : Unsatisfiable 9.72s 3.13s
% Output   : Refutation 10.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  619
% Syntax   : Number of formulae    : 1187 ( 257 unt;  52 typ;   0 def)
%            Number of atoms       : 2661 ( 588 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 17034 (1452   ~;1526   |;   0   &;14056   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   93 (  93   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  52 usr;   7 con; 0-4 aty)
%            Number of variables   : 3760 (   0   ^;3760   !;   0   ?;3760   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
    c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).

thf(v_G_Ha_type,type,
    v_G_Ha: $i ).

thf(v_tsa_type,type,
    v_tsa: $i ).

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

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

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

thf(v_Ga_type,type,
    v_Ga: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_SetInterval_Oord__class_OgreaterThan_type,type,
    c_SetInterval_Oord__class_OgreaterThan: $i > $i > $i ).

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

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

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

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

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

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

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

thf(c_SetInterval_Oord__class_OatLeast_type,type,
    c_SetInterval_Oord__class_OatLeast: $i > $i > $i ).

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

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

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

thf(c_SetInterval_Oord__class_OatMost_type,type,
    c_SetInterval_Oord__class_OatMost: $i > $i > $i ).

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

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

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

thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
    c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1_type,type,
    c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1: $i > $i > $i > $i > $i ).

thf(class_Orderings_Otop_type,type,
    class_Orderings_Otop: $i > $o ).

thf(c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1_type,type,
    c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1: $i > $i > $i > $i ).

thf(c_Orderings_Oorder__class_Omono_type,type,
    c_Orderings_Oorder__class_Omono: $i > $i > $i > $o ).

thf(c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1_type,type,
    c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1: $i > $i > $i > $i > $i ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(371,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

thf(1411,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(191,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).

thf(1024,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(439,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(1559,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(291,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ D @ E @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).

thf(1237,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ D @ E @ A )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(327,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(1315,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(153,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(941,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(777,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_1) ).

thf(1554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(559,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1823,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(557,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

thf(1818,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I8_J_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(1401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).

thf(1205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ C )
      | ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ C )
      | ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(1041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1750,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(977,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(254,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(1158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(582,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(454,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1596,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(369,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(1406,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1443,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(553,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(1808,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
      | ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(741,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
      | ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(545,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(1793,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(427,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1533,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).

thf(1078,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(460,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(1608,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(715,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).

thf(1233,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1260,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(474,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1640,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(416,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__atLeast_0) ).

thf(1507,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1458,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(411,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

thf(1497,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(530,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).

thf(1761,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(339,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ~ ( class_Lattices_Oupper__semilattice @ B )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ C @ D ) @ ( hAPP @ C @ E ) @ B ) @ ( hAPP @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ A ) ) @ B )
      | ~ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__sup_0) ).

thf(1342,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ~ ( class_Lattices_Oupper__semilattice @ B )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ C @ D ) @ ( hAPP @ C @ E ) @ B ) @ ( hAPP @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ A ) ) @ B )
      | ~ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(1001,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(540,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(462,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).

thf(1613,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(477,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

thf(1645,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1359,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(1366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(550,axiom,
    class_Lattices_Oboolean__algebra @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

thf(1803,plain,
    class_Lattices_Oboolean__algebra @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__subset__iff_1) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(651,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
      | ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(829,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
      | ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(224,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

thf(1095,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(513,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(1724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(401,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1475,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

thf(1265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(503,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(1703,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(469,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(1628,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).

thf(1287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(6,negated_conjecture,
    ! [A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ v_tsa @ t_a )
      | ~ ( c_lessequals @ v_G_Ha @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(570,plain,
    ! [A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ v_tsa @ t_a )
      | ~ ( c_lessequals @ v_G_Ha @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_0) ).

thf(1430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(333,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(1330,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(310,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(1279,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(447,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).

thf(1577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).

thf(619,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1059,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(241,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
      | ~ ( c_in @ B @ E @ F )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1132,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
      | ~ ( c_in @ B @ E @ F )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(433,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

thf(1545,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).

thf(1479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(186,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Set_Oimage @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

thf(1013,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Set_Oimage @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1568,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(1641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(536,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(1773,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(538,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(1778,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(288,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(1232,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(166,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).

thf(969,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Otop @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(1347,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Otop @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(445,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

thf(1572,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_fun @ D @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

thf(1398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_fun @ D @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1415,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(924,plain,
    ! [A: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(509,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(1714,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(335,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E )
      | ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

thf(1334,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E )
      | ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(491,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(1051,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).

thf(1109,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(1632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(243,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(1136,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).

thf(834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(1151,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(151,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

thf(937,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(359,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1383,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1020,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1183,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(29,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(124,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      | ~ ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(877,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      | ~ ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(956,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(866,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(546,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1796,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(343,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(1351,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(272,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(1201,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(456,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(1564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).

thf(774,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(1104,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).

thf(1242,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(479,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).

thf(1651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).

thf(1691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1438,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(91,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(793,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

thf(1306,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(1199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(398,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(1708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(1067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(519,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

thf(1736,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(534,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(1768,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

thf(1047,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(516,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

thf(1730,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

thf(798,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(1057,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(158,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

thf(952,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

thf(1255,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

thf(862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(102,axiom,
    ! [A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).

thf(820,plain,
    ! [A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__iff_1) ).

thf(630,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ C @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(1223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ C @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__iff_0) ).

thf(894,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1355,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).

thf(1580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).

thf(1174,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(88,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
      | ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(788,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
      | ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(1619,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(457,axiom,
    ! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).

thf(1602,plain,
    ! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

thf(625,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(114,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(852,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(665,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(496,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
      | ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
      | ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(1687,plain,
    ! [B: $i,A: $i] :
      ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
      | ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
      | ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(467,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).

thf(1624,plain,
    ! [A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(129,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(889,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(1128,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(311,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(1291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(565,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).

thf(1836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1I_0) ).

thf(1787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(1656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(269,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(1195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(521,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).

thf(1740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(842,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(1143,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(531,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(1762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(428,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

thf(1534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ( c_in @ D @ B @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(551,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1804,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(1064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(488,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(1672,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != ( c_Orderings_Otop__class_Otop @ A ) )
      | ( C
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

thf(869,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != ( c_Orderings_Otop__class_Otop @ A ) )
      | ( C
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

thf(1755,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(52,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

thf(697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).

thf(1541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(980,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(1498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).

thf(783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(1118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I2_J_0) ).

thf(1160,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

thf(1028,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(933,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(520,axiom,
    class_Finite__Set_Ofinite_Ofinite @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(1739,plain,
    class_Finite__Set_Ofinite_Ofinite @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

thf(642,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).

thf(637,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(1214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).

thf(1446,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(375,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

thf(1419,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(409,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).

thf(1493,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(494,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).

thf(1683,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(554,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(544,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

thf(1791,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__fun__def_1) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).

thf(590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeast @ B @ A )
       != ( c_SetInterval_Oord__class_OatLeast @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).

thf(679,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeast @ B @ A )
       != ( c_SetInterval_Oord__class_OatLeast @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(198,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1039,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).

thf(622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(563,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funI_0) ).

thf(1831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 @ B @ C @ D @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(654,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ C @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(1552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ C @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(173,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(984,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(1799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(1,negated_conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_G_Ha @ v_tsa @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(569,plain,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_G_Ha @ v_tsa @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(295,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_lessequals @ E @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).

thf(1246,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_lessequals @ E @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(511,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1720,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(529,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(560,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1825,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(34,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
      | ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(647,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
      | ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(451,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).

thf(1099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).

thf(1451,plain,
    ! [B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(69,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(392,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(1382,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

thf(1434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(792,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(220,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

thf(1779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1695,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

thf(1035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).

thf(1026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(1185,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(517,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

thf(1732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(396,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1466,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(1071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(266,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(674,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(309,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1278,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(478,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1648,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

thf(1698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(405,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__lessThan_0) ).

thf(1483,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I1_J_0) ).

thf(1273,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(524,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).

thf(1747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).

thf(1548,plain,
    ! [A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(116,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(856,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(72,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(745,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(321,axiom,
    ! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

thf(1301,plain,
    ! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(4,negated_conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ v_G_Ha @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(573,plain,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ v_G_Ha @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(353,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1374,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(470,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(1631,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_1) ).

thf(601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(965,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(74,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
      | ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
      | ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1251,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(532,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

thf(1764,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(564,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).

thf(694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).

thf(732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(526,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(1752,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_0) ).

thf(743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(8,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(579,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(502,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(1520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(1124,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1615,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(541,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Ovimage @ A @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D )
        = B )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

thf(1784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Ovimage @ A @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D )
        = B )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(1389,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
       != ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

thf(826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
       != ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).

thf(1428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I10_J_0) ).

thf(1669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(3,negated_conjecture,
    c_lessequals @ v_G @ v_Ga @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(572,plain,
    c_lessequals @ v_G @ v_Ga @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1312,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(472,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(1635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(1332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(222,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__Int__atLeast_0) ).

thf(1090,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(473,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(490,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(1139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

thf(1271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(919,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(804,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(276,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(1209,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(106,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(831,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(423,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(1524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1349,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).

thf(990,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(458,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(1603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(535,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(1771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).

thf(1574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(552,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).

thf(1806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(1043,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(549,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1667,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(399,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

thf(1471,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(700,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(915,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1344,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(357,axiom,
    class_Lattices_Olower__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(1381,plain,
    class_Lattices_Olower__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I7_J_0) ).

thf(1061,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(558,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).

thf(1820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).

thf(758,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(337,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ~ ( class_Lattices_Olower__semilattice @ B )
      | ( c_lessequals @ ( hAPP @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ A ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ C @ D ) @ ( hAPP @ C @ E ) @ B ) @ B )
      | ~ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__inf_0) ).

thf(1339,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ~ ( class_Lattices_Olower__semilattice @ B )
      | ( c_lessequals @ ( hAPP @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ A ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ C @ D ) @ ( hAPP @ C @ E ) @ B ) @ B )
      | ~ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(566,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(1838,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(1325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatMost @ B @ A )
       != ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatMost @ B @ A )
       != ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).

thf(1460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(1022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__iff_1) ).

thf(1293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__subset__iff_0) ).

thf(1396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(1445,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(986,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(537,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1775,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(1102,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(922,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
      | ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).

thf(912,plain,
    ! [A: $i] :
      ( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
      | ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(685,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(780,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(476,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

thf(1643,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != B )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(1176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != B )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).

thf(608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(514,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

thf(1726,plain,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1364,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(1413,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(468,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(1626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != ( c_Orderings_Otop__class_Otop @ A ) )
      | ( B
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != ( c_Orderings_Otop__class_Otop @ A ) )
      | ( B
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(323,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(1304,plain,
    ! [B: $i,A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I2_J_0) ).

thf(1166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(146,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

thf(927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(1134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(99,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ B @ C )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(812,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ B @ C )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(218,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

thf(1081,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(22,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(617,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

thf(939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).

thf(836,plain,
    ! [A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(1049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1145,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

thf(1018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(1181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(1003,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(640,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(128,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(887,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(442,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__greaterThan_0) ).

thf(1368,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatMost @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1267,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(426,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).

thf(1531,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1I_1) ).

thf(1230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(419,axiom,
    class_Orderings_Otop @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(1516,plain,
    class_Orderings_Otop @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(455,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(1598,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(252,axiom,
    class_Lattices_Odistrib__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(1156,plain,
    class_Lattices_Odistrib__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I13_J_0) ).

thf(1225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(954,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(298,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = C )
      | ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(1252,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = C )
      | ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(1432,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(555,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
      | ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

thf(1813,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
      | ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(585,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ C )
        = B )
      | ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

thf(1317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ C )
        = B )
      | ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(492,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      | ~ ( c_in @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

thf(1679,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      | ~ ( c_in @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(281,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

thf(1218,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(1336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(282,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(1220,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(907,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(507,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

thf(1053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).

thf(1262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).

thf(1235,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(482,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

thf(1658,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).

thf(1538,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).

thf(1404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(703,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(344,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(864,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(727,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

thf(1585,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(547,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).

thf(1797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ C @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(1008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).

thf(1717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(2,negated_conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ v_G_Ha @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(571,plain,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ v_G_Ha @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(859,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(533,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(1766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).

thf(1141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Ovimage @ A @ B @ D @ C ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Set_Ovimage @ A @ B @ D @ C ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(283,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1221,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__atMost_0) ).

thf(1284,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OgreaterThan @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).

thf(845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(376,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(1421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(567,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
      | ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(1839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
      | ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(1084,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(253,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1157,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(480,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1654,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).

thf(1517,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1216,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(1126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__iff_0) ).

thf(1734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OatMost @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(495,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).

thf(1685,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(903,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(315,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(391,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Set_Oimage @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

thf(1453,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Set_Oimage @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(512,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ B @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(1745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ B @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(28,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      | ~ ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(632,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      | ~ ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(1244,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(87,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
      | ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

thf(786,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
      | ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ B @ A @ C )
      | ( c_in @ B @ D @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

thf(995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ B @ A @ C )
      | ( c_in @ B @ D @ C )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(1276,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(452,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(1590,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(699,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Ovimage @ B @ ( c_Set_Oinsert @ ( hAPP @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ D @ C ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

thf(1341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Ovimage @ B @ ( c_Set_Oinsert @ ( hAPP @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ D @ C ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1689,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(5,negated_conjecture,
    ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ v_tsa @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(568,plain,
    ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ v_tsa @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(140,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(914,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(216,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(1077,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(1212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(483,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

thf(1661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I8_J_0) ).

thf(1309,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(194,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).

thf(1030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).

thf(1491,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(1440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ( c_in @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(1116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D )
      | ( c_in @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(999,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OgreaterThan @ B @ A )
       != ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__eq__iff_0) ).

thf(752,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OgreaterThan @ B @ A )
       != ( c_SetInterval_Oord__class_OgreaterThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(967,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(528,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(17,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ( B = C )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(603,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ( B = C )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

thf(1593,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(356,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1380,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1527,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1673,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(1248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(790,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).

thf(1436,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Otop__class_Otop @ A ) )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).

thf(801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Otop__class_Otop @ A ) )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(499,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I14_J_0) ).

thf(1561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeast @ B @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(543,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      | ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

thf(1789,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      | ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
      | ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(1610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(92,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(796,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(556,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

thf(1816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(410,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1495,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(259,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1172,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(767,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).

thf(1033,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(506,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(1710,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(400,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1473,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(987,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(562,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).

thf(1829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeast @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeast @ B @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(561,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(1827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

thf(1550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1357,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(982,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(1120,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(1093,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(839,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(14,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(596,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(355,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( class_Orderings_Oorder @ B )
      | ( c_lessequals @ ( hAPP @ C @ D ) @ ( hAPP @ C @ E ) @ B )
      | ~ ( c_lessequals @ D @ E @ A )
      | ~ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoD_0) ).

thf(1378,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( class_Orderings_Oorder @ B )
      | ( c_lessequals @ ( hAPP @ C @ D ) @ ( hAPP @ C @ E ) @ B )
      | ~ ( c_lessequals @ D @ E @ A )
      | ~ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(850,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(508,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1713,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(415,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(1505,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(1399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(459,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Oboolean__algebra @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

thf(1606,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Oboolean__algebra @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).

thf(1037,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

thf(1088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) @ A )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).

thf(1069,plain,
    ! [B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) @ A )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(1417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

thf(755,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(1841,plain,
    $false,
    inference(e,[status(thm)],[1665,1411,1024,1559,1237,1315,941,1179,777,1554,645,892,1823,1190,909,628,1818,1295,1005,1522,1401,1728,1205,1269,614,1041,1486,1750,977,1158,582,1596,1406,1443,1808,741,1073,1793,1533,1078,1608,715,1233,1327,1260,1640,945,1507,1458,1497,1705,1761,1342,747,898,1001,1782,1391,973,1613,1645,1359,1386,1366,1529,1803,1228,651,829,1095,1724,1475,1265,1703,1628,1055,1287,570,1430,719,1330,917,1279,1577,1323,619,1059,1132,1545,1147,1479,1013,1568,1641,1773,1778,1232,969,606,1347,1572,1398,881,1415,924,1302,1714,1334,1677,1051,905,1109,1632,1136,834,1151,937,1383,1020,1183,1283,1169,634,877,956,866,1796,1394,1351,1201,1600,1564,1622,774,1104,1242,1651,1691,1438,793,1306,1199,761,810,1470,1708,1067,1736,1768,714,1047,1730,798,1057,1163,952,1255,862,598,820,630,815,729,1223,894,1355,1580,1570,1174,788,1619,1423,847,1602,625,879,852,665,1687,1624,889,1128,1281,1291,1106,1836,1787,1210,1656,682,1195,1740,842,1143,1762,1534,1804,1064,725,1425,1672,593,869,1755,697,1541,980,1498,783,1118,884,1160,1028,1361,933,1739,642,637,1214,1446,1419,1493,1683,901,1075,1810,1791,1016,1207,590,679,1039,622,1297,1831,654,1552,1192,984,1799,569,1246,1720,1759,1825,1114,647,997,1588,1099,1451,738,1456,1382,1434,792,1086,1779,805,1695,657,1035,1663,1026,1185,662,1732,1466,1071,1187,674,1278,1648,1698,1483,1273,1747,1548,856,745,1301,573,1374,1631,601,965,750,1510,1251,1764,1154,975,1833,694,732,772,1752,743,579,958,1701,1520,1124,1488,1615,1784,1389,875,826,711,1428,1669,572,1312,611,1635,1239,1332,1090,1258,947,1638,1675,1139,1503,1271,1371,919,804,764,1209,831,1408,1524,1349,990,1603,1771,1122,1376,1574,1806,649,1043,1801,1667,1471,700,1149,915,1344,1381,1061,1820,1112,758,1339,1838,1325,1556,769,1460,943,1022,1293,668,1396,1445,986,1775,1477,1102,922,912,685,780,1643,1176,608,1726,1364,1413,1626,722,1583,1304,1166,1203,927,1134,812,1081,617,939,836,1049,1145,1018,1181,823,1003,640,872,887,971,1566,1368,1267,1531,1230,993,1516,1598,705,1156,1225,1743,954,1252,1432,1813,585,717,1317,1679,1130,1218,1336,1220,907,1711,1053,1262,1235,576,1658,1538,808,1404,703,1353,864,727,1585,1797,1008,1717,571,859,1617,1543,1766,1141,1536,1221,1284,845,1421,1839,1084,671,1157,1654,1517,1216,1126,1448,1010,1734,931,1685,688,903,1289,1453,1721,963,1481,1745,632,1244,786,995,1276,1590,588,699,1341,896,1689,568,914,1077,1212,1513,1661,1309,1045,1030,1491,1440,929,1116,999,752,967,818,854,1757,603,735,950,1097,1593,1380,1527,1673,1248,790,1436,801,1693,1561,1789,1610,796,1816,1495,1172,767,1033,1710,1197,960,1473,987,1829,1827,1550,1357,1500,982,1299,691,1120,1093,839,596,1378,850,1713,1505,1399,1606,1320,935,1681,1037,1088,1468,1069,708,1417,1463,659,755,676]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SWV837-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n031.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Fri May 19 03:16:56 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.92/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.77/1.08  % [INFO] 	 Parsing done (247ms). 
% 1.87/1.09  % [INFO] 	 Running in sequential loop mode. 
% 2.39/1.29  % [INFO] 	 eprover registered as external prover. 
% 2.39/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 2.39/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.66/1.40  % [INFO] 	 Found a conjecture and 568 axioms. Running axiom selection ... 
% 2.98/1.51  % [INFO] 	 Axiom selection finished. Selected 561 axioms (removed 7 axioms). 
% 3.53/1.66  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.82/1.67  % [INFO] 	 Type checking passed. 
% 3.82/1.67  % [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 ... 
% 9.72/3.12  % External prover 'e' found a proof!
% 9.72/3.12  % [INFO] 	 Killing All external provers ... 
% 9.72/3.12  % Time passed: 2613ms (effective reasoning time: 2032ms)
% 9.72/3.12  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.72/3.13  % Axioms used in derivation (561): cls_vimage__code_0, cls_inf__sup__aci_I2_J_0, cls_atLeastatMost__subset__iff_2, cls_Diff__cancel_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_Compl__subset__Compl__iff_1, cls_order__le__less__trans_0, cls_inj__image__mem__iff_1, cls_atLeastatMost__psubset__iff_1, cls_inf__sup__absorb_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_asm_0, cls_subset__insert_1, cls_ivl__disj__un_I8_J_0, cls_Diff__iff_2, cls_Compl__Diff__eq_0, cls_compl__sup_0, cls_insertE_0, cls_less__fun__def_1, cls_Un__Diff_0, cls_Un__subset__iff_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_sup__ge1_0, cls_ivl__disj__un_I21_J_0, cls_sup__top__left_0, cls_inj__on__Un_2, cls_xt1_I12_J_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_finite__insert_0, cls_Diff__eq_0, cls_predicate1I_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_atLeastatMost__psubset__iff_2, cls_sup__bot__right_0, cls_insert__code_1, cls_atMost__Int__atLeast_0, cls_atLeastLessThan__subset__iff_1, clsarity_bool__Lattices_Olower__semilattice, cls_finite__vimageI_0, cls_linorder__neqE_0, cls_vimage__Diff_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_image__Int_0, cls_UnCI_1, cls_distrib__sup__le_0, cls_Int__mono_0, cls_le__iff__inf_1, cls_le__fun__def_1, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Int__subset__iff_2, cls_Diff__subset__conv_0, cls_mem__def_1, cls_atLeastatMost__psubset__iff_3, cls_le__inf__iff_1, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_less__supI1_0, cls_minus__diff__eq_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_inf1E_1, cls_Diff__triv_0, cls_insert__iff_1, cls_insert__subset_0, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inj__image__subset__iff_0, cls_inj__on__Un__image__eq__iff_0, cls_less__minus__iff_0, cls_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_neg__less__iff__less_1, cls_Int__absorb1_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_Compl__partition_0, cls_disjoint__eq__subset__Compl_0, cls_inf__commute_0, cls_inj__image__mem__iff_0, cls_inj__image__Compl__subset_0, cls_sup__compl__top_0, clsarity_fun__Orderings_Otop, cls_finite__insert_1, cls_atMost__subset__iff_1, cls_diff__eq_0, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_set__mp_0, cls_ivl__disj__un_I13_J_0, clsarity_bool__HOL_Oord, cls_finite__Int_1, cls_Int__empty__right_0, cls_Compl__atMost_0, cls_order__less__asym_0, cls_Un__subset__iff_1, 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cls_ball__empty_0, cls_Int__insert__right_0, cls_psubset__eq_2, cls_atLeastatMost__empty_0, cls_empty__Diff_0, cls_lessThan__iff_1, cls_subset__insert__iff_1, cls_neg__less__iff__less_0, cls_single__Diff__lessThan_0, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0
% 9.72/3.13  % No. of inferences in proof: 1135
% 9.72/3.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2613 ms resp. 2032 ms w/o parsing
% 10.53/3.30  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.53/3.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------