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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT073-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:27:09 AM UTC 2026

% Result   : Unsatisfiable 23.49s 7.09s
% Output   : Refutation 25.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  419
% Syntax   : Number of formulae    :  839 ( 225 unt;   0 typ;   0 def)
%            Number of atoms       : 1963 ( 436 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 16872 ( 906   ~;1124   |;   0   &;14842   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   78 (  76 usr;   8 con; 0-7 aty)
%            Number of variables   : 3096 (   0   ^;3096   !;   0   ?;3096   :)

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

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

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

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

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

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

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

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

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

thf(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1: $i > $i > $i > $i ).

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

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

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

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

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

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

thf(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1: $i > $i > $i > $i ).

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

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

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1: $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1_decl,type,
    c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1: $i > $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(299,axiom,
    ! [A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).

thf(1036,plain,
    ! [A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inter__lower_0) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1024,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_11) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(353,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).

thf(1168,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).

thf(1237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
      = ( B @ ( A @ c_Relation_OId__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

thf(777,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
      = ( B @ ( A @ c_Relation_OId__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).

thf(645,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(235,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).

thf(892,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(413,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).

thf(1315,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(121,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).

thf(666,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).

thf(1200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(401,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

thf(1290,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(280,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( G @ ( A @ hAPP ) )
        = ( G @ ( F @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
       != ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).

thf(994,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( G @ ( A @ hAPP ) )
        = ( G @ ( F @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
       != ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(14,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).

thf(449,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).

thf(861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).

thf(582,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(160,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

thf(741,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(341,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1142,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Inter_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(115,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).

thf(655,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) )
      | ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_0) ).

thf(1310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) )
      | ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).

thf(550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(187,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

thf(797,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

thf(472,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).

thf(1233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(259,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).

thf(945,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).

thf(1222,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).

thf(670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).

thf(814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).

thf(1327,plain,
    ! [A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(1260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(698,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Relation_OId @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).

thf(898,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Relation_OId @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1243,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(145,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).

thf(709,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) )
      | ( A
        = ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).

thf(973,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) )
      | ( A
        = ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).

thf(565,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).

thf(651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).

thf(1055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(182,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( F @ hAPP ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_1) ).

thf(785,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( F @ hAPP ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).

thf(1279,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).

thf(1323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

thf(838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

thf(917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).

thf(751,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).

thf(902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).

thf(559,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

thf(853,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).

thf(1087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(343,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).

thf(1147,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(384,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).

thf(1247,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(223,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( D @ ( C @ ( E @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( D @ ( C @ ( E @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).

thf(870,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( D @ ( C @ ( E @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( D @ ( C @ ( E @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(11,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(443,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

thf(623,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).

thf(646,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
      = ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).

thf(514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
      = ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) )
      | ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).

thf(937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) )
      | ( A
        = ( C @ ( C @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).

thf(574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(199,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

thf(821,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(301,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(1040,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).

thf(1109,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

thf(766,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(264,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).

thf(956,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(221,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).

thf(866,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(428,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(527,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(369,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).

thf(1215,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).

thf(634,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).

thf(849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(366,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).

thf(1206,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ( B = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(127,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(678,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

thf(529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(118,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).

thf(661,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

thf(546,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).

thf(925,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

thf(761,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).

thf(810,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(439,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).

thf(1057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).

thf(910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(236,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).

thf(1091,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(292,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( A @ ( C @ c_in ) ) )
      | ~ ( E @ ( B @ ( D @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( F @ ( E @ ( E @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).

thf(1021,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ~ ( E @ ( A @ ( C @ c_in ) ) )
      | ~ ( E @ ( B @ ( D @ c_in ) ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( F @ ( E @ ( E @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(262,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

thf(952,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(387,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1255,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(356,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

thf(1174,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).

thf(598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(136,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

thf(693,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(154,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

thf(729,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(1032,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(889,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).

thf(461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( D @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI_3) ).

thf(493,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( D @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).

thf(757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(1128,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).

thf(1281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(209,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(842,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).

thf(847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(484,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Relation_OField ) @ ( B @ ( A @ c_Relation_OField ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__Field_0) ).

thf(830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Relation_OField ) @ ( B @ ( A @ c_Relation_OField ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(225,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( E @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).

thf(874,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( E @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).

thf(1121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).

thf(980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1006,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(339,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(857,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(328,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_13) ).

thf(1111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(375,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1227,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).

thf(783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

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

thf(420,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(331,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).

thf(1118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(471,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).

thf(1160,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(402,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(1292,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).

thf(537,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
      = ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(637,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_13) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).

thf(884,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).

thf(1329,plain,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b____ @ ( v_a____ @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(295,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).

thf(1028,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).

thf(1082,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(554,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).

thf(753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(131,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

thf(686,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(1075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(28,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(476,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).

thf(1016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

thf(590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(329,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).

thf(1114,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).

thf(997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).

thf(701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1150,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

thf(569,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(179,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).

thf(779,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).

thf(1099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(276,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).

thf(985,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(392,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

thf(1231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( A @ c_in ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_1) ).

thf(1060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( A @ c_in ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).

thf(1050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(92,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).

thf(605,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).

thf(1318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(191,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).

thf(805,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

thf(508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
      | ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(60,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).

thf(541,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(657,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(172,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).

thf(765,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ c_in ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_0) ).

thf(1170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ c_in ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(312,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).

thf(1071,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(360,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).

thf(674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).

thf(1026,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(352,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1167,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).

thf(662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oconverse ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).

thf(718,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).

thf(906,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).

thf(1135,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

thf(965,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__quotient_0) ).

thf(618,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(425,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onI_0) ).

thf(430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).

thf(824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Relation_Osym ) )
      | ~ ( C @ ( B @ c_Relation_Osym ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_3) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(161,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).

thf(743,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
      = ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(333,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

thf(584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(71,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

thf(562,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(904,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(202,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
      = ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).

thf(826,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
      = ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(146,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).

thf(711,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_OField ) )
      = ( B @ ( A @ c_Relation_OField ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__converse_0) ).

thf(445,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_OField ) )
      = ( B @ ( A @ c_Relation_OField ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

thf(572,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(395,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1271,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(411,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).

thf(713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).

thf(1107,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( C @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI_2) ).

thf(466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( C @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).

thf(919,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).

thf(1258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).

thf(672,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(95,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(611,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).

thf(787,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(362,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).

thf(1194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(367,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( C = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).

thf(1209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( C = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Osym ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

thf(990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).

thf(1144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).

thf(616,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

thf(863,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).

thf(1048,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).

thf(567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).

thf(880,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).

thf(890,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(316,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).

thf(1080,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(104,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).

thf(631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(65,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).

thf(552,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).

thf(816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(94,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).

thf(609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
      = ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).

thf(594,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
      = ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).

thf(621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(50,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).

thf(520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(417,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(1325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).

thf(915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(175,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( F @ ( E @ ( D @ ( C @ ( B @ c_Recdef_Ocut ) ) ) ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( A @ hAPP ) )
       != ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).

thf(769,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( F @ ( E @ ( D @ ( C @ ( B @ c_Recdef_Ocut ) ) ) ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( A @ hAPP ) )
       != ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterD_0) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).

thf(668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).

thf(912,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(959,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).

thf(868,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( A = C )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).

thf(1176,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
      | ( A = C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(282,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).

thf(1000,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = E )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(385,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).

thf(1250,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) )
      | ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).

thf(851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
      = ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(505,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(114,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_0) ).

thf(653,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

thf(1213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(768,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(137,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

thf(695,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(383,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(1245,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(1034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(490,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).

thf(1304,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = A )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( D = B )
      | ( B = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(531,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).

thf(548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).

thf(927,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

thf(648,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).

thf(812,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(48,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(516,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(291,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).

thf(1018,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(200,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

thf(823,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).

thf(795,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
      | ( B @ ( A @ c_Relation_Osym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(128,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

thf(680,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(52,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).

thf(525,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_OField ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def_0) ).

thf(872,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Relation_OField ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( A @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( C @ ( C @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).

thf(887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( A @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( C @ ( C @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(263,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

thf(954,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

thf(557,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(283,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).

thf(1003,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(80,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( F @ ( C @ ( A @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( F @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).

thf(580,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( F @ ( C @ ( A @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( F @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

thf(855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).

thf(705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).

thf(1156,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).

thf(1225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).

thf(707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(406,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).

thf(1300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(1038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).

thf(840,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(463,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).

thf(808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(336,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

thf(1130,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).

thf(1218,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(109,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).

thf(643,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(372,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).

thf(1220,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_12) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(379,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(1235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(24,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( A @ c_Relation_OField ) @ c_COMBK ) ) @ ( B @ ( A @ c_Relation_OField ) @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Field2_0) ).

thf(470,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( A @ c_Relation_OField ) @ c_COMBK ) ) @ ( B @ ( A @ c_Relation_OField ) @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).

thf(576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(388,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1257,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).

thf(613,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_12) ).

thf(1284,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).

thf(1052,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(727,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).

thf(1008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(217,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).

thf(859,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).

thf(1240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(273,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(978,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).

thf(1140,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).

thf(876,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

thf(627,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).

thf(1084,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_11) ).

thf(1180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).

thf(556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(415,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(1321,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(38,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(495,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

thf(759,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(370,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

thf(1216,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(334,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

thf(1126,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(287,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).

thf(1010,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).

thf(931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( D @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__equiv__class_0) ).

thf(539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( D @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(133,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).

thf(688,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(396,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).

thf(1276,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).

thf(961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).

thf(896,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).

thf(1062,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).

thf(1101,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( B = A )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

thf(731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(180,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

thf(781,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).

thf(588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(386,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( G @ ( E @ tc_prod ) @ ( C @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).

thf(1253,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( G @ ( E @ tc_prod ) @ ( C @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

thf(699,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(296,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).

thf(1030,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

thf(510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(253,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).

thf(929,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(409,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(1308,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(171,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).

thf(763,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(302,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).

thf(1045,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = D )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).

thf(1077,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).

thf(832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(130,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).

thf(684,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(330,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).

thf(1116,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Otrans ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_2) ).

thf(447,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(269,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).

thf(967,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ( A = B )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionE_1) ).

thf(1229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
        = ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
      | ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
        = ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(2,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(422,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(220,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).

thf(865,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(91,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

thf(603,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(157,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

thf(735,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).

thf(950,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(1097,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(835,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(72,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).

thf(564,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).

thf(801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(1314,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(192,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

thf(807,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(8,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(437,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(664,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).

thf(828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

thf(696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(231,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).

thf(886,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(355,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).

thf(1172,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
      | ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(27,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(474,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(400,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).

thf(1288,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).

thf(1197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).

thf(1065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_1) ).

thf(1165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(393,axiom,
    tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).

thf(1268,plain,
    tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(345,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(1152,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

thf(596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).

thf(723,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

thf(691,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
      = ( A @ c_Relation_OId ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).

thf(607,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
      = ( A @ c_Relation_OId ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

thf(908,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
      = ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).

thf(992,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(275,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).

thf(982,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
      | ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( B = D )
      | ( A = D )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

thf(803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(257,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( F @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).

thf(940,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( F @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Osym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OField ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_Relation_OField ) @ ( C @ ( A @ c_Relation_OField ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__Un_0) ).

thf(923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OField ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_Relation_OField ) @ ( C @ ( A @ c_Relation_OField ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(359,axiom,
    v_a____ != v_b____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1184,plain,
    v_a____ != v_b____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(117,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).

thf(659,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).

thf(543,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onI_1) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(491,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

thf(1204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(86,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).

thf(592,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(229,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).

thf(882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).

thf(1014,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
      | ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(177,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).

thf(775,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).

thf(560,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(755,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(126,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).

thf(676,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
      = ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(16,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
       != ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).

thf(454,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ~ ( C @ ( B @ ( F @ c_in ) ) )
      | ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
       != ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(311,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( F @ ( G @ tc_prod ) @ ( D @ ( F @ ( G @ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).

thf(1069,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
      | ( F @ ( G @ tc_prod ) @ ( D @ ( F @ ( G @ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(1359,plain,
    $false,
    inference(e,[status(thm)],[1036,629,1024,1190,1168,1237,468,777,645,892,1315,518,666,1295,1200,1290,994,449,861,1158,582,741,1073,1142,1269,878,655,1310,550,500,797,715,472,1233,747,945,1222,670,814,1327,1260,698,898,1243,709,973,565,651,1055,785,1279,1132,1323,838,917,751,902,559,853,1087,1147,1247,870,1302,789,443,623,646,514,937,574,821,480,1040,1109,766,687,956,866,988,428,527,1215,634,1104,849,1206,678,529,661,546,925,761,810,512,439,1057,1163,910,894,1091,1021,952,1255,1174,598,693,729,1032,625,889,461,493,757,682,1128,1281,842,1012,847,484,522,830,578,874,948,1121,725,980,1006,1138,857,1111,1227,783,420,1118,471,1160,488,1292,537,637,970,884,1329,1028,1082,554,753,686,1075,476,1016,590,1114,997,701,1150,1297,738,569,779,1099,985,1266,1231,1060,1050,457,503,605,1318,792,805,508,921,541,657,765,1170,1071,586,1187,674,1026,1167,662,718,906,1135,965,618,425,430,824,745,689,733,601,772,743,1124,584,1154,562,904,826,711,641,445,572,1271,1312,713,1107,466,919,1258,672,611,787,1194,1209,900,990,1144,616,863,1048,736,451,567,880,434,890,1080,631,552,535,816,609,594,799,621,520,1325,915,769,943,1293,668,912,959,868,1176,1000,1250,851,505,653,1213,768,695,1245,1034,490,1304,531,548,927,648,812,749,516,1018,823,795,680,525,872,887,954,557,1003,580,855,705,1156,1225,707,1300,441,1038,840,463,808,1130,1218,643,1220,1262,1235,470,576,1257,703,613,1284,1052,727,1008,859,1240,1094,978,1140,497,876,627,1084,1180,556,482,1321,495,759,1216,1126,1010,844,931,539,976,688,1276,961,963,896,1062,1101,731,781,588,1253,699,1030,510,929,1308,763,1045,1077,478,832,684,1116,447,432,967,1229,818,422,865,603,735,950,1097,835,564,801,1314,506,807,437,664,828,696,886,1172,474,1288,1197,532,1065,720,1165,464,1268,1152,596,459,723,691,607,908,992,982,1004,486,803,940,935,923,1184,659,543,639,491,1204,592,882,1014,775,560,755,676,454,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT073-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41  % Computer : n026.cluster.edu
% 0.14/0.41  % Model    : x86_64 x86_64
% 0.14/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41  % Memory   : 8046.5625MB
% 0.14/0.41  % OS       : Linux 6.8.0-71-generic
% 0.14/0.41  % CPULimit : 300
% 0.14/0.41  % WCLimit  : 300
% 0.14/0.41  % DateTime : Sat Sep 26 06:27:55 UTC 2026
% 0.14/0.41  % CPUTime  : 
% 0.14/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.81/1.51  % [INFO] 	 Parsing done (507ms). 
% 2.81/1.53  % [INFO] 	 Running in sequential loop mode. 
% 4.13/2.13  % [INFO] 	 eprover registered as external prover. 
% 4.13/2.15  % [INFO] 	 Scanning for conjecture ... 
% 5.10/2.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 548 axioms. Running axiom selection ... 
% 6.79/2.82  % [INFO] 	 Axiom selection finished. Selected 418 axioms (removed 130 axioms). 
% 8.07/3.21  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 8.07/3.25  % [INFO] 	 Type checking passed. 
% 8.07/3.26  % [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 ... 
% 23.49/7.08  % External prover 'e' found a proof!
% 23.49/7.08  % [INFO] 	 Killing All external provers ... 
% 23.49/7.08  % Time passed: 6530ms (effective reasoning time: 5540ms)
% 23.49/7.09  % Axioms used in derivation (418): cls_trancl__converseD_0, cls_in__mktop_1, cls_subset__insert_1, cls_rtrancl__idemp_0, cls_Inter__lower_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_Int__Un__distrib_0, cls_Range__Un__eq_0, cls_converse__tranclE_1, cls_wfI_3, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_in__above_11, cls_insertE_0, cls_Un__subset__iff_0, cls_wf__subset_0, cls_insert__inter__insert_0, cls_rtrancl__converseD_0, cls_in__below_14, cls_total__on__def_0, cls_converseI_0, cls_InterI_1, cls_equalityI_0, cls_Id__onE_0, cls_subset__image__iff_2, cls_trancl__subset__Sigma__aux_0, cls_finite__insert_0, cls_wfE__min_0, cls_image__mono_0, cls_tranclD2_0, cls_Int__mono_0, cls_Un__commute_0, cls_finite__Un_2, cls_COMBK__def_0, cls_acc__wfD_0, cls_in__below_3, cls_Id__O__R_0, cls_mkbot__Lin_0, cls_CHAINED_0, cls_Range__def_0, cls_Id__on__eqI_0, cls_finite__Inter_0, cls_Un__upper1_0, cls_UnCI_1, cls_tranclD_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_in__above_7, cls_Domain__iff_0, cls_wf__inv__image_0, cls_Int__subset__iff_2, cls_in__below_2, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_Int__absorb1_0, cls_in__above_4, cls_Field__converse_0, cls_refl__on__converse_0, cls_in__below_7, cls_set__rev__mp_0, cls_Times__subset__cancel2_1, cls_Image__Un_0, cls_in__mkbot_4, cls_trans__converse_1, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_rtrancl__trancl__absorb_0, cls_Un__left__commute_0, cls_rtrancl__into__trancl1_0, cls_finite__insert_1, cls_trancl__subset__Field2_0, cls_set__mp_0, cls_cut__apply_0, cls_wf__converse__trancl_0, cls_wfI_2, cls_Un__Int__distrib2_0, cls_finite__Int_1, cls_trans__Int_0, cls_Image__iff_0, cls_in__below_11, cls_sym__Id__on_0, cls_rel__compEpair_0, cls_sym__Id_0, cls_rtrancl__mono_0, cls_Un__subset__iff_1, cls_Image__subset_0, cls_rtrancl__unfold_0, cls_wf__insert_0, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_Image__iff_1, cls_rtrancl__reflcl_0, cls_rev__image__eqI_0, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_in__below_9, cls_notin__Lin__iff_0, cls_insert__ident_0, 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_Union__upper_0, cls_finite__Int_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_Image__Id__on_0, cls_Range__converse_0, cls_rtrancl__eq__or__trancl_0, cls_in__above_6, cls_Range__Int__subset_0, cls_RangeE_0, cls_UnCI_0, cls_Int__insert__right_1, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_wf__trancl_0, cls_rtrancl__converse_0, cls_trans__rtrancl_0, cls_refl__on__def_1, cls_in__below_6, cls_Lin__irrefl_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_r__comp__rtrancl__eq_0, cls_subset__iff_0, cls_wf__comp__self_0, cls_trans__O__subset_0, cls_Field__Un_0, cls_in__mkbot_3, cls_rel__comp__distrib_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_UnionE_1, cls_converse__Un_0, cls_image__insert_0, cls_equiv_Otrans_0, cls_acc__downwards__aux_0, cls_Range__iff_1, cls_Domain__Int__subset_0, cls_wf__comp__self_1, cls_tranclD_1, cls_Range__iff_0, cls_Un__insert__left_0, cls_wf__irrefl_0, cls_rtrancl__Un__rtrancl_0, cls_Id__on__iff_0, cls_IdE_0, cls_finite__surj_0, cls_trancl__reflcl_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__subset__iff_1, cls_pair__in__Id__conv_0, cls_Field__def_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_SigmaD2_0, cls_finite__UnI_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_in__above_1, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_Un__subset__iff_2, cls_in__below_10, cls_in__below_1, cls_refl__on__def_2, cls_wf__asym_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_Times__subset__cancel2_0, cls_mktop__Lin_0, cls_sym__rtrancl_0, cls_subset__trans_0, cls_in__mktop_0, cls_trans__converse_0, cls_refl__onD2_0, cls_acc_Ocases_0, cls_transD_0, cls_mono__Field_0, cls_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_rtrancl__eq__or__trancl_1, cls_trans__Id__on_0, cls_Image__Int__subset_0, cls_in__mkbot_2, cls_Id__on__subset__Times_0, cls_insertI1_0, cls_Id__onE_1, cls_Un__Int__crazy_0, cls_trans__inv__image_0, cls_in__mktop_4, cls_Int__commute_0, cls_finite__equiv__class_0, cls_rev__ImageI_0, cls_Pair__eq_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_trans__Id_0, cls_Un__absorb1_0, cls_sym__converse_0, cls_in__inv__image_1, cls_in__above_5, cls_converse__iff_1, cls_refl__onD_0, cls_subset__refl_0, cls_converse__in__Lin_0, cls_Nitpick_Ortrancl__def_0, cls_image__Un_0, cls_Image__mono_0, cls_in__below_12, cls_R__O__Id_0, cls_image__iff_2, cls_insertCI_0, cls_UnionE_0, cls_image__Int__subset_0, cls_pair__in__Id__conv_1, cls_in__above_12, cls_tranclD2_1, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_Sigma__mono_1, cls_rtrancl__Int__subset_0, cls_above__Lin_0, cls_ImageE_1, cls_trancl__unfold__left_0, cls_in__above_9, cls_rtrancl__trancl__trancl_0, cls_Int__lower2_0, cls_rel__compI_0, cls_insert__mono_0, cls_Un__assoc_0, cls_linear__alt_0, cls_trancl__id_0, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_Int__absorb_0, cls_converse__Id_0, cls_refl__on__Un_0, cls_complete__Lin_0, cls_Int__left__absorb_0, cls_wf__union__merge_0, cls_in__above_13, cls_total__on__converse_1, cls_acc__subset_0, cls_converse__inv__image_0, cls_Un__absorb_0, cls_ImageE_0, cls_trancl__rtrancl__absorb_0, cls_in__below_5, cls_equiv_Osym_0, cls_UnE_0, cls_subset__insertI2_0, cls_converseD_0, cls_acc_OaccI_0, cls_Int__lower1_0, cls_InterD_0, cls_Int__subset__iff_0, cls_trancl__range_0, cls_Union__quotient_0, cls_refl__on__converse_1, cls_refl__onI_1, cls_refl__onD1_0, cls_Nitpick_Orefl_H__def_0, cls_Domain__Id__on_0, cls_equiv__type_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_Not__Domain__rtrancl_0, cls_finite__subset_0, cls_converse__rel__comp_0, cls_insert__subset_2, cls_equiv_Orefl__on_0, cls_rtrancl__converseI_0, cls_subsetD_0, cls_symD_0, cls_sym__def_0, cls_Image__Id_0, cls_finite__Un_0, cls_Int__left__commute_0, cls_in__above_2, cls_trancl__Int__subset_0, cls_insert__absorb2_0, cls_IdI_0, cls_irrefl__trancl__rD_0, cls_notin__Lin__iff_1, cls_Un__Int__assoc__eq_1, cls_trans__reflclI_0, cls_converse__converse_0, cls_RangeI_0, cls_Int__iff_2, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_equiv__class__eq__iff_1, cls_cuts__eq_2, cls_in__mkbot_1, cls_Times__Un__distrib1_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_subset__insert_0, cls_InterI_0, cls_insert__times__insert_0, cls_in__below_0, cls_trancl_Or__into__trancl_0, cls_in__above_10, cls_Times__eq__cancel2_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_converse__in__Lin_1, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_trancl__rtrancl__trancl_0, cls_Int__greatest_0, cls_Domain__insert_0, cls_in__above_8, cls_subset__Un__eq_1, 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_rel__comp__subset__Sigma_0, cls_wf__insert_2, cls_sym__trans__comp__subset_0, cls_refl__on__Int_0, cls_trancl__mono_0, cls_wf__Int1_0, cls_trans__trancl_0, cls_r__into__rtrancl_0, cls_rel__comp__mono_0, cls_insertCI_1, cls_refl__on__comp__subset_0, cls_in__below_13, cls_rtranclD_0, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_acc__downward_0, cls_in__below_4, cls_rtrancl__Un__subset_0, cls_image__subset__iff_0, cls_finite__imageI_0, cls_rtrancl__idemp__self__comp_0, cls_UnionI_0, cls_acc_OaccI_1, cls_subset__insertI_0, cls_trancl__unfold_0, cls_Domain__mono_0, cls_total__on__converse_0, cls_Sigma__Int__distrib1_0, cls_trancl__trans_0, cls_Un__Image_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_quotient__eqI_0, cls_below__Lin_0, cls_that_0, cls_equiv__comp__eq_0, cls_converse__Int_0, cls_Domain__iff_1, cls_insert__image_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_Nitpick_Orefl_H__def_1, cls_refl__on__def_0, cls_refl__on__def_3, cls_in__below_8, cls_Un__Int__assoc__eq_0, cls_Sigma__mono_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_complete__Lin_1, cls_insert__iff_2, cls_equiv__class__eq__iff_2, cls_quotient__eq__iff_0, cls_Un__insert__right_0, cls_Pair__eq_1, cls_refl__onI_0, cls_sym__Int_0, cls_trancl__converse_0, cls_imageI_0, cls_Times__Int__distrib1_0, cls_quotientE_1, cls_equalityE_0, cls_wf__Int2_0, cls_wf__union__merge_1, cls_trans__def_0, cls_O__assoc_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_in__above_3, cls_in__mkbot_0, cls_Int__insert__right_0, cls_tfl__cut__apply_0, cls_subset__insert__iff_1, cls_in__above_14, cls_in__above_0
% 23.49/7.09  % No. of inferences in proof: 839
% 23.49/7.09  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6530 ms resp. 5540 ms w/o parsing
% 25.23/7.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.23/7.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------