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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT085-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n005.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 08:27:12 AM UTC 2026

% Result   : Unsatisfiable 29.68s 8.11s
% Output   : Refutation 32.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  564
% Syntax   : Number of formulae    : 1129 ( 189 unt;   0 typ;   0 def)
%            Number of atoms       : 3142 ( 517 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 22941 (1864   ~;2013   |;   0   &;19064   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   36 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   94 (  92 usr;  15 con; 0-6 aty)
%            Number of variables   : 3324 (   0   ^;3324   !;   0   ?;3324   :)

% Comments : 
%------------------------------------------------------------------------------
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_prod_decl,type,
    tc_prod: $i > $i > $i ).

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

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

thf(v_a_____decl,type,
    v_a____: $i ).

thf(v_b_____decl,type,
    v_b____: $i ).

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

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

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

thf(c_HOL_OIf_decl,type,
    c_HOL_OIf: $i > $i ).

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

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

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

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

thf(v_h_____decl,type,
    v_h____: $i ).

thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
    tc_Arrow__Order__Mirabelle_Oindi: $i ).

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

thf(c_HOL_Oone__class_Oone_decl,type,
    c_HOL_Oone__class_Oone: $i > $i ).

thf(v_Lab_____decl,type,
    v_Lab____: $i ).

thf(v_Lba_____decl,type,
    v_Lba____: $i ).

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

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

thf(c_HOL_Oinverse__class_Odivide_decl,type,
    c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

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

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

thf(class_Power_Opower_decl,type,
    class_Power_Opower: $i > $o ).

thf(c_Power_Opower__class_Opower_decl,type,
    c_Power_Opower__class_Opower: $i > $i > $i > $i ).

thf(c_Relation_ODomain_decl,type,
    c_Relation_ODomain: $i > $i > $i > $i ).

thf(c_Relation_OId__on_decl,type,
    c_Relation_OId__on: $i > $i > $i ).

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

thf(c_Relation_Orefl__on_decl,type,
    c_Relation_Orefl__on: $i > $i > $i > $o ).

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

thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
    class_OrderedGroup_Oordered__ab__group__add: $i > $o ).

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

thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

thf(c_Relation_ORange_decl,type,
    c_Relation_ORange: $i > $i > $i > $i ).

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

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

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

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_Orderings_Obot__class_Obot_decl,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

thf(class_Ring__and__Field_Oordered__field_decl,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

thf(c_Relation_Ototal__on_decl,type,
    c_Relation_Ototal__on: $i > $i > $i > $o ).

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

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

thf(v_sko__CHAINED__1_decl,type,
    v_sko__CHAINED__1: $i > $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_Orderings_Opreorder_decl,type,
    c_Orderings_Opreorder: $i > $i > $i > $o ).

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

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

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

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

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

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

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

thf(c_List_Oall__from__to__nat_decl,type,
    c_List_Oall__from__to__nat: $i > $i > $i > $o ).

thf(c_Product__Type_OSigma_decl,type,
    c_Product__Type_OSigma: $i > $i > $i > $i > $i ).

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

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

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

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

thf(class_OrderedGroup_Omonoid__mult_decl,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

thf(c_Orderings_Oorder_decl,type,
    c_Orderings_Oorder: $i > $i > $i > $o ).

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

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

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

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

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

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

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

thf(c_Arrow__Order__Mirabelle_OProf_decl,type,
    c_Arrow__Order__Mirabelle_OProf: $i ).

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

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

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

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

thf(c_Wellfounded_Omeasure_decl,type,
    c_Wellfounded_Omeasure: $i > $i > $i ).

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

thf(c_Wellfounded_Oacc_decl,type,
    c_Wellfounded_Oacc: $i > $i > $i ).

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

thf(c_Wellfounded_Omlex__prod_decl,type,
    c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).

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

thf(333,axiom,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1322,plain,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(564,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(1823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

thf(760,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(443,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(1559,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)],[443]) ).

thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).

thf(893,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)],[140]) ).

thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).

thf(1315,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)],[330]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).

thf(962,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).

thf(1686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(456,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_HOL_Ouminus__class_Ouminus ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).

thf(1586,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_HOL_Ouminus__class_Ouminus ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(809,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(198,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

thf(1024,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(402,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Olinear_0) ).

thf(1469,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).

thf(666,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(561,axiom,
    ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(1818,plain,
    ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(528,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).

thf(1750,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(1211,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)],[281]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).

thf(1443,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_fequal ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_fequal ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(1205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(458,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(1591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_all__from__to__nat_Osimps_2) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(430,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(1533,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
      | ~ ( 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)],[430]) ).

thf(205,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(1041,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)],[205]) ).

thf(410,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__le__trans_0) ).

thf(1486,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(509,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).

thf(1705,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).

thf(1655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(259,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_3) ).

thf(1164,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).

thf(1233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(479,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1640,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)],[479]) ).

thf(287,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(1222,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(396,axiom,
    tc_bool @ class_Orderings_Otop,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(1458,plain,
    tc_bool @ class_Orderings_Otop,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(670,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(531,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(1756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(328,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

thf(1310,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(187,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1001,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(296,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).

thf(1243,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(118,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(841,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Opreorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Opreorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Odual__preorder_0) ).

thf(1724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Opreorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Opreorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(554,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(1803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

thf(1095,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(526,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_Relation_ODomain ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

thf(1746,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_Relation_ODomain ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_1) ).

thf(898,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( v_x @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(565,plain,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( v_x @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[1]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(424,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/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).

thf(1518,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)],[424]) ).

thf(508,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(1703,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(317,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).

thf(1287,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(548,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).

thf(1792,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(719,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(92,axiom,
    tc_nat @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(785,plain,
    tc_nat @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).

thf(587,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

thf(1191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).

thf(949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(375,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ( B = C )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oneq__le__trans_0) ).

thf(1409,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ( B = C )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).

thf(724,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(533,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).

thf(1760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(1298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(1330,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(1264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).

thf(1511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).

thf(702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).

thf(1455,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oless__le_1) ).

thf(1800,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(360,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(1379,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)],[360]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(1247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(1013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) )
       != ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

thf(1773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) )
       != ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1100,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(817,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(1319,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

thf(870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__irrefl_0) ).

thf(1479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).

thf(1609,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
        = ( A @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).

thf(969,plain,
    ! [B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
        = ( A @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(1572,plain,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(1741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(1398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(513,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(357,axiom,
    tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

thf(1373,plain,
    tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(1109,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(496,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).

thf(806,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(267,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1183,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(558,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).

thf(1811,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(393,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oless__le_2) ).

thf(1450,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1334,plain,
    ! [A: $i] :
      ( ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ 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)],[340]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

thf(646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(196,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__le__not__le_2) ).

thf(1020,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(454,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__leE_0) ).

thf(1581,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).

thf(1377,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oneq__iff_1) ).

thf(692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(1447,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(218,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ c_Orderings_Opreorder ) ) )
      | ~ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Ole__less__trans_0) ).

thf(1072,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ c_Orderings_Opreorder ) ) )
      | ~ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(367,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1394,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(427,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).

thf(1526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(345,axiom,
    tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( v_h____ @ ( v_b____ @ ( v_a____ @ ( v_Lba____ @ ( v_Lab____ @ ( v_F @ v_sko__CHAINED__1 ) ) ) ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).

thf(1345,plain,
    tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( v_h____ @ ( v_b____ @ ( v_a____ @ ( v_Lba____ @ ( v_Lab____ @ ( v_F @ v_sko__CHAINED__1 ) ) ) ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(385,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(1433,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)],[385]) ).

thf(276,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(1201,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(461,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/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).

thf(1600,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)],[461]) ).

thf(425,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(1521,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)],[425]) ).

thf(505,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_Wellfounded_Omlex__prod ) ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mlex__leq_0) ).

thf(1696,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_Wellfounded_Omlex__prod ) ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(283,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(1215,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

thf(634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(239,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OleI_0) ).

thf(1119,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Opreorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oeq__refl_0) ).

thf(1651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Opreorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(503,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_1) ).

thf(1691,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(387,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1438,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(925,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)],[154]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1306,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).

thf(1199,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).

thf(1153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(342,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).

thf(1338,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(543,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(1783,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(477,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/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(1636,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)],[477]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(463,axiom,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(1604,plain,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(216,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(1067,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(537,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1768,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Opreorder ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__preorder_0) ).

thf(714,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Opreorder ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(1047,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(99,axiom,
    v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( v_h____ @ ( v_b____ @ ( v_a____ @ ( v_Lba____ @ ( v_Lab____ @ ( v_F @ v_sko__CHAINED__1 ) ) ) ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_2) ).

thf(798,plain,
    v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( v_h____ @ ( v_b____ @ ( v_a____ @ ( v_Lba____ @ ( v_Lab____ @ ( v_F @ v_sko__CHAINED__1 ) ) ) ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[99]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(1274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(957,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(74,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).

thf(746,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1343,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(350,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).

thf(1355,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).

thf(598,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(416,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

thf(1502,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Oorder ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__order_0) ).

thf(1666,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Oorder ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_List_Oall__from__to__nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_all__from__to__nat_Osimps_0) ).

thf(815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_List_Oall__from__to__nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(294,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1238,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(1123,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(128,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(862,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).

thf(788,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(1619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).

thf(1370,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).

thf(916,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)],[150]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(1178,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(257,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1159,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(545,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).

thf(1787,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(79,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(757,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(1128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(233,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1106,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)],[233]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).

thf(847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( v_x @ hAPP ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(566,plain,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( v_x @ hAPP ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[2]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(1032,plain,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(123,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).

thf(852,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(441,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__empty_0) ).

thf(1555,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(1079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Oorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Oorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Odual__order_0) ).

thf(1027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Oorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Oorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).

thf(1195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).

thf(1407,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(476,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(1634,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(366,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1392,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(319,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).

thf(1291,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ~ ( v_h____ @ ( v_b____ @ ( v_a____ @ ( v_Lba____ @ ( v_Lab____ @ ( v_F @ v_sko__CHAINED__1 ) ) ) ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1_02) ).

thf(710,plain,
    ! [A: $i] :
      ( ~ ( v_h____ @ ( v_b____ @ ( v_a____ @ ( v_Lba____ @ ( v_Lab____ @ ( v_F @ v_sko__CHAINED__1 ) ) ) ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[57]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(697,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(534,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).

thf(1762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

thf(650,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != B )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

thf(615,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != B )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(289,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(1227,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(382,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( C = B )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OneqE_0) ).

thf(1425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( C = B )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

thf(593,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

thf(610,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(783,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(989,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).

thf(578,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(549,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(1794,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(195,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oantisym_0) ).

thf(1017,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).

thf(980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(415,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/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).

thf(1498,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)],[415]) ).

thf(433,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).

thf(1540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).

thf(1006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Wellfounded_Omeasure ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ ( D @ ( D @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__measure_0) ).

thf(1138,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Wellfounded_Omeasure ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ ( D @ ( D @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(515,axiom,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(1719,plain,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(369,axiom,
    tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ c_Fun_Oinj__on ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injh_0) ).

thf(1397,plain,
    tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( v_h____ @ c_Fun_Oinj__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(447,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/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(1567,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)],[447]) ).

thf(337,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(1329,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(933,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).

thf(1461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(377,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1414,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).

thf(637,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(547,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(1791,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(282,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1214,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(1644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).

thf(706,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(413,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ouminus__class_Ouminus ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).

thf(1493,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ouminus__class_Ouminus ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(499,axiom,
    v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1683,plain,
    v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[499]) ).

thf(279,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_0) ).

thf(1207,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(467,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(1612,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(679,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1039,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)],[204]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(1155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( v_x @ ( D @ ( t_a @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = ( v_x @ ( A @ hAPP ) @ ( C @ ( t_a @ ( B @ ( v_x @ c_fequal ) ) @ ( D @ c_HOL_OIf @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__def_0) ).

thf(1744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( v_x @ ( D @ ( t_a @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = ( v_x @ ( A @ hAPP ) @ ( C @ ( t_a @ ( B @ ( v_x @ c_fequal ) ) @ ( D @ c_HOL_OIf @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

thf(1131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

thf(911,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(62,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(721,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_1) ).

thf(1002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

thf(569,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oord__class_Oless @ ( A @ c_lessequals @ c_Orderings_Opreorder ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder__class_Oaxioms_0) ).

thf(1720,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oord__class_Oless @ ( A @ c_lessequals @ c_Orderings_Opreorder ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Opreorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oorder__refl_0) ).

thf(779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Opreorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(473,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

thf(1627,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(334,axiom,
    ! [A: $i] : ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).

thf(1324,plain,
    ! [A: $i] : ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1114,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(540,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(1776,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(305,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(1263,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(997,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(457,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1588,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

thf(985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(253,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/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).

thf(1150,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)],[253]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(1249,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(1266,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(291,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

thf(1231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(1060,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)],[214]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1050,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_2) ).

thf(1241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(541,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).

thf(1779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(152,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(921,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)],[152]) ).

thf(445,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

thf(1563,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

thf(1170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).

thf(1466,plain,
    ! [A: $i] :
      ( ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[400]) ).

thf(490,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(1663,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)],[490]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(166,axiom,
    ! [A: $i] : ( c_Arrow__Order__Mirabelle_OProf @ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PiProf_0) ).

thf(953,plain,
    ! [A: $i] : ( c_Arrow__Order__Mirabelle_OProf @ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(97,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(794,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(83,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

thf(765,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(211,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(1054,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(906,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)],[146]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(1278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(1146,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(506,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).

thf(1698,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).

thf(824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(1483,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(437,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

thf(1548,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)],[437]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(1301,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( D @ ( A @ ( A @ ( B @ ( C @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_0) ).

thf(689,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( D @ ( A @ ( A @ ( B @ ( C @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ 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)],[47]) ).

thf(358,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Ole__less_0) ).

thf(1374,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).

thf(601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(1135,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(483,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(1648,plain,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).

thf(750,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(420,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1510,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).

thf(1251,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).

thf(618,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(535,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

thf(1764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(475,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(1631,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

thf(733,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

thf(584,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(819,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(49,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(694,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(468,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1615,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(86,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/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).

thf(772,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)],[86]) ).

thf(529,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(1752,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).

thf(1388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(1535,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(507,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(145,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(904,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(175,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oless__linear_0) ).

thf(975,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).

thf(843,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(242,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ ( A @ c_fequal ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1125,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ ( A @ c_fequal ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_0) ).

thf(826,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

thf(1256,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).

thf(1488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(383,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/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).

thf(1428,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)],[383]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1503,plain,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

thf(572,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(510,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).

thf(1707,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(329,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Ole__neq__trans_0) ).

thf(1312,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ouminus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).

thf(1058,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ouminus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1332,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)],[339]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).

thf(1092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(225,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ c_Orderings_Opreorder ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oorder__trans_0) ).

thf(1090,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ c_Orderings_Opreorder ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).

thf(919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).

thf(947,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(495,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

thf(604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(280,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1209,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( C @ c_Relation_Orefl__on ) ) )
      | ~ ( 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)],[280]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(900,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(114,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(831,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)],[114]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(1117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(450,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(1574,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(538,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(1771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

thf(1175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).

thf(880,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(31,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

thf(649,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(1043,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Ole__less_1) ).

thf(811,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(1471,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)],[403]) ).

thf(80,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).

thf(758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(442,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(1557,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)],[442]) ).

thf(21,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(621,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)],[21]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Relation_OId__on ) @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

thf(700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Relation_OId__on ) @ ( A @ ( A @ ( B @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(335,axiom,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(1325,plain,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(171,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(769,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).

thf(1022,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(562,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(1820,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(563,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).

thf(1821,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(521,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/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1731,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)],[521]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(65,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(726,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(1029,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(264,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1177,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(1381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(236,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Relation_OId__on ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

thf(1112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Relation_OId__on ) @ ( 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)],[236]) ).

thf(502,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).

thf(1688,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

thf(685,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)],[45]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1594,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1015,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(406,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(519,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(1726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__measure_1) ).

thf(1102,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).

thf(653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1694,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)],[504]) ).

thf(555,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).

thf(1805,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).

thf(695,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).

thf(1245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(391,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OleD_0) ).

thf(1445,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(428,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injD_0) ).

thf(1528,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(1583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(557,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(1809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(532,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_all__from__to__nat_Osimps_1) ).

thf(1758,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).

thf(944,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)],[162]) ).

thf(155,axiom,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(927,plain,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).

thf(1684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(1081,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).

thf(754,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(836,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(439,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(1551,plain,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).

thf(1748,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(551,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_Wellfounded_Omlex__prod ) ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mlex__less_0) ).

thf(1798,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ hAPP ) @ ( B @ ( D @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_Wellfounded_Omlex__prod ) ) @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(855,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(640,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(371,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).

thf(1400,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)],[371]) ).

thf(464,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).

thf(1605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(355,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(1368,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)],[355]) ).

thf(530,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_0) ).

thf(1753,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).

thf(1098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(217,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Opreorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__imp__le_0) ).

thf(1070,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Opreorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(872,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(41,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/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).

thf(673,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)],[41]) ).

thf(269,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(1186,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)],[269]) ).

thf(544,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).

thf(1785,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(293,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oantisym__conv_0) ).

thf(1235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(331,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_1) ).

thf(1317,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).

thf(1658,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(497,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/sandbox2/benchmark/theBenchmark.p',cls_Image__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_Relation_OImage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(453,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).

thf(1579,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

thf(1220,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(559,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_0) ).

thf(1813,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(323,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(1300,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)],[323]) ).

thf(432,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__asym_0) ).

thf(1538,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(165,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ ( B @ ( E @ c_Pair ) ) ) @ ( A @ ( D @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).

thf(951,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ ( B @ ( E @ c_Pair ) ) ) @ ( A @ ( D @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(316,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(1285,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(523,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/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).

thf(1738,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)],[523]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ~ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(1218,plain,
    ! [B: $i,A: $i] :
      ~ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(1336,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)],[341]) ).

thf(29,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = B )
      | ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

thf(643,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = B )
      | ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_1) ).

thf(744,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(536,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(1766,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

thf(613,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(315,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).

thf(1284,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(349,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).

thf(1052,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(864,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(514,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_Relation_ODomain ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).

thf(1717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_Relation_ODomain ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).

thf(859,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ ( D @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv3_0) ).

thf(1404,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1358,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

thf(656,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(553,axiom,
    tc_bool @ class_Lattices_Oboolean__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

thf(1802,plain,
    tc_bool @ class_Lattices_Oboolean__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(227,axiom,
    v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_2_0) ).

thf(1094,plain,
    v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[227]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(978,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(249,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_0) ).

thf(1140,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(493,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

thf(1670,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(550,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1797,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).

thf(991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).

thf(1617,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(120,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ c_Orderings_Opreorder ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__trans_0) ).

thf(845,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ c_Orderings_Opreorder ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(380,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).

thf(1421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(1459,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)],[397]) ).

thf(266,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

thf(1180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(1157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).

thf(581,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(1412,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(1126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(270,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).

thf(1453,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(1807,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(234,axiom,
    ! [A: $i] : ( c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_0_0) ).

thf(1108,plain,
    ! [A: $i] : ( c_Arrow__Order__Mirabelle_OLin @ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( A @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( 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)],[234]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1649,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)],[484]) ).

thf(223,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(1084,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).

thf(1781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).

thf(1216,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)],[284]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

thf(891,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(1010,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)],[192]) ).

thf(365,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(1390,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(451,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(1575,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(311,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(1276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(482,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/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(1646,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)],[482]) ).

thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(1326,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)],[336]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1253,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(405,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(1476,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).

thf(1508,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).

thf(1481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Oorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oeq__iff_0) ).

thf(1629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Oorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

thf(632,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).

thf(1523,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(781,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)],[90]) ).

thf(184,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(995,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).

thf(813,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)],[106]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).

thf(1385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

thf(1341,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(75,axiom,
    ! [A: $i] :
      ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).

thf(748,plain,
    ! [A: $i] :
      ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(272,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1193,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).

thf(1077,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(1513,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).

thf(1661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(327,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(1309,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1045,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(388,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1440,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(929,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(1607,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_List_Oall__from__to__nat ) ) )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_all__from__to__nat_Osimps_3) ).

thf(763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_List_Oall__from__to__nat ) ) )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Oall__from__to__nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(716,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(258,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(1161,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(246,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ ( B @ ( E @ c_Pair ) ) ) @ ( A @ ( D @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).

thf(1133,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ ( B @ ( E @ c_Pair ) ) ) @ ( A @ ( D @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(347,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

thf(1348,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(999,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(313,axiom,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(1280,plain,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(115,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_2) ).

thf(833,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( B @ ( F @ ( E @ ( A @ ( A @ ( B @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( C @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(1546,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Odual__linorder_0) ).

thf(790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
       != ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).

thf(867,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)],[130]) ).

thf(480,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(1642,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(752,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(472,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(1625,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)],[472]) ).

thf(124,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(854,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1303,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).

thf(1148,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(494,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).

thf(1673,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(1436,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(801,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(353,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(1363,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(1561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).

thf(960,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)],[169]) ).

thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).

thf(1065,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)],[215]) ).

thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(1346,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)],[346]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(796,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(886,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(560,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(1816,plain,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1495,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(262,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/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).

thf(1172,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)],[262]) ).

thf(84,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(767,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)],[84]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).

thf(1056,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(546,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).

thf(1789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(664,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(318,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(1288,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(1710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(274,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__linorder_0) ).

thf(1197,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(180,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__le__not__le_1) ).

thf(987,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(438,axiom,
    tc_bool @ class_HOL_Ouminus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).

thf(1550,plain,
    tc_bool @ class_HOL_Ouminus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(110,axiom,
    ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_1_0) ).

thf(822,plain,
    ~ ( v_Lba____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_bool @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( v_h____ @ ( tc_nat @ c_HOL_Oord__class_Oless @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_HOL_OIf @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_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)],[110]) ).

thf(512,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).

thf(1713,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(418,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(1505,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).

thf(607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(22,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(624,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)],[22]) ).

thf(117,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).

thf(839,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).

thf(740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(1268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).

thf(575,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

thf(982,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(1431,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(1004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

thf(803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(153,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_preorder_Oless__asym_H_0) ).

thf(923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Opreorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(401,axiom,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(1468,plain,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).

thf(708,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(486,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).

thf(1653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(940,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)],[160]) ).

thf(498,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(1681,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

thf(1184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(399,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1463,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

thf(659,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(412,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oeq__iff_2) ).

thf(1490,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1037,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(775,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)],[87]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).

thf(1417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
        = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).

thf(972,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
        = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(1906,plain,
    $false,
    inference(e,[status(thm)],[1322,629,1823,760,1559,893,1315,962,777,1686,1586,809,1024,1469,666,1818,1295,1750,1211,730,1443,1569,1544,1728,1205,1591,878,1533,1041,1486,1705,1655,1164,1233,1260,1640,1222,1458,670,1756,1310,1001,1243,1441,841,1724,1803,1228,829,1095,1746,898,565,1366,1518,1703,1287,1792,719,785,587,1191,949,1409,724,1760,1298,1330,1264,1511,702,1577,1455,1800,1379,1087,1247,1013,1773,1100,817,902,1319,870,1479,1609,969,1572,1741,1398,1714,1373,1109,937,1677,806,1183,1811,1450,1334,646,1383,1020,1581,966,687,1377,692,1447,1072,1394,1526,1351,1345,1433,1201,1600,1521,1696,1215,634,1119,1622,1104,849,1651,942,1691,1438,925,1306,1199,1153,1338,1783,1636,1074,1604,1067,1736,1768,714,1047,798,1274,957,746,1343,1355,598,1502,1666,815,1238,1123,862,788,1619,1370,1423,916,1178,1159,1787,757,1128,1106,847,566,1032,1602,852,1555,1079,1027,682,1195,1407,1634,1392,1291,710,1402,697,1143,1762,650,615,1121,1227,1425,593,610,783,989,742,578,1794,1017,980,1498,1540,1006,1138,1719,857,1397,1567,1329,1361,933,1461,1414,637,1791,1214,1644,706,1419,1493,1683,1207,590,1612,679,1039,1155,1744,738,1131,1668,911,721,1002,569,1720,779,1627,1324,1114,1776,1263,997,1588,985,1150,1249,1266,1231,1060,1050,792,1241,1779,921,1563,1170,1466,1663,1515,1167,953,794,765,1054,662,888,906,1278,1146,1698,824,1483,1548,1301,689,1374,601,1135,1648,750,1510,1251,618,1764,1631,733,584,819,694,1615,772,1752,1388,1535,1701,904,975,843,1125,875,826,1256,1488,1428,1503,572,1707,1271,1312,1058,1332,1092,1090,919,947,1675,1258,704,1638,1224,604,1209,900,831,1282,1117,1574,736,1542,1722,1771,1175,880,649,1043,811,1471,758,1557,621,700,1325,964,626,769,1022,1820,1821,1731,799,726,1029,895,1293,668,1177,1381,1112,1688,685,1474,1594,883,1015,1477,1726,1102,653,1694,1805,695,1245,1445,1528,722,1034,1583,1809,1758,1203,944,927,1684,1081,754,836,1551,1748,1798,712,855,640,1400,1605,954,1368,1753,1531,1098,993,1070,872,673,1186,1785,1235,1317,1658,1679,1579,1220,1813,1300,1538,951,1285,1738,1218,1336,643,744,1766,613,1284,1353,1052,864,1008,1717,595,859,1404,1358,656,1802,1094,978,1140,1670,1797,991,1617,845,1421,1459,1180,1553,1157,581,1412,1126,1189,1453,1807,1108,1649,1084,1781,1216,891,1010,1390,1575,1276,1646,1326,1253,1476,1508,1481,1629,632,1523,786,781,995,813,1385,1341,748,914,1193,1077,1513,1661,1309,1045,1440,929,1607,763,716,1161,1133,1348,999,1280,833,1546,790,867,1642,752,1395,1625,854,1303,1148,1673,1436,801,1363,1561,960,1065,1346,796,886,1816,1495,1172,767,1056,1789,664,1288,1710,1197,987,1550,908,822,1713,1505,607,624,839,728,740,1268,575,1597,982,1431,1004,803,935,923,676,1468,708,1653,940,1681,1184,1463,659,1565,1490,1037,775,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : SCT085-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.50  % Computer : n005.cluster.edu
% 0.24/0.50  % Model    : x86_64 x86_64
% 0.24/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50  % Memory   : 8046.5625MB
% 0.24/0.50  % OS       : Linux 6.8.0-71-generic
% 0.24/0.50  % CPULimit : 300
% 0.24/0.50  % WCLimit  : 300
% 0.24/0.50  % DateTime : Sat Sep 26 06:25:47 UTC 2026
% 0.24/0.50  % CPUTime  : 
% 0.24/0.50  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.40/1.39  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 3.09/2.03  % [INFO] 	 Parsing done (630ms). 
% 3.74/2.05  % [INFO] 	 Running in sequential loop mode. 
% 5.04/2.66  % [INFO] 	 eprover registered as external prover. 
% 5.04/2.67  % [INFO] 	 Scanning for conjecture ... 
% 6.49/3.10  % [INFO] 	 Found a conjecture (or negated_conjecture) and 562 axioms. Running axiom selection ... 
% 8.55/3.50  % [INFO] 	 Axiom selection finished. Selected 562 axioms (removed 0 axioms). 
% 9.54/3.81  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 9.54/3.84  % [INFO] 	 Type checking passed. 
% 9.54/3.85  % [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 ... 
% 29.68/8.09  % External prover 'e' found a proof!
% 29.68/8.10  % [INFO] 	 Killing All external provers ... 
% 29.68/8.10  % Time passed: 7379ms (effective reasoning time: 6034ms)
% 29.68/8.11  % Axioms used in derivation (562): cls_top__fun__eq_0, cls_vimage__code_0, cls_order_Ole__less_0, cls_not__one__less__zero_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_minus__le__iff_0, cls_neg__0__le__iff__le_1, cls_le__divide__eq_3, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_order__le__less__trans_0, cls_zero__less__one_0, cls_add__0__left_0, cls_in__mktop_1, cls_2_0, cls_power__0_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_order_Oeq__iff_0, cls_bot__fun__eq_0, cls_less__divide__eq_3, cls_preorder__class_Oaxioms_0, cls_divide__le__eq_2, cls_divide__pos__pos_0, cls_class__ringb_Oadd__r0__iff_1, cls_add__less__cancel__left_1, cls_eq__imp__le_0, cls_divide__less__0__iff_0, cls_card__empty_0, cls_zero__less__divide__iff_5, cls_preorder_Ole__less__trans_0, cls_le__minus__self__iff_0, cls_order_Oantisym_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_total__on__def_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_divide__self_0, cls_left__minus_0, cls_divide__nonpos__neg_0, cls_minus__zero_0, cls_zero__le__one_0, cls_fun__upd__apply_1, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_add__increasing2_0, cls_less__half__sum_0, cls_power__inject__exp_0, cls_fun__Compl__def_0, clsarity_fun__Orderings_Oorder, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_linorder__neqE_0, cls_preorder_Odual__preorder_0, cls_mkbot__Lin_0, cls_divide__1_0, cls_add__strict__right__mono_0, cls_CHAINED_0, cls_power__increasing_0, cls_Id__on__eqI_0, cls_zero__le__divide__iff_2, cls_CHAINED_1_02, cls_zero__less__divide__iff_0, cls_add__le__cancel__left_1, cls_add__is__0_0, cls_empty__iff_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, cls_divide__le__0__1__iff_1, cls_nat__add__left__cancel__less_0, cls_compl__eq__compl__iff_0, cls_mem__def_1, cls_add__le__cancel__right_1, cls_termination__basic__simps_I1_J_0, cls_minus__add__distrib_0, cls_frac__le_0, cls_preorder_Oless__irrefl_0, cls_linorder_Onot__less__iff__gr__or__eq_2, cls_minus__le__self__iff_0, cls_minus__divide__right_0, clsarity_nat__Orderings_Olinorder, cls_in__mkbot_4, cls_power__le__imp__le__exp_0, cls_power__one_0, cls_add__nonpos__neg_0, cls_le__eq__neg_0, cls_comm__monoid__add_Omult__assoc_0, cls_vimage__if_3, cls_neg__less__iff__less_1, cls_all__from__to__nat_Osimps_2, cls_add__cancel__21_1, cls_ComplD_0, cls_add__left__cancel_0, cls_comm__monoid__add_Omult__1__right_0, cls_linorder_OleI_0, cls_add__leE_0, cls_minus__minus_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_less__minus__iff_0, cls_power__less__imp__less__exp_0, cls_pred__equals__eq_0, cls_minus__unique_0, cls_COMBB__def_0, cls_gr0I_0, cls_vimage__Compl_0, cls_Range__Id__on_0, clsarity_fun__Orderings_Otop, cls_preorder_Oless__le__not__le_1, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_le__0__eq_0, cls_divide__le__0__iff_3, cls_add__gr__0_0, cls_refl__on__Id__on_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_linorder_Oantisym__conv2_0, cls_add__nonneg__pos_0, cls_nat__less__cases_0, cls_ab__left__minus_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_neg__equal__iff__equal_0, cls_dual__linorder_0, cls_one__le__power_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_add__le__mono_0, cls_order__less__asym_0, cls_add__less__mono_0, cls_order_Oneq__le__trans_0, cls_divide__neg__neg_0, cls_linorder_OneqE_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, cls_linorder__not__less_0, cls_compl__bot__eq_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_le__antisym_0, cls_add__right__mono_0, cls_linorder_Odual__linorder_0, cls_order__eq__refl_0, cls_linorder_Oneq__iff_1, cls_1_0, cls_linorder_Onot__less__iff__gr__or__eq_0, cls_order__le__less_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_linorder__antisym__conv1_0, cls_Image__empty_0, clsarity_fun__Orderings_Obot, cls_in__mktop_3, cls_fun__upd__other_0, cls_linorder__antisym__conv2_0, cls_add__cancel__end_0, cls_neg__0__le__iff__le_0, cls_minus__less__iff_1, cls_power__one__over_0, cls_SigmaI_0, cls_minus__add__cancel_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_notin__Lin__iff_0, cls_linorder_Oantisym__conv2_1, cls_vimageI_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_le__divide__eq_2, cls_refl__on__def_1, cls_add__less__cancel__right_1, cls_neg__less__eq__nonneg_0, cls_not__less__iff__gr__or__eq_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_preorder_Oless__trans_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, cls_le__minus__iff_0, cls_add__left__mono_0, cls_Lin__irrefl_0, cls_dual__order_0, cls_nat__add__left__commute_0, cls_add__divide__distrib_0, cls_trans__le__add2_0, cls_divide__le__eq_3, cls_vimage__if_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_neg__less__eq__nonneg_1, cls_CHAINED_1, cls_ATP__Linkup_OCOMBC__def_0, cls_all__from__to__nat_Osimps_1, cls_CHAINED_0_01, cls_add__strict__left__mono_0, cls_less__divide__eq_2, cls_in__mkbot_3, cls_zero__less__divide__iff_1, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_linorder_Oantisym__conv1_1, cls_Range__iff_1, cls_compl__top__eq_0, cls_preorder_Oless__asym_H_0, cls_power__eq__0__iff_2, cls_trans__le__add1_0, cls_neg__le__0__iff__le_0, cls_order_Ole__neq__trans_0, cls_class__semiring_Oadd__a_0, cls_UNIV__not__empty_0, cls_le__minus__iff_1, cls_zero__le__divide__iff_3, cls_le__eq__neg_1, cls_mlex__less_0, cls_order_Oantisym__conv_0, cls_termination__basic__simps_I4_J_0, clsarity_nat__Orderings_Obot, cls_add__right__cancel_0, cls_ex__in__conv_0, cls_termination__basic__simps_I3_J_0, cls_divide__self__if_1, cls_Compl__UNIV__eq_0, cls_divide__self__if_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_class__semiring_Oadd__0_0, cls_comm__monoid__add_Omult__commute_0, cls_fun__upd__triv_0, cls_linorder_Onot__less__iff__gr__or__eq_1, cls_Id__on__iff_0, cls_xt1_I8_J_0, cls_SigmaD2_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_order_Ole__less_1, cls_preorder_Oless__le__trans_0, cls_power__strict__mono_0, cls_zero__less__two_0, cls_le__minus__self__iff_1, cls_DomainI_0, cls_preorder_Oless__imp__le_0, cls_neg__0__less__iff__less_0, cls_neg__less__0__iff__less_0, cls_nonzero__minus__divide__right_0, cls_not__add__less1_0, cls_power__strict__decreasing_0, cls_zero__le__divide__iff_5, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_less__add__one_0, cls_not__leE_0, cls_ATP__Linkup_OCOMBB__def_0, cls_add__strict__mono_0, cls_neg__equal__0__iff__equal_0, cls_divide__less__0__iff_3, cls_in__mktop_5, cls_linorder_OleD_0, cls_zero__less__power_0, cls_minus__le__self__iff_1, cls_order__antisym_0, cls_add__cancel__21_0, cls_order__trans_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_preorder_Oeq__refl_0, cls_divide__nonneg__neg_0, clsarity_bool__HOL_Ouminus, cls_less__add__eq__less_0, cls_power__divide_0, cls_mktop__Lin_0, cls_divide__le__0__iff_2, cls_neg__equal__zero_1, cls_in__mktop_0, cls_acc_Ocases_0, cls_refl__onD2_0, cls_Compl__eq__Compl__iff_0, cls_linorder__antisym__conv1_1, cls_SigmaD1_0, cls_Image__iff_2, clsarity_bool__Orderings_Opreorder, cls_zero__neq__one_0, cls_zero__le__divide__iff_4, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_linorder_Oless__linear_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_in__mkbot_2, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_natgb_Oadd__cancel_0, cls_zero__less__divide__iff_3, cls_top__greatest_0, cls_divide__nonneg__pos_0, cls_Pair__eq_0, cls_fun__upd__twist_0, cls_neq0__conv_1, cls_divide__le__0__iff_5, cls_linorder__not__le_1, cls_in__mktop_4, cls_linorder_Onot__le_1, cls_add__less__cancel__right_0, cls_divide__zero_0, cls_minus__less__iff_0, cls_refl__onD_0, cls_le__trans_0, cls_rev__ImageI_0, cls_neg__0__equal__iff__equal_1, cls_inj__on__empty_0, cls_UNIV__I_0, cls_less__eq__neg__nonpos_1, cls_equation__minus__iff_0, cls_less__minus__iff_1, cls_order__le__neq__trans_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_add__increasing_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_total__on__empty_0, cls_not__less__iff__gr__or__eq_1, cls_nat__add__right__cancel_0, cls_fun__upd__apply_0, clsarity_fun__Lattices_Oboolean__algebra, cls_all__from__to__nat_Osimps_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_top1I_0, cls_zero__less__divide__iff_2, cls_order__eq__iff_2, cls_less__not__refl_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_CHAINED_2, cls_class__ringb_Oadd__cancel_0, cls_add__nonpos__nonpos_0, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, cls_divide__le__0__iff_1, cls_bex__empty_0, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, cls_divide__pos__neg_0, cls_order_Odual__order_0, cls_eq__divide__eq_2, cls_add__nonneg__nonneg_0, cls_eq__neg__iff__add__eq__0_1, cls_neg__le__0__iff__le_1, cls_inj__on__def_0, cls_order__antisym__conv_0, cls_add__lessD1_0, cls_even__less__0__iff_1, cls_order__neq__le__trans_0, cls_power__eq__imp__eq__base_0, cls_linorder_Oantisym__conv1_0, cls_class__ringb_Oadd__r0__iff_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_add__strict__increasing_0, cls_Domain__Id__on_0, cls_preorder_Oless__asym_0, cls_le__imp__neg__le_0, cls_linorder__less__linear_0, cls_injD_0, cls_nat__add__left__cancel__le_1, cls_Nat_Oadd__0__right_0, cls_bot__empty__eq_0, cls_vimage__eq_1, cls_divide__strict__right__mono__neg_0, cls_nat__neq__iff_0, cls_divide__less__eq_2, cls_power__strict__increasing__iff_1, cls_minus__divide__divide_0, cls_divide__less__0__1__iff_0, clsarity_nat__Power_Opower, cls_power__increasing__iff_1, cls_refl__onD1_0, cls_order__less__le_2, cls_le0_0, cls_natgb_Oadd__r0__iff_0, cls_vimage__if_1, cls_le__add2_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_in__measure_0, cls_xt1_I11_J_0, cls_zero__le__divide__iff_0, cls_add__neg__neg_0, cls_trans__less__add2_0, cls_minus__divide__left_0, cls_neg__0__less__iff__less_1, cls_vimageE_0, cls_0_0, cls_equiv_Orefl__on_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_neg__less__0__iff__less_1, cls_comm__monoid__add_Omult__left__commute_0, cls_neg__equal__zero_0, cls_add__minus__cancel_0, cls_divide__less__0__iff_2, cls_xt1_I6_J_0, cls_le__add__right__mono_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_double__compl_0, cls_RangeI_0, cls_notin__Lin__iff_1, cls_order_Oeq__iff_2, cls_nat__less__le_0, cls_fun__upd__idem__iff_0, cls_divide__less__0__iff_5, cls_nat__add__left__cancel__le_0, cls_fun__upd__idem_0, cls_linorder_Onot__le_0, cls_vimage__code_1, cls_ComplI_0, cls_order_Oless__le_2, cls_Id__on__iff_1, cls_linorder_Olinear_0, cls_minus__le__iff_1, cls_power__one__right_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_zero__less__divide__1__iff_1, cls_zero__le__divide__1__iff_1, cls_in__mkbot_1, cls_plus__nat_Oadd__0_0, cls_comm__monoid__add_Omult__1_0, cls_linorder__not__le_0, cls_in__mktop_2, cls_less__eq__neg__nonpos_0, cls_nat__le__linear_0, cls_trans__less__add1_0, cls_equiv__class__eq__iff_1, cls_injh_0, cls_nat__less__le_2, cls_divide__le__0__iff_4, clsarity_bool__Lattices_Oboolean__algebra, cls_order__less__irrefl_0, cls_power__eq__0__iff_0, cls_class__semiring_Oadd__c_0, cls_linorder_Onot__leE_0, cls_nonzero__power__divide_0, cls_one__less__power_0, cls_nat__add__left__cancel_0, cls_neg__le__iff__le_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_less__minus__self__iff_1, cls_divide__less__0__iff_1, cls_le__iff__add_1, cls_frac__less2_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_gt__half__sum_0, cls_emptyE_0, cls_preorder_Oorder__refl_0, cls_fun__upd__same_0, cls_add__nonneg__eq__0__iff_2, cls_fun__upd__def_0, cls_add__is__0_2, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_add__le__mono1_0, cls_neg__0__equal__iff__equal_0, cls_vimageI2_0, clsarity_fun__Orderings_Opreorder, cls_zero__less__divide__iff_4, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, cls_add__mono_0, cls_divide__le__0__iff_0, cls_less__minus__self__iff_0, cls_in__mkbot_5, cls_double__complement_0, cls_preorder_Oless__le__not__le_2, cls_inj__on__contraD_0, cls_equation__minus__iff_1, cls_inj__onD_0, cls_add__neg__nonpos_0, cls_dual__preorder_0, cls_add__eq__self__zero_0, cls_not__less0_0, cls_minus__add_0, cls_frac__less_0, cls_mem__Sigma__iff_2, cls_acc__downward_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_add__less__cancel__left_0, cls_divide__strict__right__mono_0, cls_right__minus_0, cls_nonzero__minus__divide__divide_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_all__from__to__nat_Osimps_3, cls_zero__le__power_0, cls_add__leE_1, cls_eq__neg__iff__add__eq__0_0, cls_class__semiring_Opwr__0_0, cls_CHAINED_0_03, cls_vimageD_0, cls_add__gr__0_2, cls_PiProf_0, cls_add__less__le__mono_0, cls_divide__nonpos__pos_0, cls_card__gt__0__iff_0, cls_power__increasing__iff_0, cls_divide__less__eq_3, cls_order__less__imp__le_0, cls_minus__equation__iff_1, cls_monoid__add__class_Oadd__0__right_0, cls_add__gr__0_1, cls_Domain__iff_1, cls_fun__upd__upd_0, cls_le__add1_0, cls_add__strict__increasing2_0, cls_divide__eq__eq_1, cls_termination__basic__simps_I2_J_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_mlex__leq_0, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_le__eq__less__or__eq_0, cls_vimage__empty_0, cls_preorder_Oorder__trans_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_order__less__le_1, clsarity_fun__HOL_Ouminus, cls_nat__less__le_1, cls_Pair__eq_1, cls_divide__less__0__1__iff_1, cls_add__le__cancel__left_0, cls_Compl__empty__eq_0, cls_power__decreasing_0, cls_vimage__if_2, cls_zero__le__divide__1__iff_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_linorder_Oantisym__conv3_0, cls_xt1_I7_J_0, cls_equiv__class__eq__iff_2, cls_linorder__not__less_1, cls_le__neq__implies__less_0, cls_not__one__le__zero_0, cls_even__less__0__iff_0, cls_power__0__left_1, cls_ball__empty_0, cls_add__le__cancel__right_0, cls_order_Oless__le_1, cls_divide__less__0__iff_4, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_power__mono_0, cls_divide__le__0__1__iff_0, cls_le__refl_0, cls_neg__less__iff__less_0, clsarity_bool__Orderings_Otop, cls_in__measure_1, cls_in__mkbot_0, cls_fun__upd__idem__iff_1, cls_right__inverse__eq_1
% 29.68/8.11  % No. of inferences in proof: 1129
% 29.68/8.11  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7379 ms resp. 6034 ms w/o parsing
% 32.55/8.70  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.55/8.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------