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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT074-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n018.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 08:27:10 AM UTC 2026

% Result   : Unsatisfiable 17.14s 5.40s
% Output   : Refutation 18.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  696
% Syntax   : Number of formulae    : 1393 ( 385 unt;   0 typ;   0 def)
%            Number of atoms       : 3219 ( 788 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 26328 (1552   ~;1826   |;   0   &;22950   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  113 ( 111 usr;  10 con; 0-7 aty)
%            Number of variables   : 5056 (   0   ^;5056   !;   0   ?;5056   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_decl,type,
    c_in: $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Relation_Orel__comp_decl,type,
    c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).

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

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

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

thf(c_Transitive__Closure_Ortrancl_decl,type,
    c_Transitive__Closure_Ortrancl: $i > $i > $i ).

thf(c_Transitive__Closure_Otrancl_decl,type,
    c_Transitive__Closure_Otrancl: $i > $i > $i ).

thf(c_Relation_OId_decl,type,
    c_Relation_OId: $i > $i ).

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

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

thf(c_Relation_Osym_decl,type,
    c_Relation_Osym: $i > $i > $o ).

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

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

thf(c_Order__Relation_Ostrict__linear__order__on_decl,type,
    c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).

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

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

thf(c_Wellfounded_Owf_decl,type,
    c_Wellfounded_Owf: $i > $i > $o ).

thf(c_Wellfounded_Oacyclic_decl,type,
    c_Wellfounded_Oacyclic: $i > $i > $o ).

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

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

thf(c_Relation_Otrans_decl,type,
    c_Relation_Otrans: $i > $i > $o ).

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

thf(c_Relation_Oantisym_decl,type,
    c_Relation_Oantisym: $i > $i > $o ).

thf(c_snd_decl,type,
    c_snd: $i > $i > $i ).

thf(c_fst_decl,type,
    c_fst: $i > $i > $i ).

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

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

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

thf(c_Relation_Oinv__image_decl,type,
    c_Relation_Oinv__image: $i > $i > $i > $i > $i ).

thf(c_List_Osko__Recdef__Xtfl__wf__induct__1__1_decl,type,
    c_List_Osko__Recdef__Xtfl__wf__induct__1__1: $i > $i > $i > $i ).

thf(c_Relation_Oirrefl_decl,type,
    c_Relation_Oirrefl: $i > $i > $o ).

thf(c_Wellfounded_OwfP_decl,type,
    c_Wellfounded_OwfP: $i > $i > $o ).

thf(c_FunDef_Oin__rel_decl,type,
    c_FunDef_Oin__rel: $i > $i > $i > $i ).

thf(c_Relation_Osingle__valued_decl,type,
    c_Relation_Osingle__valued: $i > $i > $i > $o ).

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

thf(c_List_Osko__Recdef__Xcuts__eq__1__1_decl,type,
    c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Recdef_Ocut_decl,type,
    c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).

thf(v_r_decl,type,
    v_r: $i ).

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: $i > $i > $i > $i ).

thf(c_split_decl,type,
    c_split: $i > $i > $i > $i > $i ).

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

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

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

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XId__onE__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: $i > $i > $i > $i > $i ).

thf(c_Equiv__Relations_Ocongruent2_decl,type,
    c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XIdE__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).

thf(c_Nitpick_Orefl_H_decl,type,
    c_Nitpick_Orefl_H: $i > $i > $o ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).

thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_decl,type,
    c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).

thf(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_decl,type,
    v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).

thf(v_sko__Transitive__Closure__Xtrancl__Xcases__1_decl,type,
    v_sko__Transitive__Closure__Xtrancl__Xcases__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).

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

thf(v_sko__Transitive__Closure__Xrtrancl__Xcases__1_decl,type,
    v_sko__Transitive__Closure__Xrtrancl__Xcases__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).

thf(v_sko__Wellfounded__Xacc__Xinduct__1_decl,type,
    v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1_decl,type,
    c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_Equiv__Relations_Ocongruent_decl,type,
    c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).

thf(v_sko__Wellfounded__Xacc__Xinducts__1_decl,type,
    v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).

thf(415,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).

thf(1586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(639,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(2094,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(521,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).

thf(1823,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(436,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1633,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(496,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).

thf(1767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(403,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).

thf(1559,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).

thf(846,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_fst ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_fst ) @ hAPP ) ) )
      | ( ( C @ ( B @ ( A @ c_snd ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_snd ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__fst__snd__eq_0) ).

thf(909,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_fst ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_fst ) @ hAPP ) ) )
      | ( ( C @ ( B @ ( A @ c_snd ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_snd ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).

thf(1899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(532,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_bool @ ( G @ tc_fun ) @ ( F @ ( E @ ( A @ c_split ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).

thf(1850,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_bool @ ( G @ tc_fun ) @ ( F @ ( E @ ( A @ c_split ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(112,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(941,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(226,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(519,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).

thf(1818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(399,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).

thf(1549,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(667,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).

thf(2163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

thf(2199,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(1322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(646,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ ( B @ ( A @ c_snd ) @ hAPP ) @ ( C @ ( B @ ( A @ c_fst ) @ hAPP ) @ c_Pair ) ) ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__collapse_0) ).

thf(2109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ ( B @ ( A @ c_snd ) @ hAPP ) @ ( C @ ( B @ ( A @ c_fst ) @ hAPP ) @ c_Pair ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).

thf(1554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).

thf(1110,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(236,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).

thf(1200,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(488,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).

thf(1750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1005,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(644,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(2104,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(548,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

thf(1882,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(624,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

thf(2062,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( D @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).

thf(1401,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( D @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(479,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).

thf(1728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

thf(1591,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(83,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( F @ ( C @ ( A @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( F @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).

thf(878,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( F @ ( C @ ( A @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( F @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(348,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( E @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).

thf(1437,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( E @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

thf(1173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(648,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(2114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(1142,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(589,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).

thf(1533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

thf(1041,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).

thf(861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(453,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).

thf(1655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(207,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(491,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).

thf(1756,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(602,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_11) ).

thf(1999,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(250,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osingle__valued ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

thf(1233,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osingle__valued ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(597,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).

thf(1988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(747,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1640,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).

thf(1063,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(1497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(469,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

thf(1078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(1426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(541,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).

thf(1867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(675,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

thf(2184,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(269,axiom,
    ( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
    = ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).

thf(1275,plain,
    ( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
    = ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(659,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(2141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(52,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(295,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__by__empty_0) ).

thf(1327,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).

thf(1260,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
      = ( B @ ( A @ c_Relation_OId__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

thf(1222,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
      = ( B @ ( A @ c_Relation_OId__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(930,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(898,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(526,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).

thf(1835,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(138,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1001,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(563,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).

thf(1914,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(7,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(709,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(609,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).

thf(2020,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(606,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

thf(2010,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(441,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

thf(1645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).

thf(1475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( C @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).

thf(1243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( C @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(502,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).

thf(1782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(695,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).

thf(2227,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(1391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(422,axiom,
    tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1601,plain,
    tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(671,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(2173,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(313,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(1366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(627,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).

thf(2067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(558,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( G @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( F @ ( F @ ( E @ ( D @ tc_prod ) @ ( G @ ( F @ ( E @ ( D @ ( A @ c_split ) ) ) @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__imageI_0) ).

thf(1904,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( G @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( F @ ( F @ ( E @ ( D @ tc_prod ) @ ( G @ ( F @ ( E @ ( D @ ( A @ c_split ) ) ) @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(468,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).

thf(1703,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(434,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(1628,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(471,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).

thf(1709,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(344,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1430,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(596,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).

thf(1985,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(615,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ tc_prod ) @ ( A @ ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).

thf(2039,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ tc_prod ) @ ( A @ ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(543,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_13) ).

thf(1871,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(64,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(838,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(411,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

thf(1577,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(599,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) )
      | ( E @ ( D @ ( C @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_split ) ) ) @ hAPP ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).

thf(1992,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) )
      | ( E @ ( D @ ( C @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_split ) ) ) @ hAPP ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1059,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).

thf(1760,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(448,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).

thf(1660,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).

thf(1298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(297,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).

thf(1330,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(1264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).

thf(934,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientI_0) ).

thf(1191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(511,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( C @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).

thf(1800,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( C @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(553,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).

thf(1892,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).

thf(1514,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

thf(2049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(409,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).

thf(1572,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

thf(1741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(407,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

thf(1568,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(666,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(2158,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)],[666]) ).

thf(498,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).

thf(1773,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(375,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(1494,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).

thf(1778,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).

thf(1100,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(531,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).

thf(1847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(567,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).

thf(1922,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(291,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

thf(1319,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)],[291]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(552,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

thf(1890,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(426,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_13) ).

thf(1609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(1013,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(337,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).

thf(1415,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(1465,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(516,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(1811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(637,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).

thf(2090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(316,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

thf(1373,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(206,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

thf(1136,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(536,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orefl__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).

thf(1858,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orefl__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(149,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(1020,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(456,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).

thf(1677,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

thf(1183,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
        = ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
        = ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(756,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1151,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(584,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).

thf(1960,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

thf(806,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(413,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).

thf(1581,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(123,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

thf(966,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)],[123]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).

thf(1051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(821,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(569,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).

thf(1928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(318,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1377,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(242,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1215,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(18,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(734,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(550,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).

thf(1886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(1394,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(657,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).

thf(2137,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).

thf(1433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(237,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

thf(1104,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(388,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Wellfounded_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).

thf(1521,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Wellfounded_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(529,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).

thf(1843,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(623,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( C = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).

thf(2058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( C = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(508,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).

thf(1796,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(175,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

thf(1072,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Oirrefl ) )
      | ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Oirrefl ) )
      | ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(431,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).

thf(1622,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(591,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_fst ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exI__realizer_0) ).

thf(1975,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_fst ) @ hAPP ) @ ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

thf(1564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(539,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).

thf(1863,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(444,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).

thf(1651,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(424,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(920,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(463,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).

thf(1691,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1338,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(618,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).

thf(2047,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( A @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( C @ ( C @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).

thf(1470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( A @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( C @ ( C @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(287,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(1311,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(214,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ ( B @ c_Relation_Osingle__valued ) ) )
      | ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Osingle__valued ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).

thf(1153,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ ( B @ c_Relation_Osingle__valued ) ) )
      | ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Osingle__valued ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(761,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(634,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).

thf(2083,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

thf(1067,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(482,axiom,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_Lab____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1736,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_Lab____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).

thf(1057,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(1163,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(478,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(1723,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)],[478]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(1343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(150,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).

thf(1021,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( D @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).

thf(952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( D @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

thf(1355,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1255,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(408,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).

thf(1570,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(1217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(430,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).

thf(1619,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(655,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( G @ ( E @ tc_prod ) @ ( C @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).

thf(2132,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( G @ ( E @ tc_prod ) @ ( C @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(729,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(916,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

thf(1602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(566,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1920,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(588,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).

thf(1968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(579,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(461,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).

thf(1687,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

thf(1624,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1027,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1128,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1392,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(551,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(688,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(2211,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(277,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1291,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(561,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

thf(1910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(66,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(842,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(1360,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(595,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).

thf(1983,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(642,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).

thf(2100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1270,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(513,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).

thf(1804,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(296,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).

thf(1328,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).

thf(1856,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(188,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).

thf(1096,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = C )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).

thf(1540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = C )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(546,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).

thf(1878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(476,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Oacyclic ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).

thf(1719,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Oacyclic ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(1,negated_conjecture,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_Lab____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(697,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_Lab____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_a____ @ ( v_b____ @ c_Pair ) ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(507,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).

thf(1794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(147,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).

thf(1017,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(580,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1953,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(317,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).

thf(1375,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).

thf(1121,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(459,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).

thf(1683,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(884,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(1292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(341,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( D @ ( C @ ( E @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( D @ ( C @ ( E @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).

thf(1424,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( D @ ( C @ ( E @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( D @ ( C @ ( E @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(414,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

thf(1584,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(573,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).

thf(1937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ODomain ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).

thf(1791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ODomain ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(1446,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(706,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1419,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(1082,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(610,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(2023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(586,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).

thf(1964,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(575,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_snd ) @ hAPP ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__conv_0) ).

thf(1942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_snd ) @ hAPP ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(484,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).

thf(1739,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1414,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(621,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).

thf(2053,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(681,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Oantisym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).

thf(2196,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Oantisym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(1207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(635,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OId__on ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).

thf(2085,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OId__on ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(427,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) )
      | ( A
        = ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).

thf(1612,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) )
      | ( A
        = ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(158,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1039,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(125,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

thf(970,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(215,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).

thf(1155,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(486,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
       != ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).

thf(1744,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
       != ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(196,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

thf(1114,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(131,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).

thf(985,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(701,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

thf(1131,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)],[203]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).

thf(1668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(400,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1552,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(571,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).

thf(1932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1799,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(577,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(533,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).

thf(1852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(544,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).

thf(1874,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(421,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(474,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).

thf(1715,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).

thf(1525,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(20,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(738,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(1456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(1382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(664,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).

thf(2153,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(524,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).

thf(1831,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).

thf(1231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(593,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Relation_Oirrefl ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).

thf(1979,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Relation_Oirrefl ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).

thf(779,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(1333,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(685,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).

thf(2203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(183,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(1086,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).

thf(1241,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(465,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).

thf(1695,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(631,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).

thf(2076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1187,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).

thf(1663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(692,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(2221,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).

thf(2189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

thf(1185,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(773,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

thf(888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(926,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).

thf(1286,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).

thf(1035,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(651,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).

thf(2121,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(205,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1135,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

thf(1510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(466,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( A @ ( C @ c_in ) ) )
      | ~ ( E @ ( B @ ( D @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( F @ ( E @ ( E @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).

thf(1698,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( A @ ( C @ c_in ) ) )
      | ~ ( E @ ( B @ ( D @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( F @ ( E @ ( E @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).

thf(1483,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(487,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).

thf(1747,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

thf(856,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(745,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(419,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).

thf(1595,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

thf(1278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(559,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

thf(1906,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1146,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(490,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).

thf(1754,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(613,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

thf(2033,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).

thf(2149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(55,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(819,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).

thf(975,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).

thf(1833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1007,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(564,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).

thf(1916,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).

thf(1752,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(608,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_11) ).

thf(2016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

thf(826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(394,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).

thf(1535,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(467,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(656,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).

thf(2134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(694,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).

thf(2225,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(549,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).

thf(1884,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(428,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1615,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1784,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
      = ( A @ c_Relation_OId ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).

thf(958,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
      = ( A @ c_Relation_OId ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).

thf(1403,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)],[331]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(372,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( E @ ( C @ ( B @ c_fst ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__beta_0) ).

thf(1488,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( E @ ( C @ ( B @ c_fst ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).

thf(1428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).

thf(1707,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

thf(1371,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).

thf(1635,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1107,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(1092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).

thf(1258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(115,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(246,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).

thf(1224,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).

thf(1675,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(9,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(713,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(540,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).

thf(1865,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(601,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).

thf(1997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).

thf(1765,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(1090,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(555,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).

thf(1897,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(804,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1194,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(650,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(2119,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(900,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).

thf(1282,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(554,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).

thf(1894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( C @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).

thf(1048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( C @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).

thf(1349,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

thf(1492,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(649,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).

thf(2116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).

thf(1439,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(663,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_fst ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_0) ).

thf(2151,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_fst ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(696,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(2229,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(416,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(996,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(880,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

thf(1043,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(682,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).

thf(2197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(626,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

thf(2065,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).

thf(1080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(402,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).

thf(1557,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(654,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( B @ ( E @ ( A @ c_in ) ) )
      | ~ ( B @ ( E @ ( D @ c_in ) ) )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
       != ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).

thf(2129,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( B @ ( E @ ( A @ c_in ) ) )
      | ~ ( B @ ( E @ ( D @ c_in ) ) )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
       != ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(53,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(816,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(647,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).

thf(2111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(435,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).

thf(1630,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(69,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

thf(848,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

thf(1177,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(932,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).

thf(890,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(674,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_12) ).

thf(2180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(520,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).

thf(1821,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(480,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).

thf(1731,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).

thf(799,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(726,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(527,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).

thf(1838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

thf(1325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(689,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).

thf(2212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(658,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(2139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Relation_OId @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).

thf(1477,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Relation_OId @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(376,axiom,
    ! [A: $i] : ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Osingle__valued ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

thf(1496,plain,
    ! [A: $i] : ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Osingle__valued ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

thf(1102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(665,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).

thf(2156,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(686,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eqD_0) ).

thf(2207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(590,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).

thf(1973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(628,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).

thf(2069,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).

thf(1562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(99,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).

thf(1171,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(528,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).

thf(1841,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).

thf(1396,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(620,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( G @ ( F @ ( C @ c_in ) ) )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).

thf(2051,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( G @ ( F @ ( C @ c_in ) ) )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(625,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).

thf(2064,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1015,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)],[146]) ).

thf(499,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).

thf(1775,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

thf(1435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).

thf(1364,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(604,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).

thf(2005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).

thf(1626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(515,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

thf(1809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(640,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).

thf(2096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).

thf(1758,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(598,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).

thf(1990,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(1472,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).

thf(1018,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(583,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).

thf(1958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(63,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(836,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(270,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

thf(1277,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(652,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).

thf(2124,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).

thf(939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_fst ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_fst ) @ hAPP ) ) )
      | ( ( C @ ( B @ ( A @ c_snd ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_snd ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__eqI_0) ).

thf(1340,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_fst ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_fst ) @ hAPP ) ) )
      | ( ( C @ ( B @ ( A @ c_snd ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_snd ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Ortrancl ) )
      = ( A @ c_Relation_OId ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).

thf(1181,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Ortrancl ) )
      = ( A @ c_Relation_OId ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(823,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(530,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).

thf(1845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(509,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Oirrefl ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).

thf(1798,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Oirrefl ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(72,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).

thf(855,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(385,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(1516,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(152,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).

thf(1025,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(679,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).

thf(2192,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(442,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).

thf(1780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(189,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).

thf(1098,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).

thf(1003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(1070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).

thf(872,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(660,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).

thf(2143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(607,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( A = C )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).

thf(2012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( A = C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(672,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).

thf(2175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(638,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

thf(2092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(668,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).

thf(2165,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(542,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).

thf(1869,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(263,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

thf(1262,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(457,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).

thf(1679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(617,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(2044,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).

thf(1579,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1336,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1220,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
      = ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).

thf(907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
      = ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).

thf(1711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(1053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).

thf(1813,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).

thf(1300,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(438,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).

thf(1637,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).

thf(1785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
      = ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).

thf(1317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
      = ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).

thf(1763,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(622,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(2056,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(572,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
      | ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).

thf(1934,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
      | ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) )
      | ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) )
      | ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(594,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).

thf(1981,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(1284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(77,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(864,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(452,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).

thf(1670,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(268,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(1272,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(876,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(859,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).

thf(1617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(512,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( A @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ ( C @ ( B @ c_fst ) @ hAPP ) @ c_Pair ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surjective__pairing_0) ).

thf(1802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( A @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ ( C @ ( B @ c_fst ) @ hAPP ) @ c_Pair ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1023,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).

thf(1353,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(581,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).

thf(1955,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(661,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_12) ).

thf(2145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(978,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(475,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(1717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(612,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).

thf(2030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(574,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

thf(1940,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(1421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).

thf(1459,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(587,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( C @ ( B @ c_fst ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eqD_0) ).

thf(1966,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( C @ ( B @ c_fst ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(578,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(1949,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(680,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(2194,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1412,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

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

thf(759,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(687,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).

thf(2209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(629,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).

thf(2071,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(565,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).

thf(1918,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(289,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

thf(1316,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

thf(1649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(1084,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(1157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(632,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).

thf(2078,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(690,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).

thf(2215,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).

thf(1517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(353,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ( A = B )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__disj_0) ).

thf(1448,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ( A = B )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(677,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(2187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(1189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1010,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(324,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).

thf(1390,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(410,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

thf(1575,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).

thf(844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(355,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).

thf(1453,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(481,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).

thf(1734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(514,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ tc_prod ) @ ( C @ ( B @ ( A @ c_fst ) @ c_Set_Oimage ) ) ) )
      = ( B @ ( A @ ( C @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eq__Domain_0) ).

thf(1807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ tc_prod ) @ ( C @ ( B @ ( A @ c_fst ) @ c_Set_Oimage ) ) ) )
      = ( B @ ( A @ ( C @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(477,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).

thf(1721,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(669,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).

thf(2167,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(369,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

thf(1481,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(114,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

thf(946,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(611,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).

thf(2026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(534,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( E @ ( D @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ ( C @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).

thf(1854,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( E @ ( D @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ ( C @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(896,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(641,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

thf(2098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(169,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).

thf(1062,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).

thf(786,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(538,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ tc_prod ) @ ( C @ ( B @ ( A @ c_snd ) @ c_Set_Oimage ) ) ) )
      = ( B @ ( A @ ( C @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eq__Range_0) ).

thf(1861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ tc_prod ) @ ( C @ ( B @ ( A @ c_snd ) @ c_Set_Oimage ) ) ) )
      = ( B @ ( A @ ( C @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(1030,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(100,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).

thf(914,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(616,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).

thf(2041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1294,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(1308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(1077,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(1212,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(614,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).

thf(2036,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
      = ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).

thf(1444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
      = ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(600,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = C )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).

thf(1994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = C )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(1045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).

thf(1161,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(462,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).

thf(1689,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(633,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).

thf(2081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).

thf(1512,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(272,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).

thf(1280,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(582,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1957,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

thf(950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( F @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).

thf(1546,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( F @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).

thf(818,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(545,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).

thf(1876,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(605,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).

thf(2008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(603,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

thf(2003,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(1116,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(560,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_1) ).

thf(1908,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(691,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).

thf(2218,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ c_Wellfounded_OwfP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__in__rel_0) ).

thf(1133,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ c_Wellfounded_OwfP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).

thf(1642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(643,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).

thf(2102,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(752,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).

thf(1593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(319,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

thf(1380,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)],[319]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).

thf(1527,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(454,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).

thf(1673,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(537,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).

thf(1859,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(518,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).

thf(1816,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(447,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( G @ ( A @ hAPP ) )
        = ( G @ ( F @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
       != ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).

thf(1657,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( G @ ( A @ hAPP ) )
        = ( G @ ( F @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
       != ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(676,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(2186,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(464,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).

thf(1693,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).

thf(828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

thf(1065,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(955,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(304,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( E @ ( D @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osingle__valued ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).

thf(1346,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( E @ ( D @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osingle__valued ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(684,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).

thf(2201,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(918,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(801,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ODomain ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).

thf(1363,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ODomain ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

thf(1314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(334,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).

thf(1410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(165,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

thf(1056,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)],[165]) ).

thf(505,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( F @ ( G @ tc_prod ) @ ( D @ ( F @ ( G @ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).

thf(1789,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( F @ ( G @ tc_prod ) @ ( D @ ( F @ ( G @ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).

thf(1033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(1288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(235,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( F @ ( E @ ( D @ ( C @ ( B @ c_Recdef_Ocut ) ) ) ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( A @ hAPP ) )
       != ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).

thf(1197,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( F @ ( E @ ( D @ ( C @ ( B @ c_Recdef_Ocut ) ) ) ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( A @ hAPP ) )
       != ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(693,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(2223,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(960,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).

thf(1473,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(570,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).

thf(1930,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(15,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(728,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(522,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).

thf(1827,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(266,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).

thf(1268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(1357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(992,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(568,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).

thf(1925,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(557,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).

thf(1902,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(252,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_in ) ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(1236,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_in ) ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(132,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).

thf(987,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(653,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_fst ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__conv_0) ).

thf(2127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_fst ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(523,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

thf(1829,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(592,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).

thf(1977,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(321,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(1384,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(395,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1537,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(723,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).

thf(850,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(473,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).

thf(1713,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(1597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(547,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Osingle__valued ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).

thf(1880,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Osingle__valued ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(1431,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).

thf(1505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(329,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(585,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).

thf(1962,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(142,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(1009,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(360,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(1463,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(27,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(755,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(1204,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(1468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ORange ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ORange ) ) @ ( C @ ( B @ ( A @ c_Relation_ORange ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).

thf(1069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ORange ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ORange ) ) @ ( C @ ( B @ ( A @ c_Relation_ORange ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(298,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(1331,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(425,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).

thf(1606,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(445,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(576,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).

thf(1944,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(923,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(483,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).

thf(1737,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).

thf(1681,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(630,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).

thf(2074,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).

thf(1490,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1037,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(775,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(670,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( B @ ( E @ ( A @ c_in ) ) )
      | ~ ( B @ ( E @ ( D @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
        = ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).

thf(2170,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( B @ ( E @ ( A @ c_in ) ) )
      | ~ ( B @ ( E @ ( D @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
        = ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(184,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(1088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(645,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).

thf(2106,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(636,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).

thf(2087,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(6,axiom,
    tc_bool @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(708,plain,
    tc_bool @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(562,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

thf(1912,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(673,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).

thf(2177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).

thf(1417,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( D @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).

thf(972,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( D @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(2245,plain,
    $false,
    inference(e,[status(thm)],[1586,2094,1823,1168,1633,1767,1559,846,909,1899,1850,962,941,1179,777,1818,1549,2163,892,2199,1322,2109,1454,1554,1110,1200,1750,1005,2104,1882,1522,2062,994,1401,1073,1728,1591,878,1305,1437,1173,2114,1142,1971,1533,1041,861,1671,1655,1137,1756,1999,1233,1988,747,1640,1063,1497,1705,1078,1426,1867,2184,1275,2141,814,1327,1260,698,1222,930,829,898,1835,1001,1914,709,2020,2010,1645,1475,1228,1243,1782,2227,1391,782,1441,1601,1386,2173,1366,2067,1529,1904,1703,1628,1709,1430,1985,2039,1871,838,1577,1992,1059,1760,1660,1298,1330,1264,934,1191,1800,1892,1514,2049,1572,1741,1568,2158,1773,1494,1778,1100,1847,1922,902,1319,870,1890,1479,1609,1013,770,1415,1465,1811,2090,1373,1136,1858,1020,1677,1183,905,1302,756,1151,937,1960,806,1581,966,1051,821,981,1928,1377,1215,734,1886,1394,2137,1351,1433,1405,1201,1104,1521,1843,2058,1796,1072,1119,1622,1975,1564,1863,1651,1604,920,1691,793,810,1338,2047,1470,1311,714,1153,761,2083,1067,1736,1057,1163,1723,894,1343,1021,952,1519,1355,1255,1123,1570,1217,1666,788,1619,2132,729,916,1602,1920,1968,852,1951,1687,1624,1159,1210,1027,1128,1392,1012,1888,1296,2211,1407,1291,710,1910,842,1360,742,1983,874,2100,1270,1804,1328,1856,1096,1540,1878,1719,989,697,1234,1794,1017,1953,1375,1121,1683,884,1292,1075,1424,1584,1937,1791,1446,706,1419,1082,2023,1964,1942,1739,1461,1414,2053,2196,1207,2085,1612,1039,970,1155,1744,1114,985,701,1131,1668,1552,1932,1060,1799,1947,1852,1874,1599,1715,1525,1451,738,1456,1382,1266,2153,1831,1231,1979,779,1333,2203,1086,1241,1695,2076,1187,1663,2221,2189,1185,773,888,926,1286,1035,2121,1135,1510,1698,1483,1747,856,745,1595,1278,1906,1146,1754,2033,2149,819,975,1833,1007,1916,1125,1752,2016,1388,826,1535,1701,2134,2225,1884,1615,1784,958,1403,1226,1488,1428,1707,1371,1635,1107,1092,1258,947,1224,1675,1139,1503,713,1865,1239,1997,1765,1090,1897,804,764,1194,2119,900,831,1282,1894,784,1048,1349,1492,1144,2116,1439,2151,2229,1589,996,880,1043,2197,1307,863,2065,1175,1080,1557,2129,816,2111,1630,848,943,1177,932,1112,890,2180,1821,1731,799,726,1838,1325,1149,964,983,2212,2139,1477,1496,1102,2156,2207,1973,2069,1562,912,1171,1841,1396,2051,1245,2064,1015,1775,1435,1364,1250,2005,1626,1809,2096,1758,812,749,1990,1472,1018,1958,836,1277,2124,939,1340,968,1181,823,1845,1798,855,1516,1025,2192,1647,1252,739,1780,1098,1003,1770,1070,872,1566,2143,2012,1368,2175,2092,2165,791,717,1869,1262,808,1679,2044,1579,1336,1220,907,1711,1053,1813,1300,1637,840,1785,1317,1763,2056,1934,1543,703,1981,1284,1485,864,1670,1272,876,859,1617,1802,1023,1353,1955,2145,1094,978,1717,2030,1940,1421,1459,1966,1685,1949,2194,1412,759,2209,2071,1918,1316,1649,1084,1157,2078,2215,1517,1448,2187,1189,1010,1390,1575,844,1453,1734,1807,1721,2167,1481,946,2026,1854,896,2098,1062,1508,731,786,1861,1030,914,2041,1294,1308,1193,1077,1212,2036,1444,1994,1045,1161,1689,2081,999,1512,1280,1957,833,950,1546,818,1876,2008,1248,867,735,2003,1116,1908,2218,1133,1642,2102,752,1593,1380,1527,1673,1859,1816,1657,2186,1693,828,1065,955,1346,796,2201,918,801,1363,1314,1410,767,1056,1789,1033,1288,1197,2223,960,1473,720,1165,886,928,1930,728,1827,1268,1357,992,1925,1902,1236,987,2127,1829,1977,1384,1537,1500,723,850,1713,1597,1880,1431,1505,1399,1320,1962,1009,1463,755,1204,1468,1069,1331,1606,1653,1944,923,1737,1681,2074,1490,1037,775,2170,1088,2106,2087,708,1912,882,2177,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT074-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40  % Computer : n018.cluster.edu
% 0.15/0.40  % Model    : x86_64 x86_64
% 0.15/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40  % Memory   : 8046.5625MB
% 0.15/0.40  % OS       : Linux 6.8.0-71-generic
% 0.15/0.40  % CPULimit : 300
% 0.15/0.40  % WCLimit  : 300
% 0.15/0.40  % DateTime : Sat Sep 26 06:27:06 UTC 2026
% 0.15/0.41  % CPUTime  : 
% 0.15/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.32/1.41  % [INFO] 	 Parsing done (410ms). 
% 2.32/1.43  % [INFO] 	 Running in sequential loop mode. 
% 3.05/1.81  % [INFO] 	 eprover registered as external prover. 
% 3.05/1.81  % [INFO] 	 Scanning for conjecture ... 
% 3.73/2.03  % [INFO] 	 Found a conjecture (or negated_conjecture) and 708 axioms. Running axiom selection ... 
% 4.39/2.28  % [INFO] 	 Axiom selection finished. Selected 695 axioms (removed 13 axioms). 
% 5.43/2.60  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.83/2.62  % [INFO] 	 Type checking passed. 
% 5.83/2.63  % [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 ... 
% 16.46/5.39  % External prover 'e' found a proof!
% 16.46/5.39  % [INFO] 	 Killing All external provers ... 
% 16.46/5.39  % Time passed: 4836ms (effective reasoning time: 3954ms)
% 17.14/5.40  % Axioms used in derivation (695): cls_inf__sup__absorb_0, cls_trancl__converseD_0, cls_Diff__cancel_0, cls_converse__tranclE_1, cls_subset__insert_1, cls_Diff__iff_2, cls_rtrancl__idemp_0, cls_snd__conv_0, cls_equiv__class__eq__iff_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Range__Un__eq_0, cls_inf__sup__aci_I2_J_0, cls_rtrancl__induct_3, cls_split__beta_0, cls_in__mktop_1, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_sup__ge1_0, cls_image__constant_0, cls_in__above_11, cls_insertE_0, cls_wf__subset_0, cls_snd__eqD_0, cls_union__comp__emptyL_0, cls_insert__inter__insert_0, cls_Un__Diff_0, cls_congruent_Ocongruent_0, cls_rtrancl__converseD_0, cls_in__below_14, cls_Un__subset__iff_0, cls_splitD_H_0, cls_total__on__def_0, cls_converseI_0, cls_equalityI_0, cls_Id__onE_0, cls_single__valuedD_0, cls_wf__acyclic_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_trancl__subset__Sigma__aux_0, cls_rtrancl_Ocases_0, cls_empty__is__image_1, cls_Un__empty__left_0, cls_wfE__min_0, cls_single__valued__Id__on_0, cls_strict__linear__order__on__def_0, cls_le__funD_0, cls_rel__comp__empty1_0, cls_Image__singleton__iff_0, cls_image__mono_0, cls_tranclD2_0, cls_sup__bot__right_0, cls_insert__code_1, cls_trancl_Ocases_0, clsarity_bool__Lattices_Olower__semilattice, cls_le__iff__inf_1, cls_Un__upper1_0, cls_COMBK__def_0, cls_in__below_3, cls_distrib__sup__le_0, cls_Int__mono_0, cls_Id__O__R_0, cls_mkbot__Lin_0, cls_CHAINED_0, cls_Range__def_0, cls_inf__sup__aci_I6_J_0, cls_Id__on__eqI_0, cls_Un__commute_0, cls_acc_Oinduct_2, cls_irrefl__def_0, cls_acc__wfD_0, cls_UnCI_1, cls_tranclD_0, cls_Sigma__empty1_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_in__above_7, cls_trans__diff__Id_0, cls_le__inf__iff_1, cls_mem__def_1, cls_wf__inv__image_0, cls_empty__iff_0, cls_surjective__pairing_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_in__below_2, cls_Domain__iff_0, cls_Diff__subset__conv_0, cls_wf__no__loop_0, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_inf1E_1, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_inf__sup__distrib1_0, cls_wf__empty_0, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, cls_in__above_4, clsarity_fun__Lattices_Oupper__semilattice, cls_antisymD_0, cls_refl__on__converse_0, cls_le__sup__iff_0, cls_in__below_7, cls_wf__induct__rule_0, cls_Image__Un_0, cls_in__mkbot_4, cls_Diff__triv_0, cls_Domain__empty_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_Range__empty__iff_0, cls_Times__subset__cancel2_1, cls_acc_Oinducts_0, cls_converse__rtrancl__induct_3, cls_congruent2_Ocongruent2_0, cls_inf__commute_0, cls_trans__converse_1, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_Un__left__commute_0, cls_rtrancl__into__trancl1_0, cls_wf__converse__trancl_0, cls_single__valued__Id_0, cls_rtrancl__trancl__absorb_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, cls_Un__Int__distrib2_0, cls_exI__realizer_0, cls_Int__empty__right_0, cls_trans__Int_0, cls_Image__iff_0, cls_in__below_11, cls_sym__Id__on_0, cls_rel__compEpair_0, cls_sym__Id_0, cls_equiv__class__eq__iff_3, cls_le__supI_0, cls_rtrancl__mono_0, cls_Un__subset__iff_1, cls_rtrancl__unfold_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_antisym__converse_0, cls_Image__subset_0, cls_wf__insert_0, cls_empty__is__image_0, cls_Sigma__empty2_0, cls_converse__rtranclE_1, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_Image__empty_0, clsarity_fun__Orderings_Obot, cls_Image__iff_1, cls_le__supE_1, cls_le__iff__sup_0, cls_rtrancl__reflcl_0, cls_rev__image__eqI_0, cls_rtrancl__induct_2, cls_eq__equiv__class__iff2_1, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_wf__induct_1, cls_in__below_9, cls_tranclE_1, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_cuts__eq_0, cls_acc__wfI_0, cls_SigmaI_0, cls_trancl__into__trancl2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_trancl__empty_0, cls_notin__Lin__iff_0, cls_less__by__empty_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_Image__Id__on_0, cls_Range__converse_0, cls_refl__on__empty_0, cls_r__into__trancl_H_0, cls_Un__absorb2_0, cls_fst__eqD_0, cls_rtrancl__eq__or__trancl_0, cls_in__above_6, cls_Sigma__Diff__distrib1_0, cls_sup__eq__bot__eq2_0, cls_total__on__diff__Id_1, cls_Int__insert__right_1, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_trancl_Ocases_1, cls_wf__trancl_0, cls_rtrancl__converse_0, cls_trans__rtrancl_0, cls_wf__induct__rule_1, cls_Range__Int__subset_0, cls_refl__on__def_1, cls_in__below_6, cls_RangeE_0, cls_antisym__reflcl_1, cls_Range__def__raw_0, cls_antisym__Id__on_0, cls_UnCI_0, cls_Lin__irrefl_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_subset__iff_0, cls_wf__comp__self_0, cls_trans__O__subset_0, clsarity_fun__HOL_Oord, cls_subset__empty_0, cls_in__mkbot_3, cls_rev__predicate1D_0, cls_converse__Un_0, cls_insert__Diff__single_0, cls_singleton__iff_1, cls_r__comp__rtrancl__eq_0, cls_insert__code_2, cls_CHAINED_0_01, cls_single__valued__rel__comp_0, cls_Diff__idemp_0, cls_rel__comp__distrib_0, cls_equiv__class__eq_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_rtrancl_Ocases_1, cls_image__insert_0, cls_equiv_Otrans_0, cls_acc__downwards__aux_0, cls_wf__def_1, cls_tranclD_1, cls_strict__linear__order__on__def_1, cls_snd__eq__Range_0, cls_Range__iff_0, cls_acc__induct_2, cls_doubleton__eq__iff_2, cls_subset__insert__iff_3, cls_diff__single__insert_0, cls_Range__iff_1, cls_Domain__Int__subset_0, cls_inf__absorb2_0, cls_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_pair__in__Id__conv_0, cls_wf__irrefl_0, cls_rtrancl__Un__rtrancl_0, cls_IdE_0, cls_SigmaD2_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_insert__subset_1, cls_Int__empty__left_0, cls_Image__singleton__iff_1, cls_Range__Diff__subset_0, cls_Id__on__iff_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_rtrancl__induct_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_inf__sup__aci_I3_J_0, cls_trancl__reflcl_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_Int__insert__left_1, cls_converse__rtranclE_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_irrefl__tranclI_0, cls_Domain__Diff__subset_0, cls_in__above_1, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_wf__asym_0, cls_in__below_10, cls_in__below_1, cls_linorder__linear_0, cls_Un__empty_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc_Oinduct_1, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_mktop__Lin_0, cls_sym__rtrancl_0, cls_inf__le2_0, cls_refl__onD2_0, cls_image__empty_0, cls_Times__subset__cancel2_0, cls_Pair__fst__snd__eq_0, cls_subset__trans_0, cls_in__mktop_0, cls_converse__rtrancl__induct_2, cls_double__diff_0, cls_trans__converse_0, cls_acc_Ocases_0, cls_insert__is__Un_0, cls_DiffI_0, cls_transD_0, cls_eq__equiv__class__iff2_0, cls_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_rtrancl__eq__or__trancl_1, cls_trans__Id__on_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_Diff__Int__distrib2_0, cls_acc_Oinduct_0, cls_image__constant__conv_0, cls_total__on__diff__Id_0, cls_in__mkbot_2, cls_Id__on__subset__Times_0, cls_rtrancl__r__diff__Id_0, cls_insertI1_0, cls_Id__onE_1, cls_split__case__cert_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, cls_trans__inv__image_0, cls_le__supE_0, cls_rel__comp__empty2_0, cls_acyclic__def_0, cls_acyclic__insert_1, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_in__mktop_4, cls_Diff__insert2_0, cls_Int__commute_0, cls_wfE__pf_0, cls_sup__least_0, cls_subset__refl_0, cls_tranclE_0, cls_rev__ImageI_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_empty__subsetI_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_trans__Id_0, cls_Un__absorb1_0, cls_sym__converse_0, cls_sup1E_0, cls_in__inv__image_1, cls_distrib__inf__le_0, cls_in__above_5, cls_converse__iff_1, cls_refl__onD_0, cls_Pair__eq_0, cls_rtranclE_0, cls_singletonE_0, cls_Nitpick_Ortrancl__def_0, cls_image__diff__subset_0, cls_Image__mono_0, cls_in__below_12, cls_Int__Diff_0, cls_image__iff_2, cls_insertCI_0, cls_le__infE_0, cls_image__Int__subset_0, cls_pair__in__Id__conv_1, cls_Range__empty_0, cls_tranclD2_1, cls_subset__equiv__class_0, cls_Un__Diff__cancel_0, cls_image__Un_0, cls_insert__Diff_0, cls_total__on__empty_0, cls_DiffE_0, cls_R__O__Id_0, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_union__comp__emptyR_0, cls_sup1CI_1, cls_rtrancl__Int__subset_0, cls_above__Lin_0, cls_le__inf__iff_2, cls_in__above_12, cls_ImageE_1, cls_le__infI1_0, cls_bot1E_0, cls_trancl__unfold__left_0, cls_in__above_9, cls_inf__assoc_0, cls_rtrancl__trancl__trancl_0, cls_Int__lower2_0, cls_rel__compI_0, cls_insert__mono_0, cls_le__supI2_0, cls_Un__assoc_0, cls_Un__Diff__cancel2_0, cls_antisym__reflcl_0, cls_bex__empty_0, cls_trancl__id_0, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_Int__absorb_0, cls_converse__Id_0, cls_complete__Lin_0, cls_in__rel__def_0, cls_refl__on__Un_0, cls_Int__left__absorb_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_in__above_13, cls_total__on__converse_1, cls_acc__subset_0, cls_Diff__mono_0, cls_Un__absorb_0, cls_ImageE_0, cls_equiv_Osym_0, cls_UnE_0, cls_subset__insertI2_0, cls_wf__union__merge_0, cls_Diff__disjoint_0, cls_converseD_0, cls_acc_OaccI_0, cls_converse__inv__image_0, cls_Diff__Int__distrib_0, cls_antisym__Id_0, cls_trancl__rtrancl__absorb_0, cls_in__below_5, cls_wf__def_0, cls_Int__lower1_0, cls_converse__rtrancl__induct_1, clsarity_bool__Lattices_Olattice, cls_Domain__empty__iff_0, cls_trancl__range_0, cls_eq__eqI_0, cls_refl__on__converse_1, cls_strict__linear__order__on__def_2, cls_refl__onD1_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_Nitpick_Orefl_H__def_0, cls_Domain__Id__on_0, cls_equiv__type_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_Not__Domain__rtrancl_0, cls_converse__rel__comp_0, cls_insert__subset_2, cls_le__supI1_0, cls_rtrancl__converseI_0, cls_sup__left__idem_0, cls_subsetD_0, cls_symD_0, cls_sym__def_0, cls_acc_Oinducts_2, cls_acyclic__insert_2, cls_antisym__empty_0, cls_inf__bot__left_0, cls_wf__in__rel_0, cls_inf1I_0, cls_equiv_Orefl__on_0, cls_le__eqI_0, cls_SigmaE_0, cls_insert__not__empty_0, cls_Image__Id_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_in__above_2, cls_inf__idem_0, cls_trancl__Int__subset_0, cls_prod__eqI_0, cls_single__valued__confluent_0, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_pair__imageI_0, cls_IdI_0, cls_inf__sup__aci_I4_J_0, cls_Id__on__empty_0, cls_irrefl__trancl__rD_0, cls_subset__insert__iff_0, cls_notin__Lin__iff_1, cls_acc__induct_1, cls_Un__Int__assoc__eq_1, cls_trans__reflclI_0, cls_eq__equiv__class__iff_0, cls_converse__converse_0, cls_insert__absorb2_0, cls_Product__Type_Osplit_0, cls_sup__inf__absorb_0, cls_irrefl__def_1, cls_wf__induct_0, cls_acyclic__converse_0, cls_subset__singletonD_0, cls_RangeI_0, cls_Int__iff_2, cls_doubleton__eq__iff_1, cls_rtrancl__induct_0, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_eq__equiv__class_0, cls_quotient__disj_0, cls_equiv__class__eq__iff_1, cls_cuts__eq_2, cls_in__mkbot_1, cls_tfl__wf__induct_0, cls_in__mktop_2, cls_IntI_0, cls_in__inv__image_0, cls_inf__greatest_0, cls_pair__collapse_0, cls_Diff__empty_0, cls_Times__Un__distrib1_0, cls_Un__left__absorb_0, cls_converse__tranclE_0, cls_le__iff__inf_0, cls_rtrancl__eq__or__trancl_2, cls_insert__times__insert_0, cls_singleton__inject_0, cls_tfl__wf__induct_1, cls_Times__eq__cancel2_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, cls_Times__Diff__distrib1_0, cls_emptyE_0, cls_antisym__subset_0, cls_acyclic__insert_0, cls_inf__sup__ord_I3_J_0, cls_congruent2__implies__congruent_0, cls_inf__sup__aci_I5_J_0, cls_eq__eqI_1, cls_in__below_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_trancl_Or__into__trancl_0, cls_Diff__Int_0, cls_in__above_10, cls_irrefl__diff__Id_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_Int__greatest_0, cls_Domain__insert_0, cls_in__above_8, cls_sup__ge2_0, cls_sym__Un__converse_0, cls_sym__conv__converse__eq_0, cls_IntE_0, cls_in__mkbot_5, cls_Un__least_0, cls_in__rtrancl__UnI_0, cls_trancl__rtrancl__trancl_0, cls_sup1CI_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_in__rel__def_1, cls_rel__comp__subset__Sigma_0, cls_sym__trans__comp__subset_0, cls_le__infE_1, cls_refl__on__Int_0, cls_wf__Int1_0, cls_r__into__rtrancl_0, cls_rtrancl__idemp__self__comp_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_in__below_13, cls_wf__insert_2, clsarity_bool__Lattices_Odistrib__lattice, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_acc__downward_0, cls_in__below_4, cls_acc__induct__rule_1, cls_trancl__mono_0, cls_acyclic__subset_0, cls_trans__trancl_0, cls_conjI__realizer_1, cls_rtrancl__Un__subset_0, cls_image__subset__iff_0, cls_acc__induct_0, cls_inf__le1_0, cls_rel__comp__mono_0, cls_refl__on__comp__subset_0, cls_inf__left__idem_0, cls_rtranclD_0, cls_mem__splitI_0, cls_single__valued__subset_0, cls_acc_OaccI_1, cls_Diff__subset__conv_1, cls_insert__code_0, cls_le__eqI_1, cls_acc_Oinducts_1, cls_trancl__unfold_0, cls_antisym__def_0, cls_Image__Int__eq_0, cls_total__on__converse_0, cls_Sigma__Int__distrib1_0, cls_below__Lin_0, cls_trancl__trans_0, cls_converse__rtrancl__induct_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_Domain__mono_0, cls_Diff__Int2_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_quotient__eqI_0, cls_equiv__class__nondisjoint_0, cls_fst__eq__Domain_0, cls_Un__Image_0, cls_DiffE_1, cls_converse__Int_0, cls_le__infI2_0, cls_insert__image_0, cls_rtrancl__empty_0, cls_Nitpick_Orefl_H__def_1, cls_Un__Int__assoc__eq_0, cls_refl__on__def_0, cls_quotientI_0, cls_Diff__insert__absorb_0, cls_conjI__realizer_0, cls_Diff__partition_0, cls_equiv__comp__eq_0, cls_Domain__iff_1, cls_sup__bot__left_0, cls_acc__induct__rule_0, cls_in__below_8, cls_disjoint__iff__not__equal_0, cls_strict__linear__order__on__def_3, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_complete__Lin_1, cls_insert__iff_2, cls_rtranclE_1, cls_equiv__class__eq__iff_2, cls_image__is__empty_0, cls_quotient__eq__iff_0, cls_Un__insert__right_0, cls_acyclic__impl__antisym__rtrancl_0, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_sym__Int_0, cls_trancl__converse_0, cls_imageI_0, cls_Times__Int__distrib1_0, cls_acyclic__converse_1, cls_wf__Un_0, cls_antisym__converse_1, cls_Pair__eq_1, cls_wf__Int2_0, clsarity_fun__Lattices_Odistrib__lattice, cls_wf__union__merge_1, cls_trans__def_0, cls_O__assoc_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_in__above_3, cls_in__mkbot_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_eq__equiv__class__iff_1, cls_acc__induct__rule_2, cls_tfl__cut__apply_0, cls_fst__conv_0, cls_subset__insert__iff_1, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0, cls_in__above_0, cls_empty__Diff_0, cls_in__above_14
% 17.14/5.40  % No. of inferences in proof: 1393
% 17.14/5.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4836 ms resp. 3954 ms w/o parsing
% 18.41/5.78  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.41/5.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------