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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT002-1 : 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 : n012.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 08:27:00 AM UTC 2026

% Result   : Unsatisfiable 40.49s 15.17s
% Output   : Refutation 36.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  664
% Syntax   : Number of formulae    : 1329 ( 403 unt;   0 typ;   0 def)
%            Number of atoms       : 2781 ( 612 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 24414 (1346   ~;1452   |;   0   &;21616   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  118 ( 116 usr;  12 con; 0-7 aty)
%            Number of variables   : 4694 (   0   ^;4694   !;   0   ?;4694   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_x_decl,type,
    v_x: $i ).

thf(v_y_decl,type,
    v_y: $i ).

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

thf(v_L_decl,type,
    v_L: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_curry_decl,type,
    c_curry: $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3_decl,type,
    c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: $i > $i > $i ).

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

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

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

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

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

thf(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_ATP__Linkup_Osko__Relation__Xtrans__def__1__2_decl,type,
    c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: $i > $i > $i ).

thf(c_Predicate_Oinv__imagep_decl,type,
    c_Predicate_Oinv__imagep: $i > $i > $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_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__Relation__XtransI__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XtransI__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Relation__XtransI__1__3_decl,type,
    c_ATP__Linkup_Osko__Relation__XtransI__1__3: $i > $i > $i ).

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

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

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__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__Xrtrancl__induct__1__2_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: $i > $i > $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $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__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__XImage__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__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__Transitive__Closure__Xconverse__rtranclE__1__1_decl,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: $i > $i > $i > $i > $i ).

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

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

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

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

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

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

thf(v_R_decl,type,
    v_R: $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__Wellfounded__Xwf__induct__rule__1__1_decl,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).

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

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__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__Relation__XtransI__1__2_decl,type,
    c_ATP__Linkup_Osko__Relation__XtransI__1__2: $i > $i > $i ).

thf(v_c_decl,type,
    v_c: $i ).

thf(t_c_decl,type,
    t_c: $i ).

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

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

thf(c_ATP__Linkup_Osko__Wellfounded__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__Relation__XRangeE__1__1_decl,type,
    c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $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_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(475,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( G @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( F @ ( F @ ( E @ ( D @ tc_prod ) @ ( G @ ( F @ ( E @ ( D @ ( A @ c_split ) ) ) @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__imageI_0) ).

thf(1665,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( G @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( F @ ( F @ ( E @ ( D @ tc_prod ) @ ( G @ ( F @ ( E @ ( D @ ( A @ c_split ) ) ) @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(319,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(1337,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)],[319]) ).

thf(239,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(1168,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)],[239]) ).

thf(460,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(1633,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(506,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(1729,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)],[506]) ).

thf(177,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(1031,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)],[177]) ).

thf(200,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(1083,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)],[200]) ).

thf(131,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(941,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(212,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(1110,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)],[212]) ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ tc_prod ) @ ( C @ ( B @ ( A @ c_snd ) @ c_Set_Oimage ) ) ) )
      = ( B @ ( A @ ( C @ c_Relation_ORange ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eq__Range_0) ).

thf(1686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ tc_prod ) @ ( C @ ( B @ ( A @ c_snd ) @ c_Set_Oimage ) ) ) )
      = ( B @ ( A @ ( C @ c_Relation_ORange ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(335,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(1369,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)],[335]) ).

thf(551,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).

thf(1823,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(662,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(2072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(523,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).

thf(1767,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(425,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(1559,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)],[425]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1105,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(271,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(1237,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)],[271]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(846,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(107,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(559,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).

thf(1840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(1,negated_conjecture,
    v_x != v_y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(666,plain,
    v_x != v_y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(1295,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(610,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(1956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(420,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 ) ) @ hBOOL )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).

thf(1549,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 ) ) @ hBOOL )
      | ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(353,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 ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1406,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 ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(577,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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).

thf(1882,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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(418,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1544,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(1205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(440,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).

thf(1591,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(1269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(101,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(878,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(367,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_curry ) ) ) @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__conv_0) ).

thf(1437,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_curry ) ) ) @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(46,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(762,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(596,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(163,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(1005,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)],[163]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).

thf(1569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(603,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).

thf(1939,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).

thf(1486,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Otrans ) )
      | ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(494,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(1705,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(362,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 ) ) @ hBOOL )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).

thf(1426,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 ) ) @ hBOOL )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(478,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(1671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(470,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1655,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(509,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( E @ ( D @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 ) ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).

thf(1735,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( E @ ( D @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 ) ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(237,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(1164,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)],[237]) ).

thf(573,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(1872,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)],[573]) ).

thf(38,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(747,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)],[38]) ).

thf(463,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).

thf(1640,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(377,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( 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(1458,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( 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)],[377]) ).

thf(4,negated_conjecture,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_x @ ( v_y @ c_Pair ) ) ) @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(670,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_x @ ( v_y @ c_Pair ) ) ) @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(70,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(814,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)],[70]) ).

thf(314,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(1327,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)],[314]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(1260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(698,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(594,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).

thf(1919,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(623,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).

thf(1988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1063,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(609,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).

thf(1954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(251,axiom,
    ( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
    = ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).

thf(1196,plain,
    ( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
    = ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(514,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_1) ).

thf(1746,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(591,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1914,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(369,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).

thf(1441,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(638,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).

thf(2020,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(330,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(1359,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)],[330]) ).

thf(343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(503,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).

thf(1724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(411,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).

thf(1529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(540,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ tc_prod ) @ ( A @ ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).

thf(1803,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ tc_prod ) @ ( A @ ( C @ ( B @ ( E @ ( D @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(493,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 ) ) @ hBOOL )
      | ( 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(1703,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 ) ) @ hBOOL )
      | ( 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)],[493]) ).

thf(274,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).

thf(1243,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(531,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).

thf(1782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(345,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(1391,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)],[345]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).

thf(1576,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).

thf(1650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(595,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
      | ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).

thf(1921,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
      | ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

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

thf(389,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).

thf(1482,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(294,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(1287,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)],[294]) ).

thf(496,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).

thf(1709,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(26,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(719,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)],[26]) ).

thf(588,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

thf(1907,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(568,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(82,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(838,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(64,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(802,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)],[64]) ).

thf(307,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(1313,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(135,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(949,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(403,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).

thf(1511,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(40,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(751,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)],[40]) ).

thf(555,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

thf(1832,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(249,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(1191,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)],[249]) ).

thf(379,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).

thf(1462,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(189,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(1059,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)],[189]) ).

thf(222,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(1132,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)],[222]) ).

thf(112,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(902,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)],[112]) ).

thf(202,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(1087,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)],[202]) ).

thf(448,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(1609,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)],[448]) ).

thf(529,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Oacyclic ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).

thf(1778,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Oacyclic ) )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(268,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(1232,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)],[268]) ).

thf(562,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).

thf(1847,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(311,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(1319,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)],[311]) ).

thf(97,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(870,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)],[97]) ).

thf(349,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Wellfounded_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).

thf(1398,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Wellfounded_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

thf(881,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(546,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

thf(1494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(632,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).

thf(2007,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( D @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( D @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(641,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Oantisym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).

thf(2027,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Oantisym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(590,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).

thf(1911,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(181,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(1040,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)],[181]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(1418,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(553,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(1828,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)],[553]) ).

thf(230,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(1151,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)],[230]) ).

thf(342,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(1383,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)],[342]) ).

thf(143,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(966,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)],[143]) ).

thf(186,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(1051,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)],[186]) ).

thf(637,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) @ hBOOL )
      | ( 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(2017,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) @ hBOOL )
      | ( 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)],[637]) ).

thf(544,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1811,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(373,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

thf(1450,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(483,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(80,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(834,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)],[80]) ).

thf(567,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).

thf(1858,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(570,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).

thf(1864,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(481,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).

thf(1677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(645,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).

thf(2034,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(245,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(1183,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)],[245]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(598,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(1928,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)],[598]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1215,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(100,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

thf(877,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(195,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(1072,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)],[195]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

thf(774,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(347,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(1394,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)],[347]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(1351,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(630,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ~ ( C @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ( ( 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(2002,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ~ ( C @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ( ( 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)],[630]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).

thf(1433,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(254,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(1201,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)],[254]) ).

thf(443,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).

thf(1600,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( C @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).

thf(981,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( C @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(560,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

thf(1843,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(656,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_OField ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ c_Relation_OField ) @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__insert_0) ).

thf(2058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_OField ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ c_Relation_OField ) @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(1447,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(139,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(956,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OId__on ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).

thf(1886,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OId__on ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(490,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).

thf(1697,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(273,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__by__empty_0) ).

thf(1242,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(196,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(1074,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)],[196]) ).

thf(634,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(2011,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)],[634]) ).

thf(488,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 ) ) @ hBOOL )
      | ( ( 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(1691,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 ) ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(122,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(925,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)],[122]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1306,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(253,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(1199,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)],[253]) ).

thf(68,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(810,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)],[68]) ).

thf(651,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 ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(2047,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 ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(306,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(1311,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)],[306]) ).

thf(193,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(1067,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)],[193]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(45,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(761,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)],[45]) ).

thf(383,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).

thf(1470,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(592,axiom,
    ( ( v_y @ ( v_x @ ( t_c @ ( t_b @ ( t_a @ ( v_c @ c_curry ) ) ) @ hAPP ) @ hAPP ) )
    = ( t_b @ ( t_a @ ( v_y @ ( v_x @ c_Pair ) ) ) @ ( v_c @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__def_0) ).

thf(1915,plain,
    ( ( v_y @ ( v_x @ ( t_c @ ( t_b @ ( t_a @ ( v_c @ c_curry ) ) ) @ hAPP ) @ hAPP ) )
    = ( t_b @ ( t_a @ ( v_y @ ( v_x @ c_Pair ) ) ) @ ( v_c @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(524,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 ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1768,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 ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(629,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(2000,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(461,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(1636,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)],[461]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1047,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(798,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(288,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(1274,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)],[288]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(957,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(204,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(1091,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)],[204]) ).

thf(322,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(1343,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)],[322]) ).

thf(172,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(1021,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)],[172]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(952,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(1519,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(435,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).

thf(1580,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(262,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(1217,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)],[262]) ).

thf(14,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(693,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(644,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eqD_0) ).

thf(2032,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( B @ ( A @ ( D @ c_Pair ) ) ) @ ( C @ ( B @ c_snd ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(636,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oinv__imagep ) ) ) ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__imagep_1) ).

thf(2015,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oinv__imagep ) ) ) ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(585,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

thf(1900,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(910,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1123,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(93,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(862,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)],[93]) ).

thf(399,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1502,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(516,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( t_a @ ( C @ ( v_y @ ( v_x @ ( B @ ( A @ c_Predicate_Oinv__imagep ) ) ) ) ) )
      = ( v_y @ ( B @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__imagep__def_0) ).

thf(1751,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( t_a @ ( C @ ( v_y @ ( v_x @ ( B @ ( A @ c_Predicate_Oinv__imagep ) ) ) ) ) )
      = ( v_y @ ( B @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(58,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(788,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)],[58]) ).

thf(453,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1619,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(118,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).

thf(916,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(444,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).

thf(1602,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(333,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(1365,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)],[333]) ).

thf(614,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 ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).

thf(1968,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 ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(243,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(1178,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)],[243]) ).

thf(608,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).

thf(1951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_curry ) ) ) @ c_split ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__curry_0) ).

thf(830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_curry ) ) ) @ c_split ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(105,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(889,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
      = ( A @ c_Relation_OId ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(291,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(1281,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)],[291]) ).

thf(296,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(1291,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)],[296]) ).

thf(147,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(974,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)],[147]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(852,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(423,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

thf(1555,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(580,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(1888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(5,negated_conjecture,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_y @ ( v_x @ c_Pair ) ) ) @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(665,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_y @ ( v_x @ c_Pair ) ) ) @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(660,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).

thf(2068,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1819,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(557,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

thf(1836,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(533,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1787,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(175,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(1027,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)],[175]) ).

thf(511,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(84,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(842,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)],[84]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).

thf(1402,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(521,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).

thf(1762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(526,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).

thf(1772,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(566,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).

thf(1856,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(206,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(1096,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)],[206]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1118,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(154,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(989,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)],[154]) ).

thf(91,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(857,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(16,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(697,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).

thf(1089,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transitive__Closure_Ortrancl ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(269,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

thf(1234,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(99,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(874,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(1143,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

thf(1534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(170,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).

thf(1017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orel__comp ) ) ) ) )
      = ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(615,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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1970,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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(1227,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).

thf(1498,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(438,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1587,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(416,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(1540,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)],[416]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(224,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(1138,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)],[224]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).

thf(1719,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(429,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).

thf(1567,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(1329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(235,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(1160,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)],[235]) ).

thf(331,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(1361,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)],[331]) ).

thf(472,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).

thf(1659,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(41,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(753,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)],[41]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(669,plain,
    ! [A: $i] :
      ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).

thf(1424,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(602,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( 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 ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).

thf(1937,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( 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 ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(647,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(2038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(257,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(1207,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)],[257]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ODomain ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).

thf(1644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ODomain ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

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

thf(706,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(297,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(1292,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)],[297]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(654,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 ) ) @ hBOOL )
      | ~ ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).

thf(2053,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 ) ) @ hBOOL )
      | ~ ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(679,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(232,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(1155,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)],[232]) ).

thf(513,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).

thf(1744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(207,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(1099,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)],[207]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(701,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(387,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

thf(1478,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).

thf(1297,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(376,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

thf(1456,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ODomain ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).

thf(1266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ODomain ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(617,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_in ) ) @ hBOOL )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).

thf(1974,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( A @ c_in ) ) @ hBOOL )
      | ( B = A )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(600,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).

thf(1932,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(151,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(984,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)],[151]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

thf(1799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(606,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).

thf(1947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(621,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(1984,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)],[621]) ).

thf(574,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).

thf(1874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(363,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

thf(1429,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(499,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( 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(1715,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( 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)],[499]) ).

thf(457,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 ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).

thf(1627,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 ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).

thf(1825,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(214,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(1114,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)],[214]) ).

thf(283,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(1263,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(159,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(997,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)],[159]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(1002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(564,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(619,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_1) ).

thf(1979,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(346,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(1393,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(317,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(1333,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)],[317]) ).

thf(625,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(129,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(938,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)],[129]) ).

thf(66,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(805,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(649,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(2043,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(120,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(921,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)],[120]) ).

thf(427,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 ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

thf(1563,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 ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(187,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(1054,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)],[187]) ).

thf(664,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

thf(2076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Oirrefl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(381,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_split ) ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).

thf(1466,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_split ) ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(247,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(1187,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)],[247]) ).

thf(474,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).

thf(1663,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(583,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_0) ).

thf(1895,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(246,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(1185,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)],[246]) ).

thf(627,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).

thf(1996,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1278,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(1135,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(505,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).

thf(1727,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(522,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).

thf(1764,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(482,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(1680,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)],[482]) ).

thf(12,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(689,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(337,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(1374,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)],[337]) ).

thf(227,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1146,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(518,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).

thf(1754,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(611,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).

thf(1959,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(263,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(1219,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)],[263]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(642,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).

thf(2028,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(442,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(1595,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)],[442]) ).

thf(459,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).

thf(1631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( D @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).

thf(904,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( D @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(652,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(2048,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)],[652]) ).

thf(578,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).

thf(1884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(468,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Oirrefl ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).

thf(1652,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Oirrefl ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(451,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1615,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(344,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(1389,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)],[344]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(826,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(536,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).

thf(1795,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(492,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_bool @ ( G @ tc_fun ) @ ( F @ ( E @ ( A @ c_split ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).

thf(1701,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_bool @ ( G @ tc_fun ) @ ( F @ ( E @ ( A @ c_split ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1256,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(392,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oinv__imagep ) ) ) ) ) @ hBOOL )
      | ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__imagep_0) ).

thf(1488,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oinv__imagep ) ) ) ) ) @ hBOOL )
      | ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(477,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).

thf(1669,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(128,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(936,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)],[128]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Osingle__valued ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).

thf(1707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Osingle__valued ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(508,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1733,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(281,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(380,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( C @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).

thf(1464,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( C @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(328,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(1356,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)],[328]) ).

thf(480,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(1675,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)],[480]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(336,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1371,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(584,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(1897,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(804,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(1209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(111,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(900,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)],[111]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(784,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ~ ( C @ ( A @ ( C @ ( A @ c_Relation_OField ) @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( A @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( D @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).

thf(1524,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ~ ( C @ ( A @ ( C @ ( A @ c_Relation_OField ) @ c_Relation_Orefl__on ) ) )
      | ~ ( C @ ( A @ c_Relation_Oantisym ) )
      | ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( D @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(325,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(1349,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)],[325]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).

thf(1542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( C @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(502,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

thf(1722,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(218,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(1122,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)],[218]) ).

thf(487,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orefl__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).

thf(1690,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orefl__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(681,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).

thf(1408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(432,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(167,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(1011,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)],[167]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).

thf(1589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(155,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(990,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)],[155]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(445,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).

thf(1603,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(182,axiom,
    ( ( t_a @ ( v_r @ c_Relation_OField ) )
    = ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ ( v_r @ c_Relation_ORange ) ) @ ( t_a @ ( t_a @ ( v_r @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def__raw_0) ).

thf(1043,plain,
    ( ( t_a @ ( v_r @ c_Relation_OField ) )
    = ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ ( v_r @ c_Relation_ORange ) ) @ ( t_a @ ( t_a @ ( v_r @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(539,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(431,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1571,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(338,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(1376,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)],[338]) ).

thf(368,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).

thf(1439,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(476,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).

thf(1667,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
      = ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(575,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).

thf(1877,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
       != ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(640,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Relation_Oirrefl ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).

thf(2025,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Relation_Oirrefl ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(320,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(1339,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)],[320]) ).

thf(424,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1557,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(71,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(816,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)],[71]) ).

thf(507,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).

thf(1731,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(569,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).

thf(1862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(87,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(848,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)],[87]) ).

thf(558,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(1838,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)],[558]) ).

thf(229,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(1149,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)],[229]) ).

thf(323,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(1344,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)],[323]) ).

thf(132,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(943,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)],[132]) ).

thf(341,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1061,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(549,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1820,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(589,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).

thf(1909,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1162,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(29,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(726,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)],[29]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(1029,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(378,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).

thf(1460,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(2,negated_conjecture,
    tc_Arrow__Order__Mirabelle_Oalt @ ( v_L @ c_Relation_Otrans ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(668,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( v_L @ c_Relation_Otrans ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Ortrancl ) )
      = ( A @ c_Relation_OId ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).

thf(1112,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Ortrancl ) )
      = ( A @ c_Relation_OId ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(486,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).

thf(1688,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( D @ ( C @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(597,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).

thf(1926,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(1474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Oirrefl ) )
      | ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).

thf(1699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Relation_Otrans ) )
      | ~ ( C @ ( B @ c_Relation_Oirrefl ) )
      | ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
      | ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(1213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( D @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).

thf(883,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( C @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
        = ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( D @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) )
       != ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(169,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(1015,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)],[169]) ).

thf(152,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(986,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)],[152]) ).

thf(639,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 ) ) @ hBOOL )
      | ( ( 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(2022,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 ) ) @ hBOOL )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(396,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).

thf(1496,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(489,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).

thf(1694,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(541,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OField ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__empty_0) ).

thf(1805,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OField ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(240,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(1171,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)],[240]) ).

thf(252,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

thf(1198,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(348,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(1396,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)],[348]) ).

thf(371,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).

thf(1445,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(868,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(527,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1775,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(161,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(1000,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)],[161]) ).

thf(366,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 ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

thf(1435,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 ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(504,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(1726,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(278,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(1250,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)],[278]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(436,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).

thf(1583,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(543,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 ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1809,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 ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).

thf(1304,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( C @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).

thf(1166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( C @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(255,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(1203,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)],[255]) ).

thf(133,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(944,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)],[133]) ).

thf(61,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(795,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)],[61]) ).

thf(587,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1905,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 ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(123,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(927,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)],[123]) ).

thf(484,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).

thf(1684,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(624,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1990,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(384,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

thf(1472,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

thf(1049,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(631,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).

thf(2005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(199,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ ( B @ c_Relation_Osingle__valued ) ) )
      | ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Osingle__valued ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).

thf(1081,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Relation_Osingle__valued ) ) )
      | ~ ( E @ ( D @ ( B @ c_Relation_Osingle__valued ) ) )
      | ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Osingle__valued ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(39,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(749,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)],[39]) ).

thf(144,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(968,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)],[144]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).

thf(1181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
      = ( tc_bool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(421,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).

thf(1551,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(561,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(1845,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).

thf(1770,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(690,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(612,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(1961,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)],[612]) ).

thf(174,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(1025,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)],[174]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(449,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 ) ) @ hBOOL )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).

thf(1611,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 ) ) @ hBOOL )
      | ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(446,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).

thf(1605,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 ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(466,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(530,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).

thf(1780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Otrancl ) @ ( t_a @ ( t_a @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xtrancl__Xcases__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1531,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(157,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(993,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)],[157]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1748,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(657,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 ) ) @ hBOOL )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).

thf(2060,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 ) ) @ hBOOL )
      | ( A = B )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(21,axiom,
    tc_bool @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(707,plain,
    tc_bool @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(604,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).

thf(1941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B = A )
      | ( t_a @ ( t_a @ tc_prod ) @ ( C @ ( t_a @ ( t_a @ ( B @ ( C @ ( B @ ( A @ v_sko__Transitive__Closure__Xrtrancl__Xcases__1 ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(138,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(954,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)],[138]) ).

thf(517,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 ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(1753,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 ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(285,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(1267,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)],[285]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_2) ).

thf(1484,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(497,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).

thf(1711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1869,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(270,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(1235,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)],[270]) ).

thf(201,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(1085,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)],[201]) ).

thf(67,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(808,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)],[67]) ).

thf(293,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(1285,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)],[293]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).

thf(907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(301,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(1300,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)],[301]) ).

thf(374,axiom,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).

thf(1452,plain,
    ! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(532,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_snd ) @ hAPP ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__conv_0) ).

thf(1785,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ c_snd ) @ hAPP ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(310,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).

thf(1317,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(554,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).

thf(1830,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(601,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = C )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).

thf(1934,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = C )
      | ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(744,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

thf(1849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(703,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(620,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).

thf(1981,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( E @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(1023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(264,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(1221,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)],[264]) ).

thf(94,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(864,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)],[94]) ).

thf(400,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 ) ) @ hBOOL )
      | ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).

thf(1504,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 ) ) @ hBOOL )
      | ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(537,axiom,
    ( ( v_y @ ( v_x @ ( t_b @ ( t_a @ ( v_R @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) )
    = ( t_b @ ( t_a @ tc_prod ) @ ( v_R @ ( t_b @ ( t_a @ ( v_y @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def__raw_0) ).

thf(1797,plain,
    ( ( v_y @ ( v_x @ ( t_b @ ( t_a @ ( v_R @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) )
    = ( t_b @ ( t_a @ tc_prod ) @ ( v_R @ ( t_b @ ( t_a @ ( v_y @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(655,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).

thf(2056,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(352,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(1404,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)],[352]) ).

thf(329,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(1358,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)],[329]) ).

thf(616,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).

thf(1972,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ODomain ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(401,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_2) ).

thf(1506,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

thf(1585,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(978,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(1140,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(500,axiom,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1717,plain,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(643,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).

thf(2030,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(272,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(1240,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)],[272]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).

thf(1617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(309,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(1316,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)],[309]) ).

thf(650,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).

thf(2045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(613,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).

thf(1966,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ tc_prod ) @ ( E @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( E @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(125,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(931,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)],[125]) ).

thf(422,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

thf(1553,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(607,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(547,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(1817,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)],[547]) ).

thf(148,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(976,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)],[148]) ).

thf(356,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(1412,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(406,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).

thf(1517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(44,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(759,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)],[44]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(891,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(220,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(1126,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)],[220]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(166,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(1010,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)],[166]) ).

thf(571,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).

thf(1866,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

thf(1108,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Relation_Oantisym ) )
      | ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(628,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(1998,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)],[628]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).

thf(1421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(635,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 ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

thf(2013,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 ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(233,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osingle__valued ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

thf(1157,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osingle__valued ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(312,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(1321,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(556,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

thf(1834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1289,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(542,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).

thf(1807,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(50,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(771,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)],[50]) ).

thf(289,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(1276,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)],[289]) ).

thf(279,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( E @ ( D @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osingle__valued ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).

thf(1253,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( E @ ( D @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osingle__valued ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(386,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1476,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(321,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(1341,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)],[321]) ).

thf(402,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 ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

thf(1508,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 ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(458,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

thf(1629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(565,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).

thf(1854,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 ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(158,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(995,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)],[158]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(208,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(1101,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)],[208]) ).

thf(275,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(1244,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)],[275]) ).

thf(550,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(1822,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ c_curry ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__split_0) ).

thf(731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ c_curry ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(57,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(786,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)],[57]) ).

thf(633,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( G @ ( F @ ( C @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).

thf(2009,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
      | ~ ( G @ ( F @ ( C @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(117,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(914,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)],[117]) ).

thf(648,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(2041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(528,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(1777,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(6,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(667,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_L @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(659,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(2066,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)],[659]) ).

thf(250,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(1193,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(259,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(1212,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(447,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1607,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(404,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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).

thf(1513,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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(626,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(1994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(183,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(1045,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)],[183]) ).

thf(63,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(800,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)],[63]) ).

thf(110,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(899,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(473,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).

thf(1661,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(79,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(832,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)],[79]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(684,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(582,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

thf(1893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(646,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).

thf(2036,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(305,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(1309,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)],[305]) ).

thf(215,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(1116,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)],[215]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ORange ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ORange ) ) @ ( C @ ( B @ ( A @ c_Relation_ORange ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).

thf(999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ORange ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ORange ) ) @ ( C @ ( B @ ( A @ c_Relation_ORange ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(464,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).

thf(1642,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(434,axiom,
    ( ( v_y @ ( v_x @ ( tc_bool @ ( t_b @ tc_fun ) @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) )
    = ( t_b @ ( t_a @ tc_prod ) @ ( tc_bool @ ( t_b @ ( t_a @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_b @ ( t_a @ ( v_y @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq2_0) ).

thf(1578,plain,
    ( ( v_y @ ( v_x @ ( tc_bool @ ( t_b @ tc_fun ) @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) )
    = ( t_b @ ( t_a @ tc_prod ) @ ( tc_bool @ ( t_b @ ( t_a @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_b @ ( t_a @ ( v_y @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(136,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).

thf(950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) )
      | ( B @ ( A @ c_Relation_Oantisym ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(419,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(1546,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)],[419]) ).

thf(456,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1625,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(818,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(519,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).

thf(1757,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
      | ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(388,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).

thf(1480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(441,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(1593,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)],[441]) ).

thf(340,axiom,
    ! [A: $i] : ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Osingle__valued ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

thf(1380,plain,
    ! [A: $i] : ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Osingle__valued ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(622,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

thf(1986,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(410,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).

thf(1527,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ORange ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(228,axiom,
    tc_bool @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(1148,plain,
    tc_bool @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(479,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(1673,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)],[479]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(59,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(790,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)],[59]) ).

thf(653,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 ) ) @ hBOOL )
      | ( ( 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(2050,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 ) ) @ hBOOL )
      | ( ( 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)],[653]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(918,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(471,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).

thf(1657,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(426,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).

thf(1561,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(178,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(1033,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)],[178]) ).

thf(581,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).

thf(1891,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( 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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(77,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(828,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)],[77]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(960,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ c_Wellfounded_OwfP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__in__rel_0) ).

thf(1065,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
      | ( B @ ( B @ ( B @ ( A @ c_FunDef_Oin__rel ) ) @ c_Wellfounded_OwfP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1314,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(318,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(1335,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)],[318]) ).

thf(661,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(2070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(109,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(897,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)],[109]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(1410,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(534,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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(1789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) @ hBOOL )
      | ( 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)],[534]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(1346,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(658,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(2063,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(512,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

thf(1742,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(153,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(987,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(415,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).

thf(1537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( A = B )
      | ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(1378,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(171,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(1019,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)],[171]) ).

thf(156,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(992,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(398,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

thf(1500,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(822,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(586,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(1902,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(1120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1093,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(599,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).

thf(1930,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Wellfounded_Owf ) )
      | ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_List_Osko__Recdef__Xtfl__wf__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).

thf(740,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Otrancl ) )
      = ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(618,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).

thf(1977,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(413,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_1) ).

thf(1532,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(498,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(576,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 ) ) @ hBOOL )
      | ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).

thf(1880,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 ) ) @ hBOOL )
      | ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(364,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(1431,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 ) ) @ hBOOL )
      | ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

thf(1621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(1331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(127,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(935,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(663,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 ) ) @ hBOOL )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

thf(2074,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 ) ) @ hBOOL )
      | ( B @ ( A @ c_Wellfounded_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(428,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 ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

thf(1565,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 ) ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_3) ).

thf(1416,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ c_Relation_Otrans ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).

thf(1468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
      | ~ ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(194,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(1069,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)],[194]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(146,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(972,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)],[146]) ).

thf(469,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 ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).

thf(1653,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 ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(605,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 ) ) @ hBOOL )
      | ( ( 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(1944,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 ) ) @ hBOOL )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(334,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(1367,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)],[334]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot2E_0) ).

thf(923,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(510,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(393,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 ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).

thf(1490,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 ) ) @ hBOOL )
      | ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(180,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(1037,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)],[180]) ).

thf(593,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).

thf(1917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(42,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(755,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)],[42]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12226,plain,
    $false,
    inference(e,[status(thm)],[1665,1337,1168,1633,1729,1031,1083,941,1110,1686,1369,1823,2072,1767,1559,1105,1237,846,893,1840,666,1295,1956,1549,1406,1882,1522,1443,1544,1205,1591,1269,878,1437,1158,762,1924,1005,1569,1939,1173,1486,1705,1426,1671,1655,1735,1164,1872,747,1640,1354,1458,670,814,1327,1260,698,1919,1988,1063,1954,1196,1746,1914,1441,2020,1613,1359,1386,1724,1529,1803,1703,1243,1782,1391,1576,1650,1921,1623,1482,724,1287,1709,1792,719,1907,1860,838,802,1313,949,1511,751,1832,1191,1462,1059,1132,902,1087,1609,1778,1232,1847,1319,870,1398,881,1815,1494,2007,1302,2027,1911,1040,1418,1828,1151,1383,966,1051,2017,1811,1450,1682,834,1858,1864,1677,2034,1183,1283,1928,1215,877,1072,774,1394,1351,2002,1433,1201,1600,981,766,1843,2058,1447,956,866,1886,1697,1242,1074,2011,1691,925,1306,1199,810,2047,1311,1067,1153,761,1470,1915,1768,714,2000,1636,1047,798,1274,957,1091,1343,1021,952,1519,1580,1217,693,2032,2015,1900,910,1123,862,1502,1751,820,788,1619,916,1602,1365,1968,1178,1951,830,889,757,1281,1291,974,1012,852,1555,1888,665,2068,1819,1836,1787,1079,1027,1740,842,1402,742,1762,1772,1856,1096,1118,989,857,697,1089,1234,874,1143,1534,1017,1970,1227,1498,1587,1540,1006,1138,1719,1567,1329,1160,1361,1659,753,669,686,1424,1937,2038,1207,1644,706,1292,933,1414,2053,679,970,1155,1744,1099,701,1478,1297,1456,1266,1974,1932,984,1799,1947,1984,1874,1429,1246,1715,1627,1825,1324,1114,1263,997,1002,1852,1979,779,1759,1393,1333,1991,792,938,805,2043,921,1563,1054,2076,1035,1466,1187,1663,1515,1895,1185,1996,1278,1135,1727,1764,1680,689,1374,1146,1754,1959,1103,1219,824,2028,1595,1631,733,904,694,2048,1884,772,1652,1615,1389,826,711,1795,1701,1256,1488,1669,936,1707,1733,1258,1464,1356,1675,1271,1371,1897,804,1638,1224,764,1209,900,784,1524,1349,1542,1722,737,1122,1690,1175,681,1408,1574,1011,1589,990,1492,1603,1043,1801,1571,1376,1439,1667,1877,2025,1339,1557,816,1731,1862,848,1838,1149,1344,943,1381,1061,1820,1909,1162,726,1029,895,769,1460,1293,668,1112,1688,1926,1474,1699,1213,883,1015,986,2022,1496,1694,1805,912,1171,1198,1396,1445,868,1775,1000,1435,1726,1250,722,1583,1809,1304,1166,1203,944,795,1905,927,1684,812,1990,939,1472,1049,2005,1076,1081,749,968,1181,836,1551,1845,1770,690,1961,1025,872,1611,1605,1647,1780,1531,993,776,1748,2060,707,1941,954,1753,1267,1230,1484,1711,717,1869,1235,1085,808,1285,907,1300,1452,840,1785,1317,1830,1934,744,1849,703,1981,1023,1221,864,1504,1797,1008,2056,1404,1358,1972,1506,1585,978,1140,1717,2030,1240,1617,1316,2045,1966,931,1553,1949,1817,976,1412,1517,759,891,1126,1189,1010,1866,1108,1998,1421,2013,1157,1321,1834,1289,844,1453,1807,771,1276,1253,963,1476,1341,1508,1629,1854,781,995,946,1101,1244,1822,731,786,2009,914,2041,1777,667,929,2066,1193,1212,1607,1513,1994,1045,800,899,1661,832,684,1893,2036,1309,1116,999,1642,1578,950,1546,1625,818,1757,1480,735,1593,1380,854,1986,1527,1148,1673,1248,790,2050,918,1657,1561,1033,1891,828,960,1065,1363,1314,1335,2070,897,1410,1056,1789,1346,2063,886,1742,987,1537,1378,1019,992,1500,822,1902,1120,1093,1930,728,740,1977,1129,1532,860,850,1713,1880,1431,1399,1621,1331,935,2074,1565,1416,1812,1468,1069,708,972,1653,1944,1367,923,1737,1490,1037,1917,755,676]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : SCT002-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04  % 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
% 0.06/0.53  % Computer : n012.cluster.edu
% 0.06/0.53  % Model    : x86_64 x86_64
% 0.06/0.53  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.53  % Memory   : 8046.5625MB
% 0.06/0.53  % OS       : Linux 6.8.0-71-generic
% 0.06/0.53  % CPULimit : 300
% 0.06/0.53  % WCLimit  : 300
% 0.06/0.53  % DateTime : Sat Sep 26 06:17:35 UTC 2026
% 0.06/0.53  % CPUTime  : 
% 0.06/0.53  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
% 0.09/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/1.23  % [INFO] 	 Parsing done (343ms). 
% 1.18/1.25  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.56  % [INFO] 	 eprover registered as external prover. 
% 1.76/1.57  % [INFO] 	 Scanning for conjecture ... 
% 2.12/1.77  % [INFO] 	 Found a conjecture (or negated_conjecture) and 671 axioms. Running axiom selection ... 
% 2.97/2.04  % [INFO] 	 Axiom selection finished. Selected 658 axioms (removed 13 axioms). 
% 3.69/2.33  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.69/2.35  % [INFO] 	 Type checking passed. 
% 3.69/2.36  % [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 ... 
% 40.49/15.15  % External prover 'e' found a proof!
% 40.49/15.15  % [INFO] 	 Killing All external provers ... 
% 40.49/15.16  % Time passed: 14548ms (effective reasoning time: 13905ms)
% 40.49/15.16  % Axioms used in derivation (658): cls_inf__sup__absorb_0, cls_trancl__converseD_0, cls_Diff__cancel_0, cls_converse__tranclE_1, cls_subset__insert_1, cls_Diff__iff_2, cls_rtrancl__idemp_0, cls_bot__fun__eq_0, cls_snd__conv_0, cls_equiv__class__eq__iff_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Range__Un__eq_0, cls_inf__sup__aci_I2_J_0, cls_rtrancl__induct_3, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_sup__ge1_0, cls_image__constant_0, cls_insertE_0, cls_rtrancl__converseD_0, cls_wf__subset_0, cls_snd__eqD_0, cls_union__comp__emptyL_0, cls_insert__inter__insert_0, cls_Un__Diff_0, cls_congruent_Ocongruent_0, cls_Un__subset__iff_0, cls_splitD_H_0, cls_total__on__def_0, cls_converseI_0, cls_equalityI_0, cls_Id__onE_0, cls_single__valuedD_0, cls_wf__acyclic_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_trancl__subset__Sigma__aux_0, cls_rtrancl_Ocases_0, cls_empty__is__image_1, cls_Un__empty__left_0, cls_wfE__min_0, cls_single__valued__Id__on_0, cls_strict__linear__order__on__def_0, cls_le__funD_0, cls_rel__comp__empty1_0, cls_Image__singleton__iff_0, cls_image__mono_0, cls_tranclD2_0, cls_sup__bot__right_0, cls_insert__code_1, cls_trancl_Ocases_0, cls_trans__def_1, clsarity_bool__Lattices_Olower__semilattice, cls_Id__O__R_0, cls_le__iff__inf_1, cls_Un__upper1_0, cls_COMBK__def_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_Range__def_0, cls_inf__sup__aci_I6_J_0, cls_Id__on__eqI_0, cls_Un__commute_0, cls_acc_Oinduct_2, cls_irrefl__def_0, cls_acc__wfD_0, cls_UnCI_1, cls_tranclD_0, cls_Sigma__empty1_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_empty__iff_0, cls_trans__diff__Id_0, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_mem__def_1, cls_wf__inv__image_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_Domain__iff_0, cls_Diff__subset__conv_0, cls_wf__no__loop_0, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_inf1E_1, cls_Image__Un_0, cls_split__curry_0, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_inf__sup__distrib1_0, cls_wf__empty_0, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, cls_antisymD_0, cls_refl__on__converse_0, cls_le__sup__iff_0, cls_wf__induct__rule_0, cls_Diff__triv_0, cls_Domain__empty_0, cls_Field__converse_0, clsarity_fun__Lattices_Oupper__semilattice, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_Range__empty__iff_0, cls_Times__subset__cancel2_1, cls_acc_Oinducts_0, cls_transI_0, cls_converse__rtrancl__induct_3, cls_congruent2_Ocongruent2_0, cls_inf__commute_0, cls_trans__converse_1, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_Un__left__commute_0, cls_rtrancl__into__trancl1_0, cls_trancl__subset__Field2_0, cls_wf__converse__trancl_0, cls_single__valued__Id_0, cls_rtrancl__trancl__absorb_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_trans__Int_0, cls_Image__iff_0, cls_sym__Id__on_0, cls_sym__Id_0, cls_equiv__class__eq__iff_3, cls_le__supI_0, cls_rtrancl__mono_0, cls_Un__subset__iff_1, cls_rtrancl__unfold_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_inf__fun__eq_0, cls_rel__compEpair_0, cls_antisym__converse_0, cls_Image__subset_0, cls_wf__insert_0, cls_empty__is__image_0, cls_Sigma__empty2_0, cls_converse__rtranclE_1, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_Image__empty_0, cls_rtrancl__induct_2, clsarity_fun__Orderings_Obot, cls_Image__iff_1, cls_rel__comp__distrib2_0, cls_le__supE_1, cls_le__iff__sup_0, cls_rtrancl__reflcl_0, cls_rev__image__eqI_0, cls_wf__induct_1, cls_tranclE_1, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_cuts__eq_0, cls_acc__wfI_0, cls_SigmaI_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_rtrancl__eq__or__trancl_0, cls_trancl__empty_0, cls_less__by__empty_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_Image__Id__on_0, cls_Range__converse_0, cls_refl__on__empty_0, cls_r__into__trancl_H_0, cls_Sigma__Diff__distrib1_0, cls_sup__eq__bot__eq2_0, cls_refl__on__def_1, cls_total__on__diff__Id_1, cls_Int__insert__right_1, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_trancl_Ocases_1, cls_wf__trancl_0, cls_rtrancl__converse_0, cls_trans__rtrancl_0, cls_wf__induct__rule_1, cls_Range__Int__subset_0, cls_RangeE_0, cls_antisym__reflcl_1, cls_Range__def__raw_0, cls_antisym__Id__on_0, cls_UnCI_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_subset__iff_0, cls_insert__code_2, cls_wf__comp__self_0, cls_trans__O__subset_0, clsarity_fun__HOL_Oord, cls_rev__predicate1D_0, cls_converse__Un_0, cls_insert__Diff__single_0, cls_singleton__iff_1, cls_r__comp__rtrancl__eq_0, cls_Field__Un_0, cls_curry__split_0, cls_single__valued__rel__comp_0, cls_Diff__idemp_0, cls_trans__def_2, cls_subset__empty_0, cls_rel__comp__distrib_0, cls_equiv__class__eq_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_rtrancl_Ocases_1, cls_image__insert_0, cls_equiv_Otrans_0, cls_acc__downwards__aux_0, cls_wf__def_1, cls_tranclD_1, cls_strict__linear__order__on__def_1, cls_snd__eq__Range_0, cls_Range__iff_0, cls_acc__induct_2, cls_in__inv__imagep_1, cls_doubleton__eq__iff_2, cls_subset__insert__iff_3, cls_diff__single__insert_0, cls_Range__iff_1, cls_Domain__Int__subset_0, cls_inf__absorb2_0, cls_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_wf__irrefl_0, cls_rtrancl__Un__rtrancl_0, cls_IdE_0, cls_SigmaD2_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_insert__subset_1, cls_Int__empty__left_0, cls_Image__singleton__iff_1, cls_pair__in__Id__conv_0, cls_inv__imagep__def_0, cls_Field__def_0, cls_Range__Diff__subset_0, cls_Id__on__iff_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_rtrancl__induct_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_inf__sup__aci_I3_J_0, cls_trancl__reflcl_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_Int__insert__left_1, cls_converse__rtranclE_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_irrefl__tranclI_0, cls_Domain__Diff__subset_0, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_transI_1, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_wf__asym_0, cls_linorder__linear_0, cls_Un__empty_0, cls_Int__assoc_0, cls_acc_Oinduct_1, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_sym__rtrancl_0, cls_subset__trans_0, cls_converse__rtrancl__induct_2, cls_inf__le2_0, cls_refl__onD2_0, cls_image__empty_0, cls_Times__subset__cancel2_0, cls_double__diff_0, cls_trans__converse_0, cls_acc_Ocases_0, cls_insert__is__Un_0, cls_DiffI_0, cls_transD_0, cls_mono__Field_0, cls_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_trans__Id__on_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_Diff__Int__distrib2_0, cls_acc_Oinduct_0, cls_image__constant__conv_0, cls_total__on__diff__Id_0, cls_Id__on__subset__Times_0, cls_rtrancl__r__diff__Id_0, cls_insertI1_0, cls_Id__onE_1, cls_split__case__cert_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, cls_trans__inv__image_0, cls_le__supE_0, cls_rel__comp__empty2_0, cls_rtrancl__eq__or__trancl_1, cls_Field__insert_0, cls_acyclic__def_0, cls_acyclic__insert_1, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_Refl__antisym__eq__Image1__Image1__iff_0, cls_Diff__insert2_0, cls_Int__commute_0, cls_wfE__pf_0, cls_sup__least_0, cls_subset__refl_0, cls_tranclE_0, cls_rev__ImageI_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_empty__subsetI_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_trans__Id_0, cls_Un__absorb1_0, cls_sym__converse_0, cls_sup1E_0, cls_in__inv__image_1, cls_distrib__inf__le_0, cls_converse__iff_1, cls_refl__onD_0, cls_Pair__eq_0, cls_rtranclE_0, cls_singletonE_0, cls_Nitpick_Ortrancl__def_0, cls_image__diff__subset_0, cls_Image__mono_0, cls_Int__Diff_0, cls_rtrancl__Int__subset_0, cls_image__iff_2, cls_insertCI_0, cls_le__infE_0, cls_image__Int__subset_0, cls_pair__in__Id__conv_1, cls_Range__empty_0, cls_le__inf__iff_2, cls_tranclD2_1, cls_subset__equiv__class_0, cls_Un__Diff__cancel_0, cls_image__Un_0, cls_insert__Diff_0, cls_total__on__empty_0, cls_trans__def_3, cls_DiffE_0, cls_R__O__Id_0, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_union__comp__emptyR_0, cls_sup1CI_1, cls_ImageE_1, cls_le__infI1_0, cls_bot1E_0, cls_trancl__unfold__left_0, cls_inf__assoc_0, cls_rtrancl__trancl__trancl_0, cls_Int__lower2_0, cls_rel__compI_0, cls_insert__mono_0, cls_Un__assoc_0, cls_Un__Diff__cancel2_0, cls_bex__empty_0, cls_trancl__id_0, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_Int__absorb_0, cls_converse__Id_0, cls_in__rel__def_0, cls_refl__on__Un_0, cls_le__supI2_0, cls_bot2E_0, cls_in__rel__def__raw_0, cls_antisym__reflcl_0, cls_Int__left__absorb_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_total__on__converse_1, cls_acc__subset_0, cls_Diff__mono_0, cls_Un__absorb_0, cls_ImageE_0, cls_wf__def_0, cls_bot__empty__eq2_0, cls_equiv_Osym_0, cls_UnE_0, cls_subset__insertI2_0, cls_wf__union__merge_0, cls_Diff__disjoint_0, cls_converseD_0, cls_acc_OaccI_0, cls_converse__inv__image_0, cls_Diff__Int__distrib_0, cls_antisym__Id_0, cls_trancl__rtrancl__absorb_0, cls_Int__lower1_0, cls_converse__rtrancl__induct_1, cls_Domain__empty__iff_0, cls_trancl__range_0, cls_refl__on__converse_1, cls_strict__linear__order__on__def_2, cls_refl__onD1_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_Nitpick_Orefl_H__def_0, cls_Domain__Id__on_0, cls_equiv__type_0, cls_in__inv__imagep_0, cls_transI_2, clsarity_bool__Lattices_Olattice, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_Not__Domain__rtrancl_0, cls_converse__rel__comp_0, cls_insert__subset_2, cls_le__supI1_0, cls_rtrancl__converseI_0, cls_sup__left__idem_0, cls_subsetD_0, cls_symD_0, cls_sym__def_0, cls_single__valued__confluent_0, cls_acc_Oinducts_2, cls_acyclic__insert_2, cls_antisym__empty_0, cls_inf__bot__left_0, cls_wf__in__rel_0, cls_inf1I_0, cls_equiv_Orefl__on_0, cls_le__eqI_0, cls_SigmaE_0, cls_insert__not__empty_0, cls_Image__Id_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_inf__idem_0, cls_trancl__Int__subset_0, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_sup__fun__eq_0, cls_pair__imageI_0, cls_IdI_0, cls_inf__sup__aci_I4_J_0, cls_fun__diff__def_0, cls_Id__on__empty_0, cls_irrefl__trancl__rD_0, cls_subset__insert__iff_0, cls_acc__induct_1, cls_Un__Int__assoc__eq_1, cls_trans__reflclI_0, cls_eq__equiv__class__iff_0, cls_converse__converse_0, cls_insert__absorb2_0, cls_Product__Type_Osplit_0, cls_sup__inf__absorb_0, cls_irrefl__def_1, cls_curry__def_0, cls_wf__induct_0, cls_acyclic__converse_0, cls_subset__singletonD_0, cls_RangeI_0, cls_Int__iff_2, cls_doubleton__eq__iff_1, cls_rtrancl__induct_0, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_eq__equiv__class_0, cls_inf__greatest_0, cls_equiv__class__eq__iff_1, cls_cuts__eq_2, cls_tfl__wf__induct_0, cls_IntI_0, cls_in__inv__image_0, cls_Diff__empty_0, cls_Times__Un__distrib1_0, cls_Un__left__absorb_0, cls_converse__tranclE_0, cls_le__iff__inf_0, cls_rtrancl__eq__or__trancl_2, cls_insert__times__insert_0, cls_eq__eqI_1, cls_singleton__inject_0, cls_irrefl__diff__Id_0, cls_tfl__wf__induct_1, cls_Times__eq__cancel2_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, cls_Times__Diff__distrib1_0, cls_emptyE_0, cls_antisym__subset_0, cls_acyclic__insert_0, cls_inf__sup__ord_I3_J_0, cls_congruent2__implies__congruent_0, cls_inf__sup__aci_I5_J_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_trancl_Or__into__trancl_0, cls_Diff__Int_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_IntE_1, cls_IntE_0, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_Int__greatest_0, cls_Domain__insert_0, cls_sup__ge2_0, cls_sym__Un__converse_0, cls_sym__conv__converse__eq_0, cls_Un__least_0, cls_in__rtrancl__UnI_0, cls_trancl__rtrancl__trancl_0, cls_sup1CI_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_in__rel__def_1, cls_rel__comp__subset__Sigma_0, cls_sym__trans__comp__subset_0, cls_le__infE_1, cls_refl__on__Int_0, cls_wf__Int1_0, cls_r__into__rtrancl_0, cls_rtrancl__idemp__self__comp_0, cls_insertCI_1, cls_wf__insert_2, clsarity_bool__Lattices_Odistrib__lattice, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_acc__downward_0, cls_acc__induct__rule_1, cls_trancl__mono_0, cls_acyclic__subset_0, cls_trans__trancl_0, cls_conjI__realizer_1, cls_rtrancl__Un__subset_0, cls_image__subset__iff_0, cls_acc__induct_0, cls_inf__le1_0, cls_rel__comp__mono_0, cls_refl__on__comp__subset_0, cls_inf__left__idem_0, cls_curry__conv_0, cls_doubleton__eq__iff_4, cls_rtranclD_0, cls_mem__splitI_0, cls_single__valued__subset_0, cls_acc_OaccI_1, cls_Diff__subset__conv_1, cls_insert__code_0, cls_le__eqI_1, cls_acc_Oinducts_1, cls_trancl__unfold_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_antisym__def_0, cls_Image__Int__eq_0, cls_total__on__converse_0, cls_Sigma__Int__distrib1_0, cls_trancl__trans_0, cls_Field__def__raw_0, cls_converse__rtrancl__induct_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_Domain__mono_0, cls_Diff__Int2_0, cls_equiv__class__nondisjoint_0, cls_Un__Image_0, cls_DiffE_1, cls_Diff__insert__absorb_0, cls_converse__Int_0, cls_le__infI2_0, cls_insert__image_0, cls_disjoint__iff__not__equal_0, cls_rtrancl__empty_0, cls_Nitpick_Orefl_H__def_1, cls_Un__Int__assoc__eq_0, cls_refl__on__def_0, cls_insert__iff_2, cls_Diff__partition_0, cls_equiv__comp__eq_0, cls_Domain__iff_1, cls_sup__bot__left_0, cls_acc__induct__rule_0, cls_strict__linear__order__on__def_3, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_rtranclE_1, cls_equiv__class__eq__iff_2, cls_image__is__empty_0, cls_Un__insert__right_0, cls_acyclic__impl__antisym__rtrancl_0, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_sym__Int_0, cls_trancl__converse_0, cls_imageI_0, cls_acyclic__converse_1, cls_wf__Un_0, cls_antisym__converse_1, cls_Pair__eq_1, cls_wf__Int2_0, clsarity_fun__Lattices_Odistrib__lattice, cls_wf__union__merge_1, clsarity_fun__HOL_Ominus, cls_Times__Int__distrib1_0, cls_trans__def_0, cls_O__assoc_0, cls_Field__empty_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_ball__empty_0, cls_Int__insert__right_0, cls_eq__equiv__class__iff_1, cls_empty__Diff_0, cls_acc__induct__rule_2, cls_tfl__cut__apply_0, cls_subset__insert__iff_1, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0
% 40.49/15.16  % No. of inferences in proof: 1329
% 40.49/15.17  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 14548 ms resp. 13905 ms w/o parsing
% 36.25/15.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.25/15.55  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------