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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT027-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:27:03 AM UTC 2026

% Result   : Unsatisfiable 27.41s 7.59s
% Output   : Refutation 30.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  701
% Syntax   : Number of formulae    : 1403 ( 321 unt;   0 typ;   0 def)
%            Number of atoms       : 3431 ( 858 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 27270 (1738   ~;2028   |;   0   &;23504   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   95 (  93 usr;   9 con; 0-9 aty)
%            Number of variables   : 5338 (   0   ^;5338   !;   0   ?;5338   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
    v_thesis____: $o ).

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

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

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

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

thf(tc_prod_decl,type,
    tc_prod: $i > $i > $i ).

thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
    tc_Arrow__Order__Mirabelle_Oalt: $i ).

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

thf(c_Arrow__Order__Mirabelle_OLin_decl,type,
    c_Arrow__Order__Mirabelle_OLin: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Collect_decl,type,
    c_Collect: $i > $i > $i ).

thf(c_Pair_decl,type,
    c_Pair: $i > $i > $i > $i > $i ).

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

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

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

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

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

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

thf(c_Relation_Oconverse_decl,type,
    c_Relation_Oconverse: $i > $i > $i > $i ).

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

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

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

thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
    c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Set__XbexI__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__XbexI__1__1: $i > $i > $i > $i ).

thf(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_decl,type,
    v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).

thf(c_Relation_OImage_decl,type,
    c_Relation_OImage: $i > $i > $i > $i > $i ).

thf(c_Equiv__Relations_Oequiv_decl,type,
    c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).

thf(c_SetInterval_Oord_OgreaterThanAtMost_decl,type,
    c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).

thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1_decl,type,
    c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: $i > $i > $i > $i > $i ).

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

thf(c_FuncSet_OPi_decl,type,
    c_FuncSet_OPi: $i > $i > $i > $i > $i ).

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

thf(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1_decl,type,
    c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__CHAINED__1_decl,type,
    v_sko__CHAINED__1: $i ).

thf(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3_decl,type,
    c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3: $i > $i > $i > $i ).

thf(c_Equiv__Relations_Oquotient_decl,type,
    c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).

thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
    c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).

thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
    c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Set__XbexE__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__XbexE__1__1: $i > $i > $i > $i ).

thf(c_Typedef_Otype__definition_decl,type,
    c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).

thf(c_ATP__Linkup_Osko__Set__XballE__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__XballE__1__1: $i > $i > $i > $i ).

thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
    c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).

thf(c_HOL_Oundefined_decl,type,
    c_HOL_Oundefined: $i > $i ).

thf(c_FuncSet_Oextensional_decl,type,
    c_FuncSet_Oextensional: $i > $i > $i > $i ).

thf(c_SetInterval_Oord_OgreaterThan_decl,type,
    c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).

thf(c_SetInterval_Oord_OatLeastLessThan_decl,type,
    c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).

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

thf(c_Set_OPow_decl,type,
    c_Set_OPow: $i > $i > $i ).

thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
    c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).

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

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

thf(c_SetInterval_Oord_OgreaterThanLessThan_decl,type,
    c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).

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

thf(c_Fun_Ooverride__on_decl,type,
    c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__Set__XbexCI__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__XbexCI__1__1: $i > $i > $i > $i ).

thf(c_FuncSet_Osko__FuncSet__XPi__I__1__1_decl,type,
    c_FuncSet_Osko__FuncSet__XPi__I__1__1: $i > $i > $i > $i > $i > $i ).

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

thf(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1_decl,type,
    c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1_decl,type,
    c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1_decl,type,
    c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__Equiv__Relations__XquotientE__1__1_decl,type,
    c_List_Osko__Equiv__Relations__XquotientE__1__1: $i > $i > $i > $i > $i ).

thf(c_Not_decl,type,
    c_Not: $i ).

thf(c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3_decl,type,
    c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1_decl,type,
    c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: $i > $i > $i > $i ).

thf(c_FuncSet_Osko__FuncSet__XextensionalityI__1__1_decl,type,
    c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_SetInterval_Oord_OlessThan_decl,type,
    c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3_decl,type,
    c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: $i > $i > $i > $i > $i ).

thf(c_SetInterval_Oord_OatMost_decl,type,
    c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).

thf(640,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

thf(2163,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(655,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__iff_2) ).

thf(2199,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(309,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(1411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).

thf(1633,plain,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(1767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(564,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(1995,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(1559,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(525,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).

thf(1899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(266,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(1315,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(202,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ ( D @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__image_0) ).

thf(1179,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ ( D @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

thf(1554,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(676,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(2250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(1586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Collect ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).

thf(809,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Collect ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(516,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).

thf(1879,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).

thf(1337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(493,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).

thf(1823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(207,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(1190,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(893,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(499,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(1840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(1295,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(546,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(1950,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(1549,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(1200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).

thf(977,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).

thf(1211,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_0) ).

thf(1290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(667,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

thf(2231,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(595,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(2062,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(487,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).

thf(1808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(453,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(1728,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(878,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(481,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(1793,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

thf(1305,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(395,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(1596,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(307,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).

thf(1406,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(1422,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(1569,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(675,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_4) ).

thf(2248,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(572,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(2014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(611,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(2099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(691,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).

thf(2282,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(617,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).

thf(2114,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

thf(1142,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(245,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(1269,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).

thf(1173,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(343,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(1486,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(653,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).

thf(2195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(1655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_8) ).

thf(1137,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(466,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).

thf(1756,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(582,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__emptyset_0) ).

thf(2035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(456,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(1735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Collect ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).

thf(1867,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Collect ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(1275,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(513,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( D @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ ( A @ ( C @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_0) ).

thf(1872,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( D @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ ( A @ ( C @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(642,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(2168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(533,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(468,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(413,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(1640,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(1164,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(566,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).

thf(1999,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(797,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).

thf(1222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_0) ).

thf(1196,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(587,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(2046,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(476,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).

thf(1782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(36,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(709,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(575,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(2020,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(415,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).

thf(1645,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(604,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).

thf(2082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(76,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(885,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(144,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).

thf(1046,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(644,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

thf(2173,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).

thf(1366,plain,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(597,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(2067,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

thf(1529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(2136,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(527,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

thf(1904,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(358,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_1) ).

thf(1518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).

thf(1265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(441,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(1703,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(406,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_0) ).

thf(1623,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(341,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).

thf(1482,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(408,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__mem_0) ).

thf(1628,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).

thf(1430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(584,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(2039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(686,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( tc_bool @ ( C @ ( C @ ( C @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).

thf(2269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( tc_bool @ ( C @ ( C @ ( C @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(528,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1907,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(494,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(1826,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(623,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).

thf(2126,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(148,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(508,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(1860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(662,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__mem_0) ).

thf(2217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(270,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_9) ).

thf(1323,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(838,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(688,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(2274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(1,negated_conjecture,
    ~ v_thesis____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(702,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).

thf(1279,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_0) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).

thf(1800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(130,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1013,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(175,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

thf(1115,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).

thf(1100,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1232,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(502,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1847,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(534,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( G @ ( F @ ( E @ ( D @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_ORep__inject_0) ).

thf(1922,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( G @ ( F @ ( E @ ( D @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(817,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(1247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(588,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(2049,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).

thf(1319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( D @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).

thf(1479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( D @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(401,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(1609,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).

thf(1362,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(551,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__disj_0) ).

thf(1963,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(514,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1875,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1778,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(569,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).

thf(2007,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(646,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_4) ).

thf(2178,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_12) ).

thf(1489,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(92,axiom,
    tc_nat @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(924,plain,
    tc_nat @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(544,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_3) ).

thf(1946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(608,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(2090,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(293,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(1373,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(1040,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(680,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(2259,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(312,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(1418,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1020,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(1051,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(905,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(24,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(756,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(424,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).

thf(1664,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(488,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(1811,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(326,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).

thf(1450,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1682,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(507,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1858,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(510,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( C @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensionalityI_1) ).

thf(1864,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( C @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(621,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( B @ hAPP ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).

thf(2122,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( B @ hAPP ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(191,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

thf(1151,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(98,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(937,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(550,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).

thf(1960,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(1183,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).

thf(2073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_11) ).

thf(1169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(219,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( C @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ c_HOL_Oundefined ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensional__arb_0) ).

thf(1215,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( C @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ c_HOL_Oundefined ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).

thf(956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(519,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).

thf(1886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(1072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(774,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).

thf(1394,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1351,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(318,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(1433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(397,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).

thf(1600,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(1696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = C )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).

thf(1975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(500,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1843,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(593,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(2058,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(651,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_2) ).

thf(2190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_1) ).

thf(1526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(629,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

thf(2137,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(279,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).

thf(1345,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(988,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(693,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_0) ).

thf(2286,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

thf(1104,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
       != ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).

thf(1242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
       != ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(1074,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(571,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(2011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(1206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(657,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(2204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(435,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1691,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(320,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_0) ).

thf(1438,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(925,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

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

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(619,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(2118,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexI_0) ).

thf(1067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(6,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(714,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(454,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( D @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).

thf(1730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( D @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(1915,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(443,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(1708,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(609,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(2093,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(697,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( A = E )
      | ( B = E )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).

thf(2296,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( A = E )
      | ( B = E )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(2264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(451,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_0) ).

thf(1723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

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

thf(746,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(778,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(1042,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(285,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(1355,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(238,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).

thf(1255,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1487,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(626,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(2132,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1238,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(429,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ ( B @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_OAbs__inverse_0) ).

thf(1676,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ ( B @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(627,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

thf(2133,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(634,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(2150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

thf(1883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Set_OPow ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PowD_0) ).

thf(1560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Set_OPow ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(541,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_11) ).

thf(1938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(289,axiom,
    tc_bool @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(1365,plain,
    tc_bool @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(553,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(1968,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).

thf(1457,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(54,axiom,
    tc_nat @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

thf(830,plain,
    tc_nat @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(78,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(889,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(478,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_11) ).

thf(1787,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(1079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(616,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(2112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(171,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_1) ).

thf(1106,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(1032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).

thf(1837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1392,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(666,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).

thf(2228,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(1740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( D @ hAPP ) @ hBOOL )
      | ( B @ ( D @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ballE_1) ).

thf(1573,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( D @ hAPP ) @ hBOOL )
      | ( B @ ( D @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(114,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(974,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(228,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_COMBB ) ) ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).

thf(1234,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_COMBB ) ) ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(559,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

thf(1983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(637,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).

thf(2157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(1804,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(349,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Collect ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).

thf(1498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Collect ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(315,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
        = ( F @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__in_0) ).

thf(1425,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
        = ( F @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(167,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP2__I_0) ).

thf(1096,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(449,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1719,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_5) ).

thf(1118,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).

thf(1360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(674,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).

thf(2245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(540,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).

thf(1936,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).

thf(1270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(1851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(472,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).

thf(1772,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( A = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(240,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).

thf(1259,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

thf(1534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

thf(1953,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(173,axiom,
    c_Arrow__Order__Mirabelle_OLin @ ( v_sko__CHAINED__1 @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1111,plain,
    c_Arrow__Order__Mirabelle_OLin @ ( v_sko__CHAINED__1 @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(554,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(1970,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(1856,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(857,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_13) ).

thf(1397,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(1567,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(346,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).

thf(1493,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(1160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(331,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(1461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(603,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(2080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_1) ).

thf(1584,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(480,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(1791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(520,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).

thf(1889,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(402,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ ( c_Not @ c_COMBB ) ) ) ) @ c_Collect ) )
      = ( B @ ( A @ c_Collect ) @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).

thf(1612,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ ( c_Not @ c_COMBB ) ) ) ) @ c_Collect ) )
      = ( B @ ( A @ c_Collect ) @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(706,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(160,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ ( E @ ( A @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_1) ).

thf(1082,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ ( E @ ( A @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(577,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(2023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(542,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

thf(1942,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(1659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(311,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).

thf(1414,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(590,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(2053,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(614,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).

thf(2108,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(324,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_1) ).

thf(1446,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

thf(1249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(738,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(182,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(1131,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(673,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(2243,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(1060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(721,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(560,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).

thf(1984,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(447,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(1715,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(557,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(1979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(630,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(2140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(361,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1525,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(242,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(997,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(622,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(2125,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(1588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(364,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

thf(1530,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1382,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(635,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).

thf(2153,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(208,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).

thf(1192,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(538,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(1932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(911,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(1333,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(213,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_2) ).

thf(1202,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(586,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

thf(2043,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

thf(1695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(206,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( D @ ( G @ ( E @ ( A @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_OAbs__inject_0) ).

thf(1187,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( D @ ( G @ ( E @ ( A @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(1185,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).

thf(1814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(162,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_2) ).

thf(1086,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(445,axiom,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(1712,plain,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(1286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(155,axiom,
    c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).

thf(1071,plain,
    c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(423,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).

thf(1663,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(607,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(2089,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).

thf(1515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).

thf(2221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_0) ).

thf(1167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(31,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(773,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(794,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(669,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(2235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(184,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).

thf(1135,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).

thf(2001,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(439,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(1698,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(581,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(2033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
      = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).

thf(1273,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
      = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(462,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(1747,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(536,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(1927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(681,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).

thf(2260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(111,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(965,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(236,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( A @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1251,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( A @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(469,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B = D )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).

thf(1764,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B = D )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).

thf(1146,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(579,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterD_0) ).

thf(2028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(1301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).

thf(1154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(50,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(819,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(665,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

thf(2225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(300,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1389,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(650,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(2188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).

thf(1620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(464,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(1752,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

thf(1652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(573,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(2016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(826,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(482,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).

thf(1795,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

thf(1520,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(224,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

thf(958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).

thf(1403,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(652,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).

thf(2193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(696,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(2293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(1371,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(411,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1635,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ c_Collect ) @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).

thf(1058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ c_Collect ) @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(565,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).

thf(1997,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

thf(1090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(919,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(223,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ ( A @ ( E @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).

thf(1224,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ ( A @ ( E @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(633,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(2148,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(428,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(1675,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inter__lower_0) ).

thf(1428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(639,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_0) ).

thf(2161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(186,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).

thf(1139,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(351,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).

thf(1503,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(591,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).

thf(2055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(1092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

thf(1464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(947,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(1194,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(1282,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(522,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(486,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1806,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(282,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(1349,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).

thf(1144,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(618,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(2116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(880,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(178,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

thf(1122,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(654,axiom,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).

thf(2197,plain,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(1175,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(605,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_1) ).

thf(2084,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(661,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(2214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(679,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(2257,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(990,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(692,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).

thf(2284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

thf(1603,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(698,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).

thf(2299,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(1571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(1376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(811,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1471,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(578,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

thf(2025,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).

thf(1557,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(685,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(2267,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(195,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(1162,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(509,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_3) ).

thf(1862,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(848,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(271,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(1325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1029,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(190,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(1149,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(677,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( B @ c_Collect ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).

thf(2252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( B @ c_Collect ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).

thf(1112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(890,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(425,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).

thf(1667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(647,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = E )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).

thf(2180,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = E )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(1630,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).

thf(1993,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(601,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Collect ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).

thf(2075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Collect ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).

thf(1198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(1474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(660,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_6) ).

thf(2212,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(606,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

thf(2086,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(780,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(596,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(2064,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(201,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).

thf(1176,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(339,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).

thf(1477,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(922,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(555,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1973,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(598,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ ( A @ ( E @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_0) ).

thf(2069,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ ( A @ ( E @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(380,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(1562,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(218,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_7) ).

thf(1213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

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

thf(768,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(589,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).

thf(2051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1044,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(233,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ ( E @ ( A @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).

thf(1245,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ ( E @ ( A @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(694,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_1) ).

thf(2288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(473,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).

thf(1775,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1000,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(348,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ c_Collect ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_0) ).

thf(1496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ c_Collect ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(700,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(2303,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(545,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).

thf(1948,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(610,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ ( B @ c_Typedef_Otype__definition ) ) ) ) )
      | ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_ORep__inverse_0) ).

thf(2096,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ ( B @ c_Typedef_Otype__definition ) ) ) ) )
      | ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(467,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( E @ ( C @ ( B @ ( A @ ( D @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensionalityI_0) ).

thf(1758,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( E @ ( C @ ( B @ ( A @ ( D @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(216,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

thf(1208,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(687,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).

thf(2271,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(313,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(1420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(583,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_7) ).

thf(2037,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1277,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

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

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(562,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).

thf(1990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(277,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).

thf(1340,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ooverride__on ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(549,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

thf(1958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(754,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(1049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(310,axiom,
    ! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1413,plain,
    ! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(158,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).

thf(1076,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(138,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(1034,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(671,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

thf(2239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(968,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(1181,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(836,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(374,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(1551,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(501,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1845,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(483,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( E @ ( F @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( G @ ( E @ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).

thf(1798,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( E @ ( F @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( G @ ( E @ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(1598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

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

thf(1025,plain,
    tc_nat @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(399,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( A @ c_Set_OPow ) @ c_Complete__Lattice_OSup__class_OSup ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__Pow__eq_0) ).

thf(1605,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( A @ c_Set_OPow ) @ c_Complete__Lattice_OSup__class_OSup ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(416,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( B @ ( C @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).

thf(1647,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( B @ ( C @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(475,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).

thf(1780,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).

thf(1267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(365,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
       != ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).

thf(1531,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
       != ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(1098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(993,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_0) ).

thf(1547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(471,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1770,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(594,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(2060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(460,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(1743,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(305,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).

thf(1400,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(291,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( C @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).

thf(1368,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( C @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(645,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

thf(2175,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(226,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(1230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(342,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).

thf(1484,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(1053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(561,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(1987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(641,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).

thf(2165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(1637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1038,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(512,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( C @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).

thf(1869,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( C @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_2) ).

thf(1317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(1679,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).

thf(1579,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(1220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(477,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).

thf(1785,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(689,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

thf(2276,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(663,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).

thf(2219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(624,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).

thf(2128,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(368,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(1538,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(457,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1738,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(220,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(1218,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(592,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( F @ ( C @ c_FuncSet_OPi ) ) ) @ ( E @ ( D @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( F @ hAPP ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PiE_0) ).

thf(2056,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( F @ ( C @ c_FuncSet_OPi ) ) ) @ ( E @ ( D @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( F @ hAPP ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_1) ).

thf(1934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(703,plain,
    ! [A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1023,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(252,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).

thf(1284,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(353,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1506,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(463,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(1749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).

thf(1670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

thf(859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(524,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1898,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(503,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

thf(1849,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PowI_0) ).

thf(1257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(367,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientI_0) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(558,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( D @ ( E @ ( B @ c_Typedef_Otype__definition ) ) ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_ORep_0) ).

thf(1981,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( D @ ( E @ ( B @ c_Typedef_Otype__definition ) ) ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(690,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).

thf(2279,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(548,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).

thf(1955,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(632,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).

thf(2145,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(448,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) )
      = ( C @ ( B @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ ( A @ ( D @ c_in @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__def_0) ).

thf(1717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) )
      = ( C @ ( B @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ ( A @ ( D @ c_in @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(580,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(2030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(684,axiom,
    tc_bool @ class_Lattices_Oboolean__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

thf(2266,plain,
    tc_bool @ class_Lattices_Oboolean__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(876,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(1240,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

thf(1617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ c_Collect ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( D @ ( D @ ( tc_bool @ ( C @ ( A @ ( B @ c_COMBB ) ) ) ) @ c_Collect ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).

thf(1459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ c_Collect ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( D @ ( D @ ( tc_bool @ ( C @ ( A @ ( B @ c_COMBB ) ) ) ) @ c_Collect ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(552,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(1966,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ( B = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).

thf(1685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = A )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ( B = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(84,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(903,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(659,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(2209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(180,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
        = ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).

thf(1126,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
        = ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(1448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1453,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(599,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(2071,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(1108,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(1649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(161,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).

thf(1084,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).

thf(1157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(602,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).

thf(2078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(615,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

thf(2110,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_1) ).

thf(1390,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(701,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexCI_2) ).

thf(2305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(386,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(1575,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(393,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).

thf(1590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(237,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(1253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(338,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pow__top_0) ).

thf(1476,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(896,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(695,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

thf(2290,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(568,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(2004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(461,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(1745,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(505,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(1854,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(961,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(450,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1721,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).

thf(1062,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(354,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1508,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(360,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(1523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(625,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(2130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(682,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(2262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(570,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( A @ ( A @ ( tc_bool @ ( tc_bool @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( c_Not @ c_COMBB ) ) ) ) @ c_Collect ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq_0) ).

thf(2009,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( A @ ( A @ ( tc_bool @ ( tc_bool @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( c_Not @ c_COMBB ) ) ) ) @ c_Collect ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(434,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( G @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ hAPP ) @ ( F @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( E @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UN_3) ).

thf(1689,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( G @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ hAPP ) @ ( F @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( E @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(88,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).

thf(914,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(585,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

thf(2041,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(321,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).

thf(1308,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_Collect ) )
      = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).

thf(1706,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_Collect ) )
      = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(648,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).

thf(2183,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(620,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(2120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(574,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(2019,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(400,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).

thf(1607,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(422,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( E @ c_Relation_Oconverse ) ) @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

thf(1661,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( E @ c_Relation_Oconverse ) ) @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(323,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).

thf(1444,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(322,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(1442,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(403,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ( B = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).

thf(1614,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ( B = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(183,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_10) ).

thf(1133,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1348,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).

thf(1512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(699,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(2302,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(668,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(2233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(515,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(1876,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(427,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).

thf(1673,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(865,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(529,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).

thf(1908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(631,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_13) ).

thf(2142,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = D )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(414,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).

thf(1642,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(612,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_12) ).

thf(2102,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D = B )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(752,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(636,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ hAPP ) @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UN_4) ).

thf(2155,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ hAPP ) @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(678,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

thf(2255,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(394,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(1380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1303,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(319,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).

thf(1436,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(656,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = C )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).

thf(2201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = C )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1657,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(649,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

thf(2186,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(479,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(1789,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(521,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

thf(1891,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(108,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(960,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(152,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(1065,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(490,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).

thf(1816,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(347,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(1495,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(1335,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).

thf(1693,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(1288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(576,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bexE_1) ).

thf(2021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ c_Collect ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).

thf(1346,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ c_Collect ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(886,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(1742,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(537,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1930,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(638,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(2159,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).

thf(1261,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(298,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_6) ).

thf(1384,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 ) ) @ ( E @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1378,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(389,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).

thf(1582,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__quotient_0) ).

thf(1357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(535,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__Un_5) ).

thf(1925,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).

thf(1299,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(526,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(1902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1505,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(1120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(672,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).

thf(2241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1829,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(350,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( A = E )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).

thf(1500,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( A = E )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(1331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(803,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(658,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(2206,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(670,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(2238,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(532,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(1917,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(1204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(613,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).

thf(2106,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(1069,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(530,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).

thf(1912,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(882,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(543,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( B @ ( D @ ( F @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).

thf(1944,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( B @ ( D @ ( F @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(99,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(940,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(332,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(1463,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(643,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

thf(2170,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_0) ).

thf(1088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(2437,plain,
    $false,
    inference(e,[status(thm)],[2163,2199,1411,1633,1767,1995,1559,1899,1315,1179,1554,2250,1586,809,1879,1337,1823,1190,893,1840,1818,1295,1950,1549,1200,977,1211,1005,1290,2231,2062,1808,1728,873,878,1793,1305,1596,1406,1422,1569,2248,1544,2014,2099,2282,2114,1142,1269,1173,1486,2195,1655,1137,1756,2035,1735,1867,715,1275,1872,814,2168,1919,1761,1640,945,1164,1999,797,1222,930,1196,2046,1782,782,709,2020,1645,1386,2082,885,1046,2173,1366,2067,1529,2136,1904,1518,1265,1703,1228,1623,1482,1628,1430,2039,2269,1907,1826,2126,949,1055,1409,1860,2217,1323,838,2274,702,1313,1279,1577,1455,1800,1013,1115,1100,1232,1847,1922,817,1247,2049,1319,870,1479,1609,1362,1963,1875,1778,2007,2178,1489,924,1946,2090,1373,1040,2259,1418,1020,1051,905,756,1664,1811,1450,1682,834,1858,1864,2122,1151,937,1960,806,1183,2073,981,1169,1215,956,1886,1072,774,1394,1351,1433,1600,1696,1975,1843,2058,1896,2190,1526,2137,1345,988,2286,1104,1242,1074,2011,1206,942,2204,1691,1438,925,761,2118,1067,714,1730,1915,1708,2093,1311,2296,2264,1723,746,1343,778,1042,1355,1255,862,1487,2132,1238,1676,2133,788,2150,1883,1560,916,1938,1365,1968,1457,830,889,1787,1079,2112,1106,1032,1837,1392,2228,1740,842,1573,974,742,1234,1983,2157,1804,1328,1498,1425,1096,1540,1719,1118,1360,2245,1936,1270,1851,1772,1259,1534,1953,1111,1970,1856,725,857,1397,1567,1493,1160,933,1461,901,2080,1584,1700,1791,1889,1612,706,1082,2023,1942,1659,1414,2053,2108,1446,1249,1297,738,1131,2243,1060,721,1984,1002,1715,1979,2140,1525,1263,997,2125,1588,1530,1382,2153,1831,1192,1932,984,911,1333,1202,2043,1695,1187,1185,718,1732,1814,1086,765,1712,1286,1035,1466,1071,1663,2089,1515,2221,1026,1167,773,794,2235,1135,2001,1680,1698,2033,824,1273,1747,1927,733,2260,965,1510,1251,1764,1146,1754,2028,1301,1154,819,2225,1389,2188,1620,1752,1652,2016,826,1795,1520,1124,1226,958,1403,2193,2293,1371,1635,1058,1997,1090,919,1224,2148,1675,1428,2161,1139,1503,2055,1092,1464,947,979,1194,831,1282,1894,784,1806,736,1349,1542,1144,2116,880,1122,2197,1175,2084,2214,2257,990,2284,1603,2299,1571,1376,811,1471,2025,1557,2267,1821,1162,1862,848,1325,1029,1149,2252,1293,1112,890,1667,2180,1630,1993,2075,1198,1474,2212,2086,780,2064,1176,1477,851,922,1973,2069,1562,1213,768,2051,1044,1245,986,2288,1775,1000,1496,2303,1948,2096,1758,1208,2271,1420,2037,1277,749,1990,1340,1018,1958,754,1049,1413,1076,1034,2239,968,1181,836,1551,1845,1798,1598,1025,971,1605,1647,954,1780,1267,1531,1098,993,1547,776,712,1770,2060,1743,1400,1368,2175,1230,1484,1053,1987,2165,1637,791,1038,1869,1317,1679,1579,1220,840,1785,2276,2219,2128,1538,951,1738,1218,2056,1934,744,703,1023,1284,1506,1749,1094,1670,1008,1881,859,1898,1849,1257,1536,1981,1353,2279,1955,2145,1717,2030,2266,876,1240,1617,845,1459,1966,1685,1553,903,759,2209,1126,1448,1453,2071,771,1108,1649,1084,1157,2078,1321,1834,2110,1010,1390,2305,1575,1590,1253,963,1476,896,2290,2004,1745,1854,961,1721,1062,1508,1523,2130,731,786,995,2262,2009,1689,914,2041,1440,1308,1706,2183,2120,2019,1607,763,899,1661,1444,1442,1614,800,1133,1348,1512,2302,1725,2233,1625,1876,1673,867,865,1908,2142,1642,2102,752,2155,2255,1593,1380,854,1303,1436,2201,1657,2186,1789,1891,828,960,1065,1816,1495,1335,1693,1288,1710,2021,1346,886,1742,928,1930,2159,1261,1384,1378,1582,1357,908,1925,1713,1299,1902,1505,1120,728,740,1236,2241,1829,1129,1500,723,1331,803,935,2206,2238,1917,1204,2106,1468,1069,1912,882,1944,940,1463,1565,2170,1088]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SCT027-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39  % Computer : n017.cluster.edu
% 0.14/0.39  % Model    : x86_64 x86_64
% 0.14/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39  % Memory   : 8046.5625MB
% 0.14/0.39  % OS       : Linux 6.8.0-71-generic
% 0.14/0.39  % CPULimit : 300
% 0.14/0.39  % WCLimit  : 300
% 0.14/0.39  % DateTime : Sat Sep 26 06:15:36 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.28/1.27  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 3.40/1.91  % [INFO] 	 Parsing done (638ms). 
% 3.40/1.93  % [INFO] 	 Running in sequential loop mode. 
% 4.98/2.55  % [INFO] 	 eprover registered as external prover. 
% 4.98/2.56  % [INFO] 	 Scanning for conjecture ... 
% 6.13/2.91  % [INFO] 	 Found a conjecture (or negated_conjecture) and 699 axioms. Running axiom selection ... 
% 7.49/3.24  % [INFO] 	 Axiom selection finished. Selected 699 axioms (removed 0 axioms). 
% 9.39/3.62  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 9.39/3.65  % [INFO] 	 Type checking passed. 
% 9.39/3.66  % [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 ... 
% 27.41/7.57  % External prover 'e' found a proof!
% 27.41/7.58  % [INFO] 	 Killing All external provers ... 
% 27.41/7.58  % Time passed: 6974ms (effective reasoning time: 5634ms)
% 27.41/7.59  % Axioms used in derivation (699): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_in__mktop_1, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_subset__insert_1, cls_Diff__iff_2, cls_Diff1__fold__graph_0, cls_Compl__subset__Compl__iff_1, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_PiE_0, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_Inter__lower_0, cls_order__le__less__trans_0, cls_equiv__class__eq__iff_0, cls_sup__ge1_0, cls_image__constant_0, cls_compl__sup_0, cls_insertE_0, cls_less__fun__def_1, cls_Un__Diff_0, cls_in__below_14, cls_Un__subset__iff_0, cls_ball__conj__distrib_3, cls_insert__inter__insert_0, cls_inj__on__Un_2, cls_Compl__Diff__eq_0, cls_in__above_11, cls_Pi__I_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_converseI_0, cls_InterI_1, cls_equalityI_0, cls_COMBC__def_0, cls_subset__image__iff_2, cls_Image__singleton__iff_0, cls_Diff__eq_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_funcsetI_0, cls_subset__empty_1, cls_Pi__mem_0, cls_funcset__image_0, cls_inj__on__image__Int_0, cls_sup__bot__right_0, cls_insert__code_1, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_vimage__Diff_0, cls_bexCI_0, cls_Un__upper1_0, cls_UN__extend__simps_I10_J_0, cls_Un__commute_0, clsarity_fun__Orderings_Oorder, cls_in__below_3, cls_UnCI_1, cls_Compl__eq_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_linorder__neqE_0, cls_mkbot__Lin_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_CHAINED_0, cls_inf__sup__aci_I6_J_0, cls_COMBK__def_0, cls_ord_OgreaterThan__iff_0, cls_Diff__Un_0, cls_empty__iff_0, cls_in__above_7, cls_le__inf__iff_1, cls_vimage__Collect__eq_0, cls_Diff__subset__conv_0, cls_mem__def_1, cls_bexE_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_Int__insert__left_0, cls_ball__conj__distrib_11, cls_Int__Collect_1, cls_Inf__lower_0, cls_insert__absorb_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_in__below_2, 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_minus__minus_0, cls_insert__iff_1, cls_insert__subset_0, cls_bex__UN_3, cls_sup__inf__distrib2_0, cls_in__above_4, clsarity_fun__Lattices_Oupper__semilattice, cls_fold__graph_H_Ointros_I1_J_0, cls_inj__on__Un__image__eq__iff_0, cls_less__minus__iff_0, cls_fold__graph_H_Ointros_I2_J_0, cls_setsum__diff1__nat_1, cls_Image__Un_0, cls_in__mkbot_4, cls_inf__sup__distrib1_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_in__below_7, cls_ballE_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_pred__equals__eq_0, cls_ord_OatLeastAtMost__iff_2, cls_COMBB__def_0, cls_disjoint__eq__subset__Compl_0, cls_CollectI_0, cls_inf__commute_0, cls_Collect__neg__eq_0, cls_Un__left__commute_0, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_type__definition_OAbs__inverse_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_Pi__I_H_1, cls_diff__eq_0, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_neg__equal__iff__equal_0, cls_Collect__empty__eq_0, cls_equiv__class__eq__iff_3, cls_UN__extend__simps_I1_J_0, cls_psubset__insert__iff_8, cls_CollectD_0, cls_in__below_11, cls_extensionalityI_0, cls_not__psubset__empty_0, cls_vimage__insert_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_order__less__asym_0, cls_Union__disjoint_0, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_le__supI_0, cls_inf__eq__neg__sup_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_SUP__const_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_inj__on__Un_3, cls_rev__image__eqI_0, cls_SUP1__I_0, cls_eq__equiv__class__iff2_1, cls_in__mktop_3, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_le__iff__sup_0, cls_empty__is__image_0, cls_psubset__eq_1, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_ord_OatLeastLessThan__iff_0, cls_neg__sup__eq__inf_0, cls_linorder__antisym__conv1_0, cls_ord_OgreaterThanAtMost__iff_1, cls_inj__on__insert_0, cls_Image__empty_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_fun__upd__other_0, cls_ball__conj__distrib_1, cls_in__below_9, cls_type__definition_ORep__inject_0, cls_notin__Lin__iff_0, cls_minus__less__iff_1, cls_sup__eq__neg__inf_0, cls_Union__upper_0, cls_psubset__insert__iff_5, cls_Un__absorb2_0, cls_psubset__trans_0, cls_inf__sup__aci_I8_J_0, cls_in__above_6, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_vimageI_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_override__on__apply__notin_0, cls_xt1_I10_J_0, cls_le__minus__iff_0, cls_ball__conj__distrib_9, cls_sup__eq__bot__eq2_0, cls_UnCI_0, cls_Int__insert__right_1, cls_Compl__disjoint2_0, cls_not__less__iff__gr__or__eq_0, cls_UN__Un_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_bexCI_1, cls_ball__conj__distrib_4, cls_in__below_6, cls_Lin__irrefl_0, cls_Un__upper2_0, cls_singleton__iff_1, cls_complete__lattice_OInf__empty_0, cls_subset__iff_0, cls_insert__code_2, cls_bex__Un_6, cls_Diff__idemp_0, cls_subset__empty_0, cls_in__mkbot_3, cls_equiv__class__eq_0, cls_subset__Compl__self__eq_1, cls_UnionE_1, cls_insert__Diff__single_0, cls_bexI_1, cls_UN__simps_I10_J_0, cls_ord_OgreaterThanAtMost__iff_0, cls_Collect__mem__eq_0, clsarity_fun__HOL_Oord, cls_Compl__Un_0, cls_rev__predicate1D_0, cls_extensional__arb_0, cls_image__insert_0, cls_UN__subset__iff_0, cls_vimage__Un_0, cls_diff__single__insert_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_ball__conj__distrib_0, clsarity_bool__Lattices_Oupper__semilattice, cls_le__minus__iff_1, cls_fold__graph_OinsertI_0, cls_ord_OlessThan__iff_0, cls_type__definition_ORep__inverse_0, cls_doubleton__eq__iff_2, cls_Compl__disjoint_0, cls_bex__UN_4, cls_ball__conj__distrib_10, cls_Sup__binary_0, cls_Int__Collect_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_Inf__insert_0, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_xt1_I8_J_0, cls_vimage__const_1, cls_inf__sup__aci_I3_J_0, cls_Un__mono_0, cls_less__infI1_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_Image__singleton__iff_1, cls_psubset__insert__iff_4, cls_bex__Un_5, cls_PowI_0, clsarity_nat__Lattices_Olower__semilattice, cls_Pow__top_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_Image__subset__eq_1, cls_set__eq__subset_2, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_subset__iff__psubset__eq_0, cls_neg__inf__eq__sup_0, cls_in__above_1, cls_compl__inf__bot_0, cls_not__leE_0, cls_Un__subset__iff_2, cls_fold__graph_OemptyI_0, cls_in__below_10, cls_in__below_1, cls_linorder__linear_0, cls_Un__empty_0, cls_bex__Un_7, clsarity_fun__Lattices_Olattice, cls_in__mktop_5, cls_Int__assoc_0, cls_extensionalityI_1, cls_order__antisym_0, cls_order__trans_0, cls_bexE_0, cls_psubset__insert__iff_9, cls_mktop__Lin_0, cls_subset__trans_0, cls_in__mktop_0, cls_double__diff_0, cls_inf__le2_0, cls_Compl__eq__Compl__iff_0, cls_insert__is__Un_0, cls_ord_OatLeastAtMost__iff_1, cls_ord_OgreaterThanLessThan__iff_0, cls_image__empty_0, cls_Compl__subset__Compl__iff_0, cls_DiffI_0, cls_eq__equiv__class__iff2_0, cls_psubset__insert__iff_6, cls_ord_OgreaterThanAtMost__iff_2, cls_Image__iff_2, cls_le__supE_0, cls_subset__Compl__self__eq_0, cls_empty__not__insert_0, cls_inf__compl__bot_0, cls_sup__assoc_0, cls_Diff__Int__distrib2_0, cls_image__constant__conv_0, cls_in__mkbot_2, cls_insertI1_0, cls_linorder__antisym__conv1_1, cls_inj__on__insert_1, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_singleton__conv_0, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_empty__subsetI_0, cls_fun__upd__twist_0, cls_linorder__not__le_1, cls_ord_OatLeastLessThan__iff_1, cls_in__mktop_4, cls_Un__absorb1_0, cls_type__definition_ORep_0, cls_Diff__insert2_0, cls_Int__commute_0, cls_Sup__upper_0, cls_sup__least_0, cls_ball__conj__distrib_8, cls_rev__ImageI_0, cls_Pair__eq_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_override__on__apply__in_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_in__above_5, cls_converse__iff_1, cls_minus__less__iff_0, cls_subset__refl_0, cls_converse__in__Lin_0, cls_singletonE_0, cls_image__diff__subset_0, cls_Pow__bottom_0, clsarity_nat__Lattices_Olattice, cls_DiffE_0, cls_Int__Diff_0, cls_above__Lin_0, cls_image__iff_2, cls_less__minus__iff_1, cls_insertCI_0, cls_psubset__eq_0, cls_image__Int__subset_0, cls_ball__conj__distrib_5, cls_pred__subset__eq_1, cls_Un__Diff__cancel_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_not__less__iff__gr__or__eq_1, cls_ord_OlessThan__iff_1, cls_inj__on__empty_0, cls_in__below_12, cls_equation__minus__iff_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_order__le__neq__trans_0, cls_le__infE_0, cls_UnionE_0, cls_SUP2__iff_2, cls_fun__upd__apply_0, cls_complete__lattice_OSup__binary_0, clsarity_fun__Lattices_Oboolean__algebra, cls_le__inf__iff_2, cls_in__above_12, cls_subset__equiv__class_0, cls_vimage__Int_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_Int__absorb_0, cls_in__above_9, cls_inf__assoc_0, cls_linorder__neqE__ordered__idom_0, cls_insert__mono_0, cls_le__supI2_0, cls_less__le__not__le_1, cls_Un__assoc_0, cls_Un__Diff__cancel2_0, cls_linear__alt_0, cls_Collect__def_0, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_Int__lower2_0, cls_UN__constant_1, cls_bexI_0, cls_bex__empty_0, cls_PowD_0, cls_Pi__I_1, cls_Diff__disjoint_0, cls_inf__sup__ord_I4_J_0, cls_Diff__Int__distrib_0, cls_psubset__insert__iff_1, cls_in__below_5, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_Compl__Int_0, cls_psubset__insert__iff_0, cls_in__above_13, cls_converseD_0, cls_inj__on__fun__updI_0, cls_complete__lattice_Odual__complete__lattice_0, cls_Diff__mono_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_inj__on__def_0, cls_Un__absorb_0, cls_order__antisym__conv_0, cls_psubsetD_0, cls_ord_OatLeastAtMost__iff_0, cls_SUP2__I_0, cls_Int__lower1_0, cls_InterD_0, clsarity_bool__Lattices_Olattice, cls_psubset__insert__iff_3, cls_Union__quotient_0, cls_eq__eqI_0, cls_vimage__eq_1, cls_bexCI_3, cls_order__less__le_2, cls_Un__Int__distrib_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_le__imp__neg__le_0, cls_override__on__emptyset_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_linorder__less__linear_0, cls_type__definition_OAbs__inject_0, cls_insert__subset_2, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_complete__lattice_OSup__insert_0, cls_subsetD_0, cls_rev__bexI_0, cls_xt1_I11_J_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_quotientE_0, cls_complete__lattice_OInf__lower_0, cls_vimageE_0, cls_inf__bot__left_0, cls_inf1I_0, cls_Union__Pow__eq_0, cls_insert__not__empty_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_in__above_2, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_insert__absorb2_0, cls_Image__subset__eq_0, cls_UNION__empty__conv_I1_J_0, cls_fun__upd__idem_0, cls_inf__sup__aci_I4_J_0, cls_sup__inf__absorb_0, cls_double__compl_0, cls_subset__singletonD_0, cls_Int__iff_2, cls_notin__Lin__iff_1, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_eq__equiv__class__iff_0, cls_fun__upd__idem__iff_0, cls_Sup__insert_0, cls_vimage__singleton__eq_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_vimage__code_1, cls_UN__I_0, cls_ComplI_0, cls_converse__converse_0, cls_ord_OgreaterThanLessThan__iff_1, cls_quotient__disj_0, cls_equiv__class__eq__iff_1, cls_subset__psubset__trans_0, cls_in__mkbot_1, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_empty__Collect__eq_0, cls_in__mktop_2, cls_IntI_0, cls_eq__equiv__class_0, cls_minus__le__iff_1, cls_complete__lattice_OInf__singleton_0, cls_inf__greatest_0, cls_Sup__empty_0, cls_Un__left__absorb_0, cls_linorder__not__le_0, cls_order__less__irrefl_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_Diff__Int_0, cls_in__above_10, cls_less__supI2_0, cls_neg__le__iff__le_0, cls_ord_OatLeastLessThan__iff_2, cls_less__fun__def_2, cls_Un__empty_1, cls_le__iff__inf_0, clsarity_bool__Lattices_Oboolean__algebra, cls_subset__insert_0, cls_sup__idem_0, clsarity_nat__Lattices_Oupper__semilattice, cls_InterI_0, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_less__infI2_0, cls_ball__conj__distrib_7, cls_funcset__mem_0, cls_ball__conj__distrib_6, cls_eq__eqI_1, cls_in__below_0, cls_Diff__Compl_0, cls_insert__def_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_subset__inj__on_0, cls_singleton__inject_0, cls_bex__Un_4, cls_less__eqI_0, cls_vimageI2_0, cls_sup__ge2_0, clsarity_fun__Orderings_Opreorder, cls_converse__in__Lin_1, cls_UN__upper_0, cls_IntE_1, cls_Un__least_0, cls_double__complement_0, cls_inj__on__contraD_0, cls_Int__greatest_0, cls_in__above_8, cls_IntE_0, cls_in__mkbot_5, cls_equation__minus__iff_1, cls_sup1CI_0, cls_inj__onD_0, cls_Union__disjoint_2, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_le__infE_1, cls_image__eqI_0, cls_pred__subset__eq_0, cls_in__below_4, cls_image__subset__iff_0, cls_inf__le1_0, cls_insertCI_1, cls_inf__left__idem_0, cls_in__below_13, cls_complete__lattice_OSup__upper_0, cls_compl__inf_0, cls_empty__fold__graphE_0, clsarity_bool__Lattices_Odistrib__lattice, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_funcsetI_1, cls_setsum__negf_0, cls_doubleton__eq__iff_4, cls_ord_OatMost__iff_0, cls_UnionI_0, cls_Diff__subset__conv_1, cls_rev__bexI_1, cls_insert__code_0, cls_le__eqI_1, cls_vimageD_0, cls_Diff__Int2_0, cls_quotient__eqI_0, cls_vimage__def_0, cls_complete__lattice_OSup__empty_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_ord_OgreaterThanLessThan__iff_2, cls_bexCI_2, cls_order__less__imp__le_0, cls_minus__equation__iff_1, cls_below__Lin_0, cls_that_0, cls_DiffE_1, cls_equiv__class__nondisjoint_0, cls_Diff__partition_0, cls_insert__image_0, cls_fun__upd__upd_0, cls_psubset__insert__iff_2, cls_ord_OatMost__iff_1, cls_inj__on__Un_1, cls_sup__inf__distrib1_0, cls_vimage__empty_0, cls_Un__Int__assoc__eq_0, cls_insert__commute_0, cls_quotientI_0, cls_insert__iff_2, cls_image__image_0, cls_Diff__insert__absorb_0, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_ord_OgreaterThan__iff_1, cls_in__below_8, cls_disjoint__iff__not__equal_0, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_image__is__empty_0, cls_imageI_0, clsarity_fun__Lattices_Odistrib__lattice, cls_disjoint__eq__subset__Compl_1, cls_less__eqI_1, cls_order__less__le_1, cls_less__fun__def_0, cls_equiv__class__eq__iff_2, cls_linorder__not__less_1, cls_UN__insert_0, cls_quotient__eq__iff_0, cls_Un__insert__right_0, cls_ballE_1, cls_psubset__insert__iff_7, cls_Pair__eq_1, cls_quotientE_1, cls_equalityE_0, cls_Pi__I_H_0, cls_inf__sup__distrib2_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_neg__less__iff__less_0, cls_Union__disjoint_1, cls_in__above_3, cls_in__mkbot_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_singleton__conv2_0, cls_UN__empty2_0, cls_psubset__eq_2, cls_subset__insert__iff_1, cls_eq__equiv__class__iff_1, cls_ball__conj__distrib_2, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0, cls_Int__Collect_2, cls_empty__Diff_0, cls_in__above_14, cls_fun__upd__idem__iff_1, cls_in__above_0
% 27.41/7.59  % No. of inferences in proof: 1403
% 27.41/7.59  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6974 ms resp. 5634 ms w/o parsing
% 30.89/8.34  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.89/8.36  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------