%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SCT058-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:50:18 EDT 2023

% Result   : Unsatisfiable 13.37s 3.76s
% Output   : Refutation 14.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  755
% Syntax   : Number of formulae    : 1395 ( 361 unt; 116 typ;   0 def)
%            Number of atoms       : 2748 ( 599 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 23189 (1360   ~;1469   |;   0   &;20360   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  295 ( 295   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  118 ( 116 usr;  14 con; 0-7 aty)
%            Number of variables   : 4516 (   0   ^;4516   !;   0   ?;4516   :)

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

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

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

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

thf(v_c_____type,type,
    v_c____: $i ).

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

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

thf(v_P_H_____type,type,
    v_P_H____: $i ).

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

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

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

thf(c_Fun_Ocomp_type,type,
    c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).

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

thf(v_P_____type,type,
    v_P____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_sko__Wellfounded__Xacc__Xinducts__1_type,type,
    v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).

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

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: $i > $i > $i ).

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

thf(c_FunDef_Oin__rel_type,type,
    c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1_type,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_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: $i > $i > $i > $i ).

thf(c_Relation_OField_type,type,
    c_Relation_OField: $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Relation__XconverseE__1__2_type,type,
    c_ATP__Linkup_Osko__Relation__XconverseE__1__2: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XconverseE__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XconverseE__1__1: $i > $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: $i > $i > $i > $i > $i ).

thf(v_sko__Transitive__Closure__Xtrancl__Xcases__1_type,type,
    v_sko__Transitive__Closure__Xtrancl__Xcases__1: $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: $i > $i > $i > $i > $i ).

thf(c_List_Osko__Recdef__Xtfl__wf__induct__1__1_type,type,
    c_List_Osko__Recdef__Xtfl__wf__induct__1__1: $i > $i > $i > $i ).

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

thf(c_List_Osko__Recdef__Xcuts__eq__1__1_type,type,
    c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).

thf(v_sko__Wellfounded__Xacc__Xinduct__1_type,type,
    v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XId__onE__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).

thf(v_sko__Transitive__Closure__Xrtrancl__Xcases__1_type,type,
    v_sko__Transitive__Closure__Xrtrancl__Xcases__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).

thf(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_type,type,
    v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).

thf(c_Equiv__Relations_Ocongruent2_type,type,
    c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).

thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_type,type,
    c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1_type,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XIdE__1__1_type,type,
    c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1_type,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).

thf(474,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

thf(1665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(439,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(1586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(322,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1337,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(360,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(1411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ A @ B @ C )
      = ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).

thf(1469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ A @ B @ C )
      = ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(378,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).

thf(1454,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(627,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1315,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(962,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__2 @ B @ A @ C @ D ) @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__1 @ B @ A @ C @ D ) @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ B ) @ ( tc_prod @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseE_0) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__2 @ B @ A @ C @ D ) @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__1 @ B @ A @ C @ D ) @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ B ) @ ( tc_prod @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(605,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1950,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(484,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(1369,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(546,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

thf(1823,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).

thf(1237,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

thf(1031,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(893,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(554,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).

thf(1840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).

thf(1295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(562,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).

thf(1855,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(513,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).

thf(1750,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(260,axiom,
    v_b____ != v_c____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).

thf(1211,plain,
    v_b____ != v_c____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(593,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(1924,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(410,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(1522,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(453,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(994,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(355,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Wellfounded_Oacyclic @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

thf(1401,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Wellfounded_Oacyclic @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(600,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
      | ~ ( hBOOL @ ( c_in @ C @ F @ G ) )
      | ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ G @ D @ E )
      | ~ ( c_Equiv__Relations_Oequiv @ F @ H @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).

thf(1939,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
      | ~ ( hBOOL @ ( c_in @ C @ F @ G ) )
      | ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ G @ D @ E )
      | ~ ( c_Equiv__Relations_Oequiv @ F @ H @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(503,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).

thf(1728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).

thf(1205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(441,axiom,
    class_HOL_Ominus @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(1591,plain,
    class_HOL_Ominus @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).

thf(1269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(878,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(234,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

thf(1158,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(762,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(574,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1882,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).

thf(1443,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(539,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
        = ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).

thf(1808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
        = ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(180,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).

thf(1041,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(99,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).

thf(861,plain,
    ! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(241,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

thf(1173,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

thf(1486,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = B )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).

thf(1497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = B )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1310,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(506,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).

thf(1735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(568,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(1867,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(1164,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1327,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).

thf(1342,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(607,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).

thf(1954,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(331,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1354,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

thf(1507,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(1458,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(1078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(530,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).

thf(1788,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).

thf(1426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(588,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).

thf(1914,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(149,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(973,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(634,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ ( c_Relation_OField @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__insert_0) ).

thf(2010,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ ( c_Relation_OField @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( A = B )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).

thf(1359,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(613,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).

thf(1967,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(455,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(274,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1243,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(527,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).

thf(1782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(350,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).

thf(1391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( D
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(1576,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( D
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osingle__valued @ A @ B @ C )
      | ~ ( c_Relation_Osingle__valued @ D @ B @ C )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).

thf(1475,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osingle__valued @ A @ B @ C )
      | ~ ( c_Relation_Osingle__valued @ D @ B @ C )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(583,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

thf(1904,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).

thf(1265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(296,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1287,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(368,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
       != ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ B ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).

thf(1430,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
       != ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ B ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(622,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(1985,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

thf(719,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C )
      | ~ ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Relation_Oirrefl @ B @ C )
      | ~ ( c_Relation_Otrans @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).

thf(785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C )
      | ~ ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Relation_Oirrefl @ B @ C )
      | ~ ( c_Relation_Otrans @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(319,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).

thf(1330,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).

thf(1826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(1132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(1055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(359,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(1409,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(88,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).

thf(838,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(405,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

thf(1511,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(123,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      | ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).

thf(917,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      | ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
      = ( c_Relation_ORange @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).

thf(751,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
      = ( c_Relation_ORange @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( c_Wellfounded_Owf @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

thf(1313,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( c_Wellfounded_Owf @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(292,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1279,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).

thf(1545,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(276,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(1247,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
      = ( c_Relation_ODomain @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

thf(770,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
      = ( c_Relation_ODomain @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

thf(881,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(463,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1641,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(571,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(1875,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1100,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Relation_OImage @ C @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_Wellfounded_Owf @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).

thf(1232,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Relation_OImage @ C @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_Wellfounded_Owf @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(557,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).

thf(1847,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(592,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1922,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      | ~ ( c_Relation_Osym @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

thf(902,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      | ~ ( c_Relation_Osym @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(578,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( c_in @ A @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).

thf(1892,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( c_in @ A @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(343,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).

thf(1379,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(313,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_FunDef_Oin__rel @ E @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).

thf(1319,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_FunDef_Oin__rel @ E @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).

thf(1704,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(577,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).

thf(1890,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).

thf(1479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(147,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(969,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(327,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(596,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(1931,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(431,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
       != ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
      | ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
        = ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).

thf(1568,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
       != ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
      | ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
        = ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(334,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ A ) @ C ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

thf(1362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ A ) @ C ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(611,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(362,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Relation_Osym @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).

thf(1415,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Relation_Osym @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(1465,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
      = ( c_Relation_ODomain @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).

thf(1373,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
      = ( c_Relation_ODomain @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(224,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).

thf(1136,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(619,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      = ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).

thf(1978,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      = ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(169,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

thf(1020,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_OField @ A @ B ) @ ( c_Relation_OField @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__Field_0) ).

thf(1677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_OField @ A @ B ) @ ( c_Relation_OField @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
      | ~ ( c_Relation_Osingle__valued @ B @ D @ E )
      | ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).

thf(806,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
      | ~ ( c_Relation_Osingle__valued @ B @ D @ E )
      | ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).

thf(1581,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).

thf(1051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(637,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(2017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(304,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).

thf(1302,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).

thf(756,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(473,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1664,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(540,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(1811,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(376,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ A @ E @ F @ ( tc_fun @ G @ tc_bool ) ) @ ( c_Pair @ B @ C @ E @ F ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).

thf(1450,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ A @ E @ F @ ( tc_fun @ G @ tc_bool ) ) @ ( c_Pair @ B @ C @ E @ F ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).

thf(1109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(231,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
      = ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).

thf(1151,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
      = ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Osym @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).

thf(981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Osym @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ D ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).

thf(1377,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ D ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(1447,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(575,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).

thf(1886,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(774,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(329,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).

thf(1351,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

thf(660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Relation_OId @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).

thf(1345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Relation_OId @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).

thf(1433,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(357,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
      = ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).

thf(1405,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
      = ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(445,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(489,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).

thf(1696,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).

thf(1169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(534,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
      | ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).

thf(1796,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
      | ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(1072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(602,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).

thf(1943,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(255,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).

thf(1201,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

thf(1104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Otrans @ A @ B )
      | ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

thf(849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Otrans @ A @ B )
      | ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(566,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1863,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(196,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).

thf(1074,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(135,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(942,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(678,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(371,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
        = ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).

thf(1438,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
        = ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ A @ B )
      | ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).

thf(1306,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ A @ B )
      | ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

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

thf(1199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).

thf(1153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(323,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).

thf(1338,plain,
    ! [B: $i,A: $i] : ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(1708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
       != B )
      | ( c_Relation_Osym @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

thf(1067,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
       != B )
      | ( c_Relation_Osym @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(629,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(2000,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(521,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nitpick_Orefl_H @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).

thf(1768,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nitpick_Orefl_H @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(183,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(1047,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(504,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).

thf(1730,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(188,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).

thf(1057,plain,
    ! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).

thf(1274,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(1223,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(636,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).

thf(2015,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1560,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      = ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

thf(1387,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      = ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(581,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).

thf(1900,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Relation_OField @ A @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OField @ A @ C ) @ C ) )
      | ~ ( c_Relation_Oantisym @ A @ C )
      | ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ A @ C ) @ A @ C )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).

thf(1123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Relation_OField @ A @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OField @ A @ C ) @ C ) )
      | ~ ( c_Relation_Oantisym @ A @ C )
      | ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ A @ C ) @ A @ C )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(401,axiom,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1502,plain,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(365,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
        = ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).

thf(1423,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
        = ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(599,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(1938,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).

thf(1365,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(591,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
      | ~ ( c_Relation_Orefl__on @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

thf(1920,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
      | ~ ( c_Relation_Orefl__on @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(576,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).

thf(1888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(544,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).

thf(1819,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(552,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Relation_Oantisym @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).

thf(1836,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Relation_Oantisym @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(1656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(173,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ E ) @ ( tc_prod @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

thf(1027,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ E ) @ ( tc_prod @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).

thf(1281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(298,axiom,
    ( ( c_Relation_ORange @ v_r @ t_a @ t_b )
    = ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ t_a @ t_b ) @ v_r ) @ t_b @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).

thf(1291,plain,
    ( ( c_Relation_ORange @ v_r @ t_a @ t_b )
    = ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ t_a @ t_b ) @ v_r ) @ t_b @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(1555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
      | ~ ( c_Relation_Ototal__on @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

thf(1407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
      | ~ ( c_Relation_Ototal__on @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1740,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(598,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).

thf(1936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(418,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId__on @ B @ A ) )
      = ( c_Relation_OId__on @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

thf(1541,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId__on @ B @ A ) )
      = ( c_Relation_OId__on @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(621,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(1983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(518,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1762,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(138,axiom,
    v_a____ != v_b____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_05) ).

thf(948,plain,
    v_a____ != v_b____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(537,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1804,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).

thf(1328,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
        = B )
      | ~ ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).

thf(1064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
        = B )
      | ~ ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(477,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1672,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_FunDef_Oin__rel @ A @ B @ C @ D @ E )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ A @ ( tc_prod @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).

thf(1006,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_FunDef_Oin__rel @ A @ B @ C @ D @ E )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ A @ ( tc_prod @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(572,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(1878,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(869,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(1755,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(442,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).

thf(1592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

thf(874,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(559,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1851,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).

thf(1772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
      | ~ ( c_Wellfounded_Owf @ B @ C )
      | ~ ( c_Wellfounded_Owf @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).

thf(1259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
      | ~ ( c_Wellfounded_Owf @ B @ C )
      | ~ ( c_Wellfounded_Owf @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Relation_Otrans @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).

thf(1534,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Relation_Otrans @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(533,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).

thf(1794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1375,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Oantisym @ C @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).

thf(1121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Oantisym @ C @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(214,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).

thf(1111,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(615,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Relation_Oirrefl @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).

thf(1970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Relation_Oirrefl @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).

thf(1227,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(499,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).

thf(1719,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Oirrefl @ A @ B )
      | ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

thf(783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Oirrefl @ A @ B )
      | ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(1118,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(1397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).

thf(1160,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

thf(1082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ D @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).

thf(1182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).

thf(1461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(555,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).

thf(1842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).

thf(1584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(532,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(1791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).

thf(1214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(465,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1644,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(1039,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(233,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(1155,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
      = ( c_Relation_ORange @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).

thf(1207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
      = ( c_Relation_ORange @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(87,axiom,
    ! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

thf(837,plain,
    ! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(547,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(1825,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Transitive__Closure_Otrancl @ A @ B )
        = A )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).

thf(701,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Transitive__Closure_Otrancl @ A @ B )
        = A )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(550,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).

thf(1831,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).

thf(654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(617,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).

thf(1974,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

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

thf(1060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(120,axiom,
    ! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

thf(911,plain,
    ! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(36,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != B )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != B )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(1799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(1715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(457,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iff_0) ).

thf(1627,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(1776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(159,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(997,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(208,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(1099,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(985,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(379,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
      | ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
      | ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).

thf(1456,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
      | ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
      | ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(345,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).

thf(1382,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(560,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ F @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).

thf(1852,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ F @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(517,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).

thf(1759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(351,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(1393,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(563,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).

thf(1857,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(67,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

thf(792,plain,
    ! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).

thf(1241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(526,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1779,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(488,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

thf(1695,plain,
    ! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Otrans @ A @ B )
      | ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Otrans @ A @ B )
      | ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(429,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
      | ~ ( c_Relation_Osingle__valued @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).

thf(1563,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
      | ~ ( c_Relation_Osingle__valued @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).

thf(1035,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(579,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).

thf(1895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).

thf(1616,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(1732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(542,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

thf(1086,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(906,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(584,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).

thf(1906,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(630,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).

thf(2001,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(277,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Otrans @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).

thf(1251,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Otrans @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(609,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).

thf(1959,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Oantisym @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).

thf(1483,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Oantisym @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(511,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

thf(1747,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(594,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).

thf(1927,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(745,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(689,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

thf(1219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(303,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(1301,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(551,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).

thf(1833,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(589,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1916,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

thf(772,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(514,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
        = ( hAPP @ ( hAPP @ A @ D ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ E @ F @ F ) @ G @ ( tc_prod @ F @ F ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ H @ H ) @ I @ ( tc_prod @ H @ H ) ) )
      | ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).

thf(1752,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
        = ( hAPP @ ( hAPP @ A @ D ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ E @ F @ F ) @ G @ ( tc_prod @ F @ F ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ H @ H ) @ I @ ( tc_prod @ H @ H ) ) )
      | ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(612,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(1965,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(904,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(150,axiom,
    v_b____ != v_c____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I2_J_0) ).

thf(975,plain,
    v_b____ != v_c____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(528,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(1784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(349,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ ( c_Set_Oimage @ ( c_split @ A @ D @ E @ F ) @ G @ ( tc_prod @ D @ E ) @ F ) @ F ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ G @ ( tc_prod @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__imageI_0) ).

thf(1389,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ ( c_Set_Oimage @ ( c_split @ A @ D @ E @ F ) @ G @ ( tc_prod @ D @ E ) @ F ) @ F ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ G @ ( tc_prod @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(468,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1652,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(595,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).

thf(1929,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).

thf(958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(1403,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(279,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).

thf(1256,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(395,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(1488,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(226,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(1139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

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

thf(1312,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Wellfounded_Owf @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).

thf(1865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Wellfounded_Owf @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1635,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(1239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(320,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(1332,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(205,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Otrans @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).

thf(1092,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Otrans @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

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

thf(1675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(15,axiom,
    ! [A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ A ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).

thf(672,plain,
    ! [A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(2,negated_conjecture,
    ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
    | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(641,plain,
    ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
    | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(367,axiom,
    ( ( c_Relation_OField @ v_r @ t_a )
    = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ v_r @ t_a @ t_a ) @ ( c_Relation_ORange @ v_r @ t_a @ t_a ) @ ( tc_fun @ t_a @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def__raw_0) ).

thf(1428,plain,
    ( ( c_Relation_OField @ v_r @ t_a )
    = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ v_r @ t_a @ t_a ) @ ( c_Relation_ORange @ v_r @ t_a @ t_a ) @ ( tc_fun @ t_a @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(529,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).

thf(1786,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(476,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
        = ( c_Transitive__Closure_Ortrancl @ C @ B ) )
      | ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).

thf(1669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
        = ( c_Transitive__Closure_Ortrancl @ C @ B ) )
      | ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(287,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(1271,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(339,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(189,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1058,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(212,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).

thf(1107,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(520,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).

thf(1765,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(580,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
        = ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).

thf(1897,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
        = ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
      = ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).

thf(919,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
      = ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(252,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1194,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(259,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(328,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).

thf(1349,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(486,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Oantisym @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).

thf(1690,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Oantisym @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(1571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(614,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1969,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(1175,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).

thf(1574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(538,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

thf(1806,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(165,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

thf(1011,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(440,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1589,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(597,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(1933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).

thf(1603,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(649,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(181,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(1043,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(75,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
      = ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).

thf(811,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
      = ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
      = ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).

thf(1471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
      = ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(199,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).

thf(1080,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(425,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).

thf(1557,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

thf(816,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
      = ( c_Relation_OId @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).

thf(1993,plain,
    ! [A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
      = ( c_Relation_OId @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(545,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).

thf(1821,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(174,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Relation_Orel__comp @ C @ D @ A @ E @ B ) )
      = ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ E @ B ) @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ E ) @ C ) @ B @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).

thf(1029,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Relation_Orel__comp @ C @ D @ A @ E @ B ) )
      = ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ E @ B ) @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ E ) @ C ) @ B @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).

thf(964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(122,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ A @ B )
      = ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

thf(915,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ A @ B )
      = ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(381,axiom,
    class_Lattices_Olower__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(1460,plain,
    class_Lattices_Olower__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(1022,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(299,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

thf(1293,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(606,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_Wellfounded_Owf @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).

thf(1952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_Wellfounded_Owf @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(485,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).

thf(1688,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(890,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(475,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ A )
      | ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).

thf(1667,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ A )
      | ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(52,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).

thf(758,plain,
    ! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ C @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B )
      | ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).

thf(1339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ C @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B )
      | ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(586,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(236,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1162,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(553,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).

thf(1838,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(316,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).

thf(1325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(243,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1177,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(344,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

thf(1381,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(153,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oirrefl @ A @ B )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).

thf(983,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oirrefl @ A @ B )
      | ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(490,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(1699,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_Wellfounded_Owf @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_Wellfounded_Owf @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(883,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(215,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
        = B )
      | ~ ( c_Relation_Osym @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

thf(1113,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
        = B )
      | ~ ( c_Relation_Osym @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = D )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).

thf(1435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = D )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(658,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(1562,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(912,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).

thf(1171,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).

thf(768,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(82,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(827,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1445,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(413,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).

thf(1528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(502,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ A @ B @ C ) @ ( c_Relation_ORange @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).

thf(1364,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ A @ B @ C ) @ ( c_Relation_ORange @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(94,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

thf(851,plain,
    ! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(210,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).

thf(1102,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(604,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).

thf(1948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
       != B )
      | ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ B @ A @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).

thf(1166,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
       != B )
      | ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ B @ A @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(1203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(944,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1420,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(128,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).

thf(927,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(483,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

thf(1684,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(291,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C )
      | ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).

thf(1277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C )
      | ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).

thf(1134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(625,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1990,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(80,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).

thf(823,plain,
    ! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).

thf(1049,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(632,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
       != ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
      | ( ( hAPP @ A @ G )
        = ( hAPP @ F @ G ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).

thf(2005,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
       != ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
      | ( ( hAPP @ A @ G )
        = ( hAPP @ F @ G ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(1413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(1076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(17,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(675,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(437,axiom,
    hBOOL @ ( c_in @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1583,plain,
    hBOOL @ ( c_in @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(305,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1304,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(570,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(1873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(229,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

thf(1145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).

thf(1018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(421,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).

thf(1547,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
       != ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).

thf(1770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( c_Wellfounded_Owf @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(855,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

thf(1025,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(450,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

thf(1611,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).

thf(971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ A @ B @ C )
      | ~ ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

thf(1605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ A @ B @ C )
      | ~ ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(601,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

thf(1941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(739,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(285,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
      = ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).

thf(1267,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
      = ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = B )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = B )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Osym @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).

thf(1230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Osym @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(1,negated_conjecture,
    ( ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
    | ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(640,plain,
    ( ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
    | ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(610,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

thf(1961,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).

thf(1070,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Relation_Oantisym @ A @ B )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
      | ~ ( c_Relation_Otrans @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

thf(872,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
      | ~ ( c_Relation_Otrans @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).

thf(1225,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(509,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).

thf(1743,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(30,axiom,
    ! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

thf(707,plain,
    ! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(635,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).

thf(2012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(673,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

thf(717,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(270,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
      = ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).

thf(1235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
      = ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(620,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(1980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(471,axiom,
    v_a____ != v_b____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I1_J_0) ).

thf(1658,plain,
    v_a____ != v_b____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iff_1) ).

thf(1679,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(495,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(1711,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(186,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).

thf(1053,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(531,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(1790,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(623,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).

thf(1987,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(541,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1813,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).

thf(1452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(1637,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(248,axiom,
    class_Lattices_Odistrib__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(1188,plain,
    class_Lattices_Odistrib__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

thf(1186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(312,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1317,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(519,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(1763,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

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

thf(951,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(221,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(1130,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(435,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1579,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(491,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

thf(1702,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1221,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(330,axiom,
    hBOOL @ ( c_in @ v_P____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(1353,plain,
    hBOOL @ ( c_in @ v_P____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(616,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Osingle__valued @ D @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).

thf(1972,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Relation_Osingle__valued @ D @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(101,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(864,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(512,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).

thf(1749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(498,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(1717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(876,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(859,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(558,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_OField @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def_0) ).

thf(1849,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_OField @ A @ B )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A ) @ B @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) )
      | ~ ( c_Relation_Otrans @ B @ A )
      | ~ ( c_Relation_Osym @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).

thf(1257,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A ) @ B @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) )
      | ~ ( c_Relation_Otrans @ B @ A )
      | ~ ( c_Relation_Osym @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      = ( c_Relation_OField @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__converse_0) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      = ( c_Relation_OField @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(416,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(656,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(536,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

thf(1802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

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

thf(1023,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(206,axiom,
    v_a____ != v_c____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I3_J_0) ).

thf(1094,plain,
    v_a____ != v_c____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(978,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(931,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__1 @ A @ B @ C @ D ) @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__2 @ A @ B @ C @ D ) @ C @ D ) @ A @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) @ ( tc_prod @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseE_1) ).

thf(1321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__1 @ A @ B @ C @ D ) @ ( c_ATP__Linkup_Osko__Relation__XconverseE__1__2 @ A @ B @ C @ D ) @ C @ D ) @ A @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ A ) @ ( tc_prod @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ( A = C )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).

thf(1844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
      | ( A = C )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).

thf(1654,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).

thf(1517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(262,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
        = ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ B ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).

thf(1216,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
        = ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ B ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( B = A )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).

thf(1126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( B = A )
      | ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(249,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

thf(1189,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ A @ C ) @ ( c_Relation_OField @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__Un_0) ).

thf(1998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ A @ C ) @ ( c_Relation_OField @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(590,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).

thf(1918,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(1084,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(297,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osym @ A @ B )
      | ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).

thf(844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osym @ A @ B )
      | ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).

thf(1276,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(466,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(1646,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).

thf(1062,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(392,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
      | ~ ( c_Relation_Osym @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

thf(652,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
      | ~ ( c_Relation_Osym @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(510,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(561,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1854,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
      | ~ ( c_Relation_Osym @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

thf(781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
      | ~ ( c_Relation_Osym @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(426,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1558,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(278,axiom,
    v_a____ != v_c____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).

thf(1253,plain,
    v_a____ != v_c____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(699,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(813,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

thf(1721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(114,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(896,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1674,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(462,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(565,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).

thf(1308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
      | ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(448,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(1607,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ F @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(406,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).

thf(1513,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
      | ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(84,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

thf(832,plain,
    ! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(638,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(2019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(1045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

thf(1614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(493,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Relation_Oantisym @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

thf(1706,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      | ~ ( c_Relation_Oantisym @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(251,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1193,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(472,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(1661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( B = D )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).

thf(999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( B = D )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(464,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1642,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(524,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ A @ B )
      | ~ ( c_Relation_Otrans @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).

thf(1774,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ A @ B )
      | ~ ( c_Relation_Otrans @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(608,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

thf(1957,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ A @ B )
      = ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

thf(818,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ A @ B )
      = ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(633,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).

thf(2008,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ A @ B @ C )
      | ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

thf(790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Orefl__on @ A @ B @ C )
      | ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(631,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).

thf(2003,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
      | ~ ( c_Relation_Otrans @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).

thf(1116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(585,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1908,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(146,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

thf(967,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(207,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).

thf(1097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

thf(835,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(456,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).

thf(1625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(1527,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).

thf(1148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(867,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(516,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_Oinv__image @ B @ C @ D @ A ) )
      = ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ B ) @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).

thf(1757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_Oinv__image @ B @ C @ D @ A ) )
      = ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ B ) @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(564,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

thf(1859,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

thf(664,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Oacyclic @ A @ B )
      | ~ ( c_Wellfounded_Owf @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(696,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(955,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(639,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

thf(2021,plain,
    ! [B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ A @ B )
      | ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(624,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(1989,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(543,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).

thf(1816,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(398,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1495,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(321,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1335,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).

thf(1693,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Wellfounded_Owf @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).

thf(1033,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(388,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).

thf(1473,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(549,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(1261,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(346,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).

thf(1384,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Relation_Ototal__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Relation_OId @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).

thf(1357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Ototal__on @ A @ B @ C )
      | ~ ( c_Relation_Ototal__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Relation_OId @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(992,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(400,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1500,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(496,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).

thf(1713,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      = ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

thf(1299,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
      = ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).

thf(1399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(618,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(644,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(422,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).

thf(1597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(573,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).

thf(1880,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(162,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).

thf(1004,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(582,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1902,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(691,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Relation_Osym @ B @ C )
      | ~ ( c_Relation_Osym @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
      | ~ ( c_Relation_Osym @ B @ C )
      | ~ ( c_Relation_Osym @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(50,axiom,
    ! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

thf(755,plain,
    ! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(1088,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(1367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).

thf(940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(603,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).

thf(1945,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
      | ~ ( c_Wellfounded_Owf @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

thf(923,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
      | ~ ( c_Wellfounded_Owf @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(507,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(1737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(482,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).

thf(1681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1184,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(178,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_split @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Pair @ F @ G @ C @ D ) ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ B @ F ) @ G ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).

thf(1037,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_split @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Pair @ F @ G @ C @ D ) ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ B @ F ) @ G ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(587,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(1912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(166,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(1014,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
      | ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( B = C )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).

thf(1417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
      | ( B = C )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(569,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).

thf(1870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(2073,plain,
    $false,
    inference(cvc4,[status(thm)],[1665,1586,1337,1411,1469,1454,1995,1315,962,1179,777,1950,1686,1369,1823,1237,846,909,1031,893,1840,666,1295,1855,1750,1211,1924,1522,1618,994,1401,1939,1728,1205,1591,1269,878,1158,762,730,1882,1443,1808,1041,861,1173,1486,1497,1310,1735,1867,1164,1327,1342,1954,1354,1507,1458,1078,1788,1426,1914,1441,973,2010,1359,1386,1967,1623,1243,1782,1391,1576,1724,1475,1904,1265,1287,1430,1985,719,785,1330,1826,1191,1132,724,1055,1409,1323,838,1511,917,751,1313,1279,1545,1247,770,881,1641,1875,1100,1232,1847,1922,902,1892,1379,1319,1704,1890,1479,1609,969,1347,1931,1568,1362,1963,1415,1465,1373,646,1136,1978,1020,1677,806,1581,1283,1051,2017,1302,756,1664,1811,1450,1109,1632,1151,937,981,1377,1447,1886,774,1351,660,1345,1433,1405,1600,1696,1169,687,1796,1072,1943,1201,1104,849,1863,1074,942,678,1438,793,925,1306,1199,1153,1338,1708,1067,2000,1768,714,1047,1730,1057,1274,1223,1519,693,2015,1560,1387,1900,1123,862,1502,820,1423,1938,1365,1920,1888,1819,830,1836,1656,1027,1281,1291,852,1555,682,1407,1740,842,1936,1541,1983,1762,948,1804,1328,1064,1672,1006,1878,869,1755,989,1592,742,874,1143,1851,1772,1259,1534,1794,1375,1121,1111,1970,1227,1138,1719,783,1118,857,1397,1160,1082,933,753,1182,1461,669,1842,1584,1791,1214,1644,1039,1155,1016,1207,837,1825,701,1297,1831,654,1974,1060,911,721,1799,1715,779,1627,1776,1263,997,1099,985,1456,1382,1002,1852,1759,1393,1857,792,1241,1779,1695,921,1563,765,1035,1515,1895,1616,953,1732,1814,1086,662,888,906,1906,2001,1251,1959,1483,1747,1927,745,689,733,1219,824,1301,1595,1833,1916,772,1620,1752,711,1965,904,975,1784,1389,1652,1929,958,1403,1256,1488,1139,1312,787,1865,1635,1239,1332,1092,704,1675,672,641,1428,1786,1669,1271,1371,1058,1107,1765,1090,1897,919,1194,1209,1524,1349,737,1690,1571,1969,1175,1574,1806,1011,1589,1933,1492,1603,649,1043,811,1471,1080,1557,816,1993,1821,1029,964,915,1460,1022,1293,1952,1688,890,1667,758,1339,799,1909,1162,726,1838,1325,1177,1381,983,1699,1245,883,1113,1435,1477,658,1562,912,685,1171,768,827,1445,1528,1726,1364,851,1102,1948,1166,1203,944,1467,680,1420,927,1684,1277,1134,1509,1990,823,1049,2005,1413,1076,675,1583,1304,1873,1145,1018,1547,1770,855,1025,1611,971,1605,1941,739,1267,1531,1230,640,1961,1070,872,1225,1743,707,1566,2012,673,717,840,1235,1980,1658,1679,1285,1711,1053,1790,1987,1813,1452,1637,1188,1186,1317,1763,1538,951,808,1130,1579,1543,1702,1221,1353,1972,864,1749,1504,1008,1717,1272,876,859,1849,1257,1141,1536,656,1802,1023,1094,978,931,1553,1321,1844,1654,1517,759,1216,1126,1189,1998,1918,1649,1084,1289,844,1276,1646,1062,1481,946,652,1629,1745,1854,781,1558,1253,699,813,1721,896,748,1674,1639,1861,929,1308,1607,1513,832,2019,1045,1614,1706,1193,899,1661,999,1642,1774,1957,818,2008,790,735,2003,1116,1908,833,967,1097,835,1395,1625,1527,1148,867,1757,1859,664,696,955,2021,796,886,801,1989,1816,1495,1335,1693,1033,1197,960,1473,728,987,1829,1261,1384,1357,992,1500,1713,1299,1399,1976,644,1550,1597,1880,1004,1902,691,803,1463,755,1088,1367,940,935,1945,923,1737,1681,1184,1490,1037,708,1912,1014,1417,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SCT058-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May 18 15:29:28 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.88/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.56/1.07  % [INFO] 	 Parsing done (221ms). 
% 1.56/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.30/1.28  % [INFO] 	 eprover registered as external prover. 
% 2.30/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 2.30/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.76/1.42  % [INFO] 	 Found a conjecture and 639 axioms. Running axiom selection ... 
% 3.38/1.54  % [INFO] 	 Axiom selection finished. Selected 637 axioms (removed 2 axioms). 
% 4.06/1.72  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.06/1.74  % [INFO] 	 Type checking passed. 
% 4.06/1.74  % [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 ... 
% 13.37/3.76  % External prover 'cvc4' found a proof!
% 13.37/3.76  % [INFO] 	 Killing All external provers ... 
% 13.37/3.76  % Time passed: 3231ms (effective reasoning time: 2675ms)
% 13.37/3.76  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.37/3.76  % Axioms used in derivation (637): cls_inf__sup__absorb_0, cls_trancl__converseD_0, cls_Diff__cancel_0, cls_converse__tranclE_1, cls_in__mktop_1, cls_Int__absorb2_0, cls_subset__insert_1, cls_Diff__iff_2, cls_rtrancl__idemp_0, cls_bot__fun__eq_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_image__constant_0, cls_insertE_0, cls_rtrancl__converseD_0, cls_wf__subset_0, cls_CHAINED_0_05, cls_sup__ge1_0, cls_Un__Diff_0, cls_congruent_Ocongruent_0, cls_Un__subset__iff_0, cls_splitD_H_0, cls_order__eq__iff_0, cls_total__on__def_0, cls_converseI_0, cls_equalityI_0, cls_Id__onE_0, cls_insert__inter__insert_0, cls_iff_1, cls_single__valuedD_0, cls_wf__acyclic_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_rtrancl_Ocases_0, cls_Image__singleton__iff_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_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_Id__O__R_0, cls_le__iff__inf_1, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_CHAINED_0, cls_Range__def_0, cls_inf__sup__aci_I6_J_0, cls_Id__on__eqI_0, cls_A_I3_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_acc_Oinduct_2, cls_irrefl__def_0, cls_acc__wfD_0, cls_UnCI_1, cls_tranclD_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_empty__iff_0, cls_trans__diff__Id_0, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_mem__def_1, cls_wf__inv__image_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_Domain__iff_0, cls_Diff__subset__conv_0, cls_CHAINED_0_04, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_inf1E_1, cls_Diff__triv_0, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_inf__sup__distrib1_0, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, cls_K__record__comp_0, cls_antisymD_0, cls_refl__on__converse_0, cls_le__sup__iff_0, cls_acc_Oinducts_0, cls_wf__induct__rule_0, cls_Image__Un_0, cls_in__mkbot_4, cls_Field__converse_0, clsarity_fun__Lattices_Oupper__semilattice, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_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_Int__empty__right_0, cls_Image__iff_0, cls_sym__Id__on_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_antisym__converse_0, cls_rtrancl__unfold_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_inf__fun__eq_0, cls_rel__compEpair_0, cls_wf__insert_0, cls_empty__is__image_0, cls_order__eq__refl_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_tranclE_1, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_r__into__trancl_H_0, cls_cuts__eq_0, cls_acc__wfI_0, cls_SigmaI_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_inf__sup__aci_I8_J_0, cls_rtrancl__eq__or__trancl_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_Image__Id__on_0, cls_Range__converse_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_wf__induct__rule_1, cls_Sigma__Diff__distrib1_0, cls_sup__eq__bot__eq2_0, cls_refl__on__def_1, 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_A_I2_J_0, cls_RangeE_0, cls_antisym__reflcl_1, cls_Range__def__raw_0, cls_antisym__Id__on_0, cls_UnCI_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_trans__rtrancl_0, cls_CHAINED_1, cls_subset__iff_0, cls_wf__comp__self_0, cls_trans__O__subset_0, clsarity_fun__HOL_Oord, cls_Field__Un_0, 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_inf__absorb2_0, cls_wf__def_1, cls_tranclD_1, cls_strict__linear__order__on__def_1, 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_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_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_pair__in__Id__conv_0, cls_Field__def_0, 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_Domain__Diff__subset_0, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_wf__asym_0, cls_linorder__linear_0, cls_Un__empty_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc_Oinduct_1, cls_order__antisym_0, cls_order__trans_0, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_image__empty_0, cls_sym__rtrancl_0, cls_subset__trans_0, cls_inf__le2_0, cls_refl__onD2_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_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_le__supE_0, 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_in__mkbot_2, cls_rtrancl__r__diff__Id_0, cls_insertI1_0, cls_Id__onE_1, cls_eq__equiv__class__iff2_0, cls_mono__Field_0, 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, clsarity_bool__Orderings_Opreorder, cls_trans__inv__image_0, cls_rtrancl__eq__or__trancl_1, cls_Field__insert_0, cls_acyclic__def_0, cls_acyclic__insert_1, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_A_I1_J_0, cls_converseE_1, cls_total__on__diff__Id_0, cls_Refl__antisym__eq__Image1__Image1__iff_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_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_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_le__inf__iff_2, 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_sup1CI_1, cls_ImageE_1, cls_order__eq__iff_2, cls_le__infI1_0, cls_bot1E_0, cls_trancl__unfold__left_0, 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__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_in__rel__def_0, cls_refl__on__Un_0, cls_o__eq__dest_0, cls_Un__assoc_0, cls_Int__left__absorb_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_total__on__converse_1, cls_acc__subset_0, cls_o__eq__dest__lhs_0, cls_Diff__mono_0, cls_Un__absorb_0, cls_ImageE_0, cls_wf__def_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_order__antisym__conv_0, cls_Int__lower1_0, cls_converseE_0, cls_converse__rtrancl__induct_1, clsarity_bool__Lattices_Olattice, cls_trancl__range_0, cls_CHAINED_0_02, 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_Domain__Id__on_0, cls_Nitpick_Orefl_H__def_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_bot__empty__eq_0, cls_eq__eqI_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_acyclic__insert_2, 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_inf__idem_0, cls_single__valued__confluent_0, cls_inf__bot__left_0, cls_inf1I_0, cls_equiv_Orefl__on_0, cls_le__eqI_0, cls_insert__not__empty_0, cls_Image__Id_0, cls_Int__left__commute_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_acc_Oinducts_2, cls_o__def_0, cls_sup__fun__eq_0, cls_pair__imageI_0, cls_IdI_0, cls_inf__sup__aci_I4_J_0, cls_fun__diff__def_0, cls_irrefl__trancl__rD_0, 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_xt1_I6_J_0, cls_subset__insert__iff_0, 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_inf__greatest_0, cls_equiv__class__eq__iff_1, cls_cuts__eq_2, cls_in__mkbot_1, cls_Diff__empty_0, cls_tfl__wf__induct_0, cls_in__mktop_2, cls_IntI_0, cls_in__inv__image_0, cls_Un__left__absorb_0, cls_converse__tranclE_0, cls_rtrancl__eq__or__trancl_2, cls_eq__eqI_1, cls_singleton__inject_0, cls_irrefl__diff__Id_0, cls_tfl__wf__induct_1, cls_Un__empty_1, cls_comp__cong_0, cls_le__iff__inf_0, cls_subset__insert_0, cls_sup__idem_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_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_trancl_Or__into__trancl_0, cls_Diff__Int_0, cls_rtrancl_Ortrancl__into__rtrancl_0, clsarity_fun__Orderings_Opreorder, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_Int__greatest_0, cls_Domain__insert_0, 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_sym__trans__comp__subset_0, cls_le__infE_1, cls_iff_0, cls_trans__trancl_0, cls_r__into__rtrancl_0, cls_rtrancl__idemp__self__comp_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_wf__insert_2, clsarity_bool__Lattices_Odistrib__lattice, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_acc__downward_0, cls_acc__induct__rule_1, cls_trancl__mono_0, cls_acyclic__subset_0, 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_acc_Oinducts_1, cls_trancl__unfold_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_antisym__def_0, cls_Image__Int__eq_0, cls_total__on__converse_0, cls_trancl__trans_0, cls_Field__def__raw_0, cls_converse__rtrancl__induct_0, cls_le__eqI_1, cls_CHAINED_0_03, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_Domain__mono_0, cls_Diff__Int2_0, cls_equiv__class__nondisjoint_0, cls_Un__Image_0, cls_DiffE_1, cls_Diff__insert__absorb_0, cls_le__infI2_0, cls_insert__image_0, cls_disjoint__iff__not__equal_0, cls_Nitpick_Orefl_H__def_1, cls_Un__Int__assoc__eq_0, cls_insert__commute_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_strict__linear__order__on__def_3, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_complete__Lin_1, cls_insert__iff_2, cls_rtranclE_1, cls_image__compose_0, cls_equiv__class__eq__iff_2, cls_image__is__empty_0, cls_Un__insert__right_0, cls_acyclic__impl__antisym__rtrancl_0, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_trancl__converse_0, cls_imageI_0, clsarity_fun__HOL_Ominus, cls_acyclic__converse_1, cls_wf__Un_0, cls_antisym__converse_1, cls_Pair__eq_1, clsarity_fun__Lattices_Odistrib__lattice, cls_wf__union__merge_1, cls_trans__def_0, cls_O__assoc_0, cls_o__apply_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_in__mkbot_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_eq__equiv__class__iff_1, cls_empty__Diff_0, cls_acc__induct__rule_2, cls_tfl__cut__apply_0, cls_o__assoc_0, cls_subset__insert__iff_1, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0
% 13.37/3.76  % No. of inferences in proof: 1279
% 13.37/3.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3231 ms resp. 2675 ms w/o parsing
% 14.01/4.00  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.01/4.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------