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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL786-1 : 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 : n008.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 07:52:53 AM UTC 2026

% Result   : Unsatisfiable 16.79s 5.07s
% Output   : Refutation 17.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  203
% Syntax   : Number of formulae    :  407 ( 161 unt;   0 typ;   0 def)
%            Number of atoms       :  737 ( 262 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 6050 ( 338   ~; 330   |;   0   &;5382   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   65 (  63 usr;  25 con; 0-5 aty)
%            Number of variables   : 1380 (   0   ^;1380   !;   0   ?;1380   :)

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

thf(c_List_Olist_ONil_decl,type,
    c_List_Olist_ONil: $i > $i ).

thf(c_List_Olist_OCons_decl,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(c_Type_Otypings_decl,type,
    c_Type_Otypings: $i > $i > $i > $o ).

thf(c_List_Omap_decl,type,
    c_List_Omap: $i > $i > $i > $i > $i ).

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

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

thf(c_Lambda_Osubst_decl,type,
    c_Lambda_Osubst: $i ).

thf(tc_Lambda_OdB_decl,type,
    tc_Lambda_OdB: $i ).

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

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

thf(c_Type_Oshift_decl,type,
    c_Type_Oshift: $i > $i > $i > $i > $i ).

thf(tc_Type_Otype_decl,type,
    tc_Type_Otype: $i ).

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

thf(c_Type_Otyping_decl,type,
    c_Type_Otyping: $i > $i ).

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

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

thf(c_ListOrder_Ostep1_decl,type,
    c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).

thf(c_List_Ofoldl_decl,type,
    c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).

thf(c_List_Olistsp_decl,type,
    c_List_Olistsp: $i > $i > $i > $o ).

thf(c_InductTermi_OIT_decl,type,
    c_InductTermi_OIT: $i ).

thf(c_Lambda_Olift_decl,type,
    c_Lambda_Olift: $i ).

thf(c_Lambda_OdB_OApp_decl,type,
    c_Lambda_OdB_OApp: $i ).

thf(c_List_Ofoldr_decl,type,
    c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).

thf(c_Lambda_Oliftn_decl,type,
    c_Lambda_Oliftn: $i > $i > $i > $i ).

thf(c_Lambda_OdB_OVar_decl,type,
    c_Lambda_OdB_OVar: $i > $i ).

thf(c_Lambda_Osubstn_decl,type,
    c_Lambda_Osubstn: $i > $i > $i > $i ).

thf(c_Lambda_OdB_OAbs_decl,type,
    c_Lambda_OdB_OAbs: $i > $i ).

thf(c_Transitive__Closure_Ortranclp_decl,type,
    c_Transitive__Closure_Ortranclp: $i > $i > $i ).

thf(c_Predicate_Oconversep_decl,type,
    c_Predicate_Oconversep: $i > $i > $i > $i ).

thf(c_Lambda_Obeta_decl,type,
    c_Lambda_Obeta: $i ).

thf(v_rs_____decl,type,
    v_rs____: $i ).

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

thf(v_as_____decl,type,
    v_as____: $i ).

thf(c_Wellfounded_Oaccp_decl,type,
    c_Wellfounded_Oaccp: $i > $i > $i > $o ).

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

thf(c_Type_Otype_Otype__case_decl,type,
    c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).

thf(c_Type_Otype_OAtom_decl,type,
    c_Type_Otype_OAtom: $i > $i ).

thf(c_Lambda_OdB_OdB__case_decl,type,
    c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $i ).

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

thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_decl,type,
    c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).

thf(c_Lambda_OdB_OdB__rec_decl,type,
    c_Lambda_OdB_OdB__rec: $i > $i > $i > $i > $i > $i ).

thf(c_Type_Otype_Otype__rec_decl,type,
    c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xtyping__elims__3__1_decl,type,
    c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xtyping__elims__3__2_decl,type,
    c_Type_Osko__Type__Xtyping__elims__3__2: $i > $i > $i > $i ).

thf(c_Type_Otype_OFun_decl,type,
    c_Type_Otype_OFun: $i ).

thf(c_Type_Osko__Type__Xtyping__elims__2__1_decl,type,
    c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xlist__app__typeD__1__1_decl,type,
    c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xtype__induct__1__1_decl,type,
    c_Type_Osko__Type__Xtype__induct__1__1: $i > $i ).

thf(v_e_____decl,type,
    v_e____: $i ).

thf(v_u_____decl,type,
    v_u____: $i ).

thf(v_T_____decl,type,
    v_T____: $i ).

thf(c_Type_Osko__Type__Xvar__app__types__1__1_decl,type,
    c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).

thf(v_ua_______decl,type,
    v_ua______: $i ).

thf(c_Type_Osko__Type__Xlist__app__typeE__1__1_decl,type,
    c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).

thf(v_i_____decl,type,
    v_i____: $i ).

thf(v_n_____decl,type,
    v_n____: $i ).

thf(v_T_H_____decl,type,
    v_T_H____: $i ).

thf(c_Type_Osko__Type__Xvar__app__typesE__1__1_decl,type,
    c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).

thf(v_ea_______decl,type,
    v_ea______: $i ).

thf(v_ia_______decl,type,
    v_ia______: $i ).

thf(v_T_Ha_______decl,type,
    v_T_Ha______: $i ).

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

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).

thf(629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Osubstn ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).

thf(468,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(14,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( F @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
      | ( C = D )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).

thf(234,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( F @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
      | ( C = D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

thf(352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(408,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

thf(582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(32,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

thf(276,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).

thf(379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

thf(597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).

thf(440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

thf(655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

thf(511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).

thf(385,plain,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(139,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).

thf(533,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(147,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
      = ( E @ ( D @ ( B @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).

thf(550,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
      = ( E @ ( D @ ( B @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

thf(500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(37,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(288,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).

thf(301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( D @ c_Type_Otype_OAtom @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_0) ).

thf(436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( D @ c_Type_Otype_OAtom @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(195,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( tc_Type_Otype @ ( C @ ( D @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

thf(651,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( tc_Type_Otype @ ( C @ ( D @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Osubst @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).

thf(257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Osubst @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).

thf(389,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

thf(587,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Type_Otype_OAtom )
     != ( C @ ( B @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).

thf(542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Type_Otype_OAtom )
     != ( C @ ( B @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).

thf(421,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

thf(606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

thf(416,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(26,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(261,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(6,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(216,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(113,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

thf(475,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

thf(591,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

thf(376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
      = ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Oliftn ) ) )
      = ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).

thf(485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

thf(574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OAbs )
        = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

thf(480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OAbs )
        = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).

thf(280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(39,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( C = B )
      | ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).

thf(293,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( C = B )
      | ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Predicate_Oconversep ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).

thf(396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Predicate_Oconversep ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(199,axiom,
    v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( v_a____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(660,plain,
    v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( v_a____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( c_Lambda_Olift @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).

thf(243,plain,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( c_Lambda_Olift @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Otype_OAtom )
       != ( B @ c_Type_Otype_OAtom ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).

thf(428,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Otype_OAtom )
       != ( B @ c_Type_Otype_OAtom ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

thf(265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Type_Otype @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).

thf(527,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Type_Otype @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

thf(307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

thf(452,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(20,axiom,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(248,plain,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(200,axiom,
    v_T____ @ ( v_ua______ @ ( v_ea______ @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).

thf(661,plain,
    v_T____ @ ( v_ua______ @ ( v_ea______ @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

thf(529,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(8,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).

thf(220,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

thf(366,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Type_Otype_OAtom @ ( B @ ( A @ c_Type_Otype_Otype__case ) ) ) )
      = ( C @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).

thf(334,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Type_Otype_OAtom @ ( B @ ( A @ c_Type_Otype_Otype__case ) ) ) )
      = ( C @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(151,axiom,
    v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

thf(561,plain,
    v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( c_Lambda_Olift @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).

thf(252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( c_Lambda_Olift @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(69,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(361,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(183,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(625,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

thf(522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(52,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).

thf(324,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

thf(285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

thf(519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).

thf(317,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(179,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).

thf(615,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

thf(403,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

thf(356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(167,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).

thf(593,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OVar @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ ( D @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).

thf(610,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ ( D @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).

thf(328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

thf(225,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

thf(537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

thf(642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(189,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

thf(637,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

thf(489,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(193,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(647,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(130,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ ( D @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_1) ).

thf(515,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ ( D @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).

thf(457,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).

thf(569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

thf(503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(173,axiom,
    v_T_Ha______ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_ia______ @ ( v_ea______ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).

thf(605,plain,
    v_T_Ha______ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_ia______ @ ( v_ea______ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(47,axiom,
    ( v_rs____
    = ( tc_Lambda_OdB @ ( v_as____ @ ( v_a____ @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_0) ).

thf(311,plain,
    ( v_rs____
    = ( tc_Lambda_OdB @ ( v_as____ @ ( v_a____ @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(143,axiom,
    v_T____ @ ( v_u____ @ ( v_e____ @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).

thf(541,plain,
    v_T____ @ ( v_u____ @ ( v_e____ @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

thf(398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(150,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

thf(558,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(163,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

thf(586,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(201,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).

thf(662,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(61,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).

thf(343,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(15,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(237,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

thf(298,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

thf(513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

thf(296,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).

thf(601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(162,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).

thf(584,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(152,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).

thf(562,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
        = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).

thf(423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
        = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(159,axiom,
    v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).

thf(579,plain,
    v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

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

thf(204,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Lambda_OdB_OAbs @ ( B @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).

thf(545,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Lambda_OdB_OAbs @ ( B @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

thf(259,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

thf(413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(80,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

thf(391,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

thf(445,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

thf(382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).

thf(313,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

thf(498,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(64,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).

thf(350,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(86,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( c_Lambda_Olift @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).

thf(406,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( c_Lambda_Olift @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( tc_Type_Otype @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( D @ c_Type_Otype_OAtom @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).

thf(419,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( D @ c_Type_Otype_OAtom @ ( C @ ( B @ c_Type_Otype_Otype__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(12,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).

thf(230,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( F @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( F @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(154,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( D @ ( E @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_Type_Otypings ) ) )
      | ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

thf(567,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( D @ ( E @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_Type_Otypings ) ) )
      | ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(19,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

thf(245,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).

thf(303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otype_Otype__case ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).

thf(599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otype_Otype__case ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(127,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
      = ( D @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).

thf(509,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
      = ( D @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).

thf(649,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(78,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
      = ( D @ ( C @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).

thf(387,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__case ) ) ) ) )
      = ( D @ ( C @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(120,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).

thf(494,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).

thf(631,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(140,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
      = ( D @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).

thf(535,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OVar @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
      = ( D @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

thf(483,plain,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( A @ c_Type_Osko__Type__Xtype__induct__1__1 )
       != ( C @ ( B @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_0) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( A @ c_Type_Osko__Type__Xtype__induct__1__1 )
       != ( C @ ( B @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).

thf(330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(107,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

thf(462,plain,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

thf(345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(148,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( C @ c_Type_Otypings ) ) )
      | ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Type_Otype @ ( tc_Type_Otype @ ( B @ ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).

thf(552,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( C @ c_Type_Otypings ) ) )
      | ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Type_Otype @ ( tc_Type_Otype @ ( B @ ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).

thf(455,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

thf(608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).

thf(394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( D @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).

thf(267,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( D @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).

thf(438,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( E @ c_Lambda_OdB_OAbs @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(198,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) )
      = ( E @ ( D @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) @ ( E @ ( C @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).

thf(658,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) )
      = ( E @ ( D @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) @ ( E @ ( C @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(17,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).

thf(241,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( D @ ( D @ ( E @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).

thf(653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(112,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).

thf(473,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Type_Otype_OAtom @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) )
      = ( C @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).

thf(426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Type_Otype_OAtom @ ( B @ ( A @ c_Type_Otype_Otype__rec ) ) ) )
      = ( C @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(165,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).

thf(589,plain,
    v_n____ = v_i____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(138,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).

thf(531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

thf(548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

thf(617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(3,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( tc_Type_Otype @ ( F @ ( C @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Osubst @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).

thf(209,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( tc_Type_Otype @ ( F @ ( C @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) )
      | ( E @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Osubst @ c_COMBC ) ) ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ c_List_Omap ) ) ) @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
      = ( A @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

thf(487,plain,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
      = ( A @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(160,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).

thf(580,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).

thf(263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

thf(370,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(124,axiom,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

thf(502,plain,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Lambda_OdB_OAbs @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( tc_Type_Otype @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).

thf(463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Lambda_OdB_OAbs @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( tc_Type_Otype @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(338,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( c_Lambda_Olift @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(68,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
      = ( E @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( D @ ( C @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).

thf(359,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ c_Lambda_OdB_OAbs @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
      = ( E @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( D @ ( C @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(111,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).

thf(470,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

thf(576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).

thf(336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(178,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
      | ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).

thf(613,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
      | ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

thf(571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(168,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
      = ( F @ ( E @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).

thf(595,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) )
      = ( F @ ( E @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OdB__rec ) ) ) ) @ ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(177,axiom,
    v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

thf(612,plain,
    v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).

thf(450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

thf(539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_Type_Osko__Type__Xtype__induct__1__1 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_2) ).

thf(524,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_Type_Osko__Type__Xtype__induct__1__1 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(7,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(218,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).

thf(368,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).

thf(250,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Lambda_OdB_OAbs ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).

thf(465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Lambda_OdB_OAbs ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

thf(517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

thf(319,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(187,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( tc_Type_Otype @ ( A @ ( E @ ( F @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( F @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).

thf(632,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( tc_Type_Otype @ ( A @ ( E @ ( F @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( F @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).

thf(401,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

thf(433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( A @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_a____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( v_as____ @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).

thf(667,plain,
    ! [A: $i] :
      ( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( v_T_H____ @ ( A @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( v_a____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( v_as____ @ ( tc_Type_Otype @ ( v_T____ @ ( v_i____ @ ( v_e____ @ c_Type_Oshift ) ) ) @ c_Type_Otypings ) ) )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).

thf(478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).

thf(214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
     != ( C @ c_Type_Otype_OAtom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).

thf(620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
     != ( C @ c_Type_Otype_OAtom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

thf(447,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).

thf(315,plain,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).

thf(273,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).

thf(373,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(172,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).

thf(603,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( F @ ( E @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Lambda_OdB_OdB__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(153,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( tc_Type_Otype @ ( B @ ( E @ ( F @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( F @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).

thf(564,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( tc_Type_Otype @ ( B @ ( E @ ( F @ c_Type_Oshift ) ) ) @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( F @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).

thf(305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_fequal @ c_Predicate_Oconversep ) ) )
      = ( A @ c_fequal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).

thf(326,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_fequal @ c_Predicate_Oconversep ) ) )
      = ( A @ c_fequal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(16,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(239,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

thf(506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

thf(664,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(188,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).

thf(635,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(35,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(283,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

thf(332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

thf(644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OVar )
        = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

thf(459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OVar )
        = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(33,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( F @ ( A @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).

thf(277,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( F @ ( A @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

thf(442,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).

thf(354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).

thf(309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Type_Otyping @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( A @ c_Type_Osko__Type__Xtype__induct__1__1 )
       != ( C @ ( B @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_1) ).

thf(639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( A @ c_Type_Osko__Type__Xtype__induct__1__1 )
       != ( C @ ( B @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(222,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(121,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
      = ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).

thf(496,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
      = ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(13,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(232,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(254,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(227,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(888,plain,
    $false,
    inference(e,[status(thm)],[629,347,468,234,555,352,408,582,276,379,597,440,655,511,385,533,550,500,340,288,301,436,651,257,389,587,542,421,606,416,261,216,475,591,376,623,211,485,574,480,280,293,396,660,243,428,265,527,206,307,452,248,661,270,529,220,366,334,561,252,361,625,522,324,285,519,317,615,403,356,593,610,328,225,537,642,526,637,489,647,515,457,569,503,605,311,541,398,558,586,662,343,237,298,513,296,601,584,562,423,579,204,545,259,413,391,445,382,313,498,350,406,419,230,567,245,303,599,509,649,387,494,631,535,483,626,330,462,345,552,455,608,394,267,438,658,241,653,473,426,589,531,548,617,209,487,580,263,370,502,463,338,359,470,576,336,613,571,595,612,450,539,524,218,368,250,465,517,319,632,401,290,433,667,478,214,620,447,315,273,373,603,564,305,326,239,506,664,635,283,332,644,459,277,442,354,309,639,222,496,232,254,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL786-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40  % Computer : n008.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Fri Sep 25 23:34:57 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.98/1.36  % [INFO] 	 Parsing done (375ms). 
% 1.98/1.37  % [INFO] 	 Running in sequential loop mode. 
% 3.01/1.77  % [INFO] 	 eprover registered as external prover. 
% 3.01/1.78  % [INFO] 	 Scanning for conjecture ... 
% 3.50/1.97  % [INFO] 	 Found a conjecture (or negated_conjecture) and 496 axioms. Running axiom selection ... 
% 4.47/2.19  % [INFO] 	 Axiom selection finished. Selected 202 axioms (removed 294 axioms). 
% 5.26/2.37  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.65/2.40  % [INFO] 	 Type checking passed. 
% 5.65/2.41  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 16.79/5.07  % External prover 'e' found a proof!
% 16.79/5.07  % [INFO] 	 Killing All external provers ... 
% 16.79/5.07  % Time passed: 4530ms (effective reasoning time: 3687ms)
% 16.79/5.07  % Axioms used in derivation (202): cls_map_Osimps_I2_J_0, cls_type_Orecs_I2_J_0, cls_Nil__is__map__conv_1, cls_dB_Osplit_0, cls_dB_Orecs_I1_J_0, cls_MI1_0, cls_subst__lt_0, cls_subst__map_0, cls_dB_Osimps_I6_J_0, cls_apps__eq__Abs__conv_0, cls_lift_Osimps_I2_J_0, cls_subst__App_0, cls_Cons__step1__Cons_0, cls_Var__eq__apps__conv_1, cls_subst__eq_0, cls_COMBC__def_0, cls_dB_Osimps_I8_J_0, cls_termi__implies__IT_0, cls_type_Osimps_I3_J_0, cls_typing__elims_I3_J_0, cls_subject__reduction_0, cls_list_Oinject_0, cls_conversepD_0, cls_liftn_Osimps_I2_J_0, cls_CHAINED_0, cls_var__app__typesE_0, cls_Cons__eq__map__conv_3, cls_accp__downwards_0, cls_MI2_0, cls_substn__subst__0_0, cls_rtrancl__beta__Abs_0, cls_uIT_0, cls_not__Cons__self2_0, cls_app__Var__IT_0, cls_type_Osimps_I4_J_0, cls_dB_Osimps_I12_J_0, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_dB_Osplit__asm_0, cls_substn_Osimps_I1_J_2, cls_type_Osplit__asm_1, cls_head__Var__reduction_1, cls_rtranclp__trans_0, cls_Cons__step1__Cons_5, cls_beta_0, cls_COMBB__def_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_Nil__is__map__conv_0, cls_Abs_0, cls_dB_Orecs_I3_J_0, cls_gr0I_0, cls_lift__type_0, cls_foldr_Osimps_I1_J_0, cls_nat__less__cases_0, cls_Var__apps__eq__Var__apps__conv_0, cls_gr__implies__not0_0, cls_shift__eq_0, cls_substn__subst__n_0, cls_dB_Osimps_I3_J_0, cls_linorder__neqE__nat_0, cls_subst__Var_2, cls_Var_I2_J_0, cls_liftn__0_0, cls_Cons_0, cls_Var__apps__eq__Var__apps__conv_1, cls_typing__elims_I2_J_0, cls_typing__elims_I3_J_1, cls_Var__eq__apps__conv_2, cls_dB_Osimps_I11_J_0, cls_App__eq__foldl__conv_0, cls_map__eq__Cons__conv_3, cls_dB_Osimps_I4_J_0, cls_Cons__step1__Cons_1, cls_type_Osimps_I5_J_0, cls_type_Osimps_I2_J_1, cls_typing__elims_I1_J_0, cls_map__is__Nil__conv_0, cls_var__app__types_0, cls_Var__IT_0, cls_Cons__step1__Cons_3, cls_subject__reduction_H_0, cls_var__app__typesE_1, cls_Var_I3_J_0, cls_converse__rtranclp__into__rtranclp_0, cls_list__app__typeD_1, cls_dB_Osimps_I10_J_0, cls_App_0, cls_apps__preserves__betas_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_foldl__Cons_0, cls_nT_0, cls_True_0, cls_head__Var__reduction_0, cls_IT__implies__termi_0, cls_apps__eq__Abs__conv_2, cls_lift__map_0, cls_uT_0, cls_type_Osplit_0, cls_not__Cons__self_0, cls_conversep__conversep_0, cls_dB_Osimps_I1_J_0, cls_Abs__App__neq__Var__apps_0, cls_rtrancl__beta__App_0, cls_type_Osimps_I1_J_0, cls_subst__Var_1, cls_Cons__step1__Cons_2, cls_rtrancl__beta__AppL_0, cls_neq__Nil__conv_1, cls_Nitpick_Ortranclp__def_1, cls_type_Osimps_I2_J_0, cls_type_Orecs_I1_J_0, cls_neq0__conv_1, cls_not__Nil__step1_0, cls_foldr_Osimps_I2_J_0, cls_apps__eq__Abs__conv_1, cls_type_Osplit_1, cls_lift__preserves__beta_0, cls_lifts__IT_0, cls_Var__apps__neq__Abs__apps_0, cls_subst__lemma_0, cls_Cons__step1__Cons_4, cls_less__not__refl_0, cls_conversep_Ointros_0, cls_dB_Osimps_I2_J_1, cls_accp__downwards__aux_0, cls_var__app__types_1, cls_dB_Osplit__asm_2, cls_lift__preserves__beta_H_0, cls_list__app__typeD_0, cls_substn_Osimps_I2_J_0, cls_rtranclp_Ortrancl__refl_0, cls_map__is__Nil__conv_1, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_abs_0, cls_accp__downward_0, cls_Abs__eq__apps__conv_2, cls_dB_Orecs_I2_J_0, cls_rtranclp__idemp_0, cls_list__app__typeE_1, cls_typing_OVar_0, cls_dB_Osplit_1, cls_lift__IT_0, cls_IT_OVar_0, cls_Var_I4_J_0, cls_apps__eq__tail__conv_0, cls_accp_Ocases_0, cls_typing__elims_I2_J_1, cls_apps__preserves__beta2_0, cls_liftn_Osimps_I1_J_0, cls_list__app__typeI_0, cls_apps__preserves__beta_0, cls_App__eq__foldl__conv_4, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_Abs__eq__apps__conv_0, cls_list_Oinject_1, cls_substn_Osimps_I1_J_1, cls_type__induct_2, cls_not__less0_0, cls_dB_Osimps_I5_J_0, cls_conversep__eq_0, cls_subst__Var__IT_0, cls_shift__gt_0, cls_type__induct_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_foldl__Nil_0, cls_Lambda_0, cls_type_Osplit__asm_0, cls_list__app__typeE_0, cls_lift_Osimps_I1_J_0, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_that_0, cls_dB_Osplit__asm_1, cls_lift__types_0, cls_dB_Osplit_2, cls_type__induct_1, cls_subst__lift_0, cls_substs__lemma_0, cls_Abs__eq__apps__conv_1, cls_subst__preserves__beta2_0, cls_conversep__iff_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_subst__preserves__beta2_H_0, cls_conversep_Ocases_0, cls_dB_Osimps_I9_J_0, cls_list_Osimps_I2_J_0, cls_rtranclp__converseD_0, cls_rtranclp__converseI_0, cls_double__induction__lemma_0, cls_rtrancl__beta__AppR_0, cls_type_Osimps_I6_J_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0
% 16.79/5.07  % No. of inferences in proof: 407
% 16.79/5.07  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4530 ms resp. 3687 ms w/o parsing
% 17.44/5.29  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.84/5.30  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------