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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL764-1 : 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 : n009.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 07:52:47 AM UTC 2026

% Result   : Unsatisfiable 11.30s 4.02s
% Output   : Refutation 12.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  329
% Syntax   : Number of formulae    :  659 ( 249 unt;   0 typ;   0 def)
%            Number of atoms       : 1265 ( 432 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 7630 ( 528   ~; 606   |;   0   &;6496   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  111 ( 109 usr;   7 con; 0-5 aty)
%            Number of variables   : 2078 (   0   ^;2078   !;   0   ?;2078   :)

% Comments : 
%------------------------------------------------------------------------------
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_List_Olist_ONil_decl,type,
    c_List_Olist_ONil: $i > $i ).

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

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

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

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

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

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

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

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

thf(c_List_Otake_decl,type,
    c_List_Otake: $i > $i > $i > $i ).

thf(c_List_Otl_decl,type,
    c_List_Otl: $i > $i > $i ).

thf(c_Suc_decl,type,
    c_Suc: $i > $i ).

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

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

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

thf(c_List_Orotate_decl,type,
    c_List_Orotate: $i > $i > $i > $i ).

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

thf(c_List_Olist_Olist__rec_decl,type,
    c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).

thf(c_List_Olist__all2_decl,type,
    c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).

thf(c_List_Ofilter_decl,type,
    c_List_Ofilter: $i > $i > $i > $i ).

thf(c_List_Oappend_decl,type,
    c_List_Oappend: $i > $i > $i > $i ).

thf(c_List_Odistinct_decl,type,
    c_List_Odistinct: $i > $i > $o ).

thf(c_List_Odrop_decl,type,
    c_List_Odrop: $i > $i > $i > $i ).

thf(c_List_Orev_decl,type,
    c_List_Orev: $i > $i > $i ).

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

thf(c_List_Olinorder__class_Osorted_decl,type,
    c_List_Olinorder__class_Osorted: $i > $i > $o ).

thf(c_List_OdropWhile_decl,type,
    c_List_OdropWhile: $i > $i > $i > $i ).

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

thf(c_List_Oremove1_decl,type,
    c_List_Oremove1: $i > $i > $i > $i ).

thf(c_List_Olist__update_decl,type,
    c_List_Olist__update: $i > $i > $i > $i > $i ).

thf(c_List_Osplice_decl,type,
    c_List_Osplice: $i > $i > $i > $i ).

thf(c_List_Oremdups_decl,type,
    c_List_Oremdups: $i > $i > $i ).

thf(c_List_Onull_decl,type,
    c_List_Onull: $i > $i > $o ).

thf(c_List_Olist__all_decl,type,
    c_List_Olist__all: $i > $i > $i > $o ).

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

thf(c_List_Olist_Olist__case_decl,type,
    c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).

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

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

thf(c_List_Oconcat__map_decl,type,
    c_List_Oconcat__map: $i > $i > $i > $i > $i ).

thf(c_List_Orotate1_decl,type,
    c_List_Orotate1: $i > $i > $i ).

thf(c_List_Omember_decl,type,
    c_List_Omember: $i > $i > $i > $o ).

thf(c_List_Osublist_decl,type,
    c_List_Osublist: $i > $i > $i > $i ).

thf(c_List_Olist__ex_decl,type,
    c_List_Olist__ex: $i > $i > $i > $o ).

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

thf(c_List_Olinorder__class_Osort__key_decl,type,
    c_List_Olinorder__class_Osort__key: $i > $i > $i > $i > $i ).

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

thf(c_List_Ohd_decl,type,
    c_List_Ohd: $i > $i > $i ).

thf(c_List_Olistrelp_decl,type,
    c_List_Olistrelp: $i > $i > $i > $i > $o ).

thf(v_sko__List__Xremdups__Xinduct__2_decl,type,
    v_sko__List__Xremdups__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlist__Xinduct__2_decl,type,
    v_sko__List__Xlist__Xinduct__2: $i > $i ).

thf(v_sko__List__XdropWhile__Xinduct__2_decl,type,
    v_sko__List__XdropWhile__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlist__Xinduct__1_decl,type,
    v_sko__List__Xlist__Xinduct__1: $i > $i ).

thf(v_sko__List__Xtl__Xinduct__2_decl,type,
    v_sko__List__Xtl__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlist__update__Xinduct__2_decl,type,
    v_sko__List__Xlist__update__Xinduct__2: $i > $i ).

thf(c_List_Osko__List__Xrev__induct__1__2_decl,type,
    c_List_Osko__List__Xrev__induct__1__2: $i > $i > $i ).

thf(v_sko__List__Xdrop__Xinduct__2_decl,type,
    v_sko__List__Xdrop__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlistsp__Xcases__2_decl,type,
    v_sko__List__Xlistsp__Xcases__2: $i > $i > $i ).

thf(v_sko__List__Xtl__Xinduct__1_decl,type,
    v_sko__List__Xtl__Xinduct__1: $i > $i ).

thf(c_List_Osko__List__Xrev__induct__1__1_decl,type,
    c_List_Osko__List__Xrev__induct__1__1: $i > $i > $i ).

thf(v_sko__List__Xdrop__Xinduct__1_decl,type,
    v_sko__List__Xdrop__Xinduct__1: $i > $i ).

thf(v_sko__List__Xlist__Xinducts__2_decl,type,
    v_sko__List__Xlist__Xinducts__2: $i > $i ).

thf(v_sko__List__Xzip__Xinduct__1_decl,type,
    v_sko__List__Xzip__Xinduct__1: $i > $i ).

thf(v_sko__List__Xzip__Xinduct__2_decl,type,
    v_sko__List__Xzip__Xinduct__2: $i > $i ).

thf(v_sko__List__Xrev__Xinduct__2_decl,type,
    v_sko__List__Xrev__Xinduct__2: $i > $i ).

thf(v_sko__List__Xrev__Xinduct__1_decl,type,
    v_sko__List__Xrev__Xinduct__1: $i > $i ).

thf(v_sko__List__Xlistsp__Xinduct__1_decl,type,
    v_sko__List__Xlistsp__Xinduct__1: $i > $i > $i ).

thf(v_sko__List__Xlistsp__Xinduct__2_decl,type,
    v_sko__List__Xlistsp__Xinduct__2: $i > $i > $i ).

thf(v_sko__List__Xremove1__Xinduct__1_decl,type,
    v_sko__List__Xremove1__Xinduct__1: $i > $i ).

thf(v_sko__List__Xremove1__Xinduct__2_decl,type,
    v_sko__List__Xremove1__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlistset__Xinduct__2_decl,type,
    v_sko__List__Xlistset__Xinduct__2: $i > $i ).

thf(v_sko__List__Xhd__Xinduct__1_decl,type,
    v_sko__List__Xhd__Xinduct__1: $i > $i ).

thf(v_sko__List__Xhd__Xinduct__2_decl,type,
    v_sko__List__Xhd__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlistsp__Xcases__1_decl,type,
    v_sko__List__Xlistsp__Xcases__1: $i > $i > $i ).

thf(c_List_Ofiltermap_decl,type,
    c_List_Ofiltermap: $i > $i > $i > $i > $i ).

thf(v_sko__List__Xconcat__Xinduct__2_decl,type,
    v_sko__List__Xconcat__Xinduct__2: $i > $i ).

thf(v_sko__List__Xtake__Xinduct__2_decl,type,
    v_sko__List__Xtake__Xinduct__2: $i > $i ).

thf(v_sko__List__XremoveAll__Xinduct__1_decl,type,
    v_sko__List__XremoveAll__Xinduct__1: $i > $i ).

thf(v_sko__List__XremoveAll__Xinduct__2_decl,type,
    v_sko__List__XremoveAll__Xinduct__2: $i > $i ).

thf(v_sko__List__Xset__Xinduct__2_decl,type,
    v_sko__List__Xset__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlistsp__Xinducts__1_decl,type,
    v_sko__List__Xlistsp__Xinducts__1: $i > $i > $i ).

thf(v_sko__List__Xlistsp__Xinducts__2_decl,type,
    v_sko__List__Xlistsp__Xinducts__2: $i > $i > $i ).

thf(v_sko__List__Xlist__Xinducts__1_decl,type,
    v_sko__List__Xlist__Xinducts__1: $i > $i ).

thf(v_sko__List__Xlast__Xinduct__1_decl,type,
    v_sko__List__Xlast__Xinduct__1: $i > $i ).

thf(v_sko__List__Xlast__Xinduct__2_decl,type,
    v_sko__List__Xlast__Xinduct__2: $i > $i ).

thf(v_sko__List__Xlistsum__Xinduct__2_decl,type,
    v_sko__List__Xlistsum__Xinduct__2: $i > $i ).

thf(v_sko__List__Xfoldl__Xinduct__1_decl,type,
    v_sko__List__Xfoldl__Xinduct__1: $i > $i ).

thf(v_sko__List__Xfoldl__Xinduct__2_decl,type,
    v_sko__List__Xfoldl__Xinduct__2: $i > $i ).

thf(v_sko__List__Xset__Xinduct__1_decl,type,
    v_sko__List__Xset__Xinduct__1: $i > $i ).

thf(c_List_Olist__inter_decl,type,
    c_List_Olist__inter: $i > $i > $i > $i ).

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

thf(c_List_Osko__List__Xin__listsp__conv__set__1__1_decl,type,
    c_List_Osko__List__Xin__listsp__conv__set__1__1: $i > $i > $i > $i ).

thf(v_sko__List__Xlist__update__Xinduct__1_decl,type,
    v_sko__List__Xlist__update__Xinduct__1: $i > $i ).

thf(v_sko__List__Xsplice__Xinduct__2_decl,type,
    v_sko__List__Xsplice__Xinduct__2: $i > $i ).

thf(c_Map_Omap__upds_decl,type,
    c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).

thf(v_sko__List__Xlistset__Xinduct__1_decl,type,
    v_sko__List__Xlistset__Xinduct__1: $i > $i ).

thf(v_sko__List__Xlistsum__Xinduct__1_decl,type,
    v_sko__List__Xlistsum__Xinduct__1: $i > $i ).

thf(v_sko__List__Xmap__Xinduct__2_decl,type,
    v_sko__List__Xmap__Xinduct__2: $i > $i ).

thf(v_sko__List__Xsplice__Xinduct__1_decl,type,
    v_sko__List__Xsplice__Xinduct__1: $i > $i ).

thf(v_sko__List__Xdistinct__Xinduct__2_decl,type,
    v_sko__List__Xdistinct__Xinduct__2: $i > $i ).

thf(v_sko__List__XtakeWhile__Xinduct__1_decl,type,
    v_sko__List__XtakeWhile__Xinduct__1: $i > $i ).

thf(v_sko__List__XtakeWhile__Xinduct__2_decl,type,
    v_sko__List__XtakeWhile__Xinduct__2: $i > $i ).

thf(v_sko__List__Xremdups__Xinduct__1_decl,type,
    v_sko__List__Xremdups__Xinduct__1: $i > $i ).

thf(v_sko__List__Xconcat__Xinduct__1_decl,type,
    v_sko__List__Xconcat__Xinduct__1: $i > $i ).

thf(v_sko__List__Xmap__Xinduct__1_decl,type,
    v_sko__List__Xmap__Xinduct__1: $i > $i ).

thf(v_sko__List__XdropWhile__Xinduct__1_decl,type,
    v_sko__List__XdropWhile__Xinduct__1: $i > $i ).

thf(v_sko__List__Xdistinct__Xinduct__1_decl,type,
    v_sko__List__Xdistinct__Xinduct__1: $i > $i ).

thf(v_sko__List__Xtake__Xinduct__1_decl,type,
    v_sko__List__Xtake__Xinduct__1: $i > $i ).

thf(138,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(314,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).

thf(1036,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ v_sko__List__Xmap__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).

thf(1024,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ v_sko__List__Xmap__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(365,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xfoldl__Xinduct__2 @ ( A @ v_sko__List__Xfoldl__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl_Oinduct_1) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xfoldl__Xinduct__2 @ ( A @ v_sko__List__Xfoldl__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(81,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Otake ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).

thf(518,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Otake ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) )
        = ( C @ ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) @ ( C @ ( B @ c_List_Ohd ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc_0) ).

thf(962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) )
        = ( C @ ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) @ ( C @ ( B @ c_List_Ohd ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oconcat__map ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).

thf(777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oconcat__map ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ c_List_Omap ) ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__sort__key_0) ).

thf(666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) @ ( B @ c_List_Omap ) ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).

thf(352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).

thf(628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(1031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(289,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(977,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)],[289]) ).

thf(301,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Oinduct_0) ).

thf(1005,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_1) ).

thf(683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_0) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(329,axiom,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(1068,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_2) ).

thf(994,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(182,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ ( B @ ( A @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_2) ).

thf(741,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ ( B @ ( A @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ v_sko__List__Xlast__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Oinduct_1) ).

thf(873,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ v_sko__List__Xlast__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).

thf(379,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).

thf(677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( A @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).

thf(511,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).

thf(861,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(163,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).

thf(698,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xset__Xinduct__2 @ ( A @ v_sko__List__Xset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set_Oinduct_1) ).

thf(898,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xset__Xinduct__2 @ ( A @ v_sko__List__Xset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_List_Olistsp ) ) )
      | ~ ( C @ ( D @ ( B @ c_List_Olistsp ) ) )
      | ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).

thf(1001,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_List_Olistsp ) ) )
      | ~ ( C @ ( D @ ( B @ c_List_Olistsp ) ) )
      | ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).

thf(841,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_2) ).

thf(1046,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__filter_0) ).

thf(389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(372,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).

thf(504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(9,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__map_0) ).

thf(344,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Osko__List__Xin__listsp__conv__set__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).

thf(934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Osko__List__Xin__listsp__conv__set__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I1_J_0) ).

thf(949,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(58,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_1) ).

thf(460,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(216,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(817,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)],[216]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).

thf(853,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(41,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).

thf(421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
        = ( C @ c_List_Olist_ONil ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).

thf(881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
        = ( C @ c_List_Olist_ONil ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

thf(416,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(71,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(492,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)],[71]) ).

thf(113,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).

thf(591,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).

thf(443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(129,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(623,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)],[129]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ v_sko__List__XremoveAll__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Oinduct_1) ).

thf(834,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ v_sko__List__XremoveAll__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( B @ ( A @ v_sko__List__Xlistsp__Xcases__1 ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_1) ).

thf(821,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( B @ ( A @ v_sko__List__Xlistsp__Xcases__1 ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(66,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(480,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)],[66]) ).

thf(64,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(475,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)],[64]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ v_sko__List__Xconcat__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).

thf(1020,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ v_sko__List__Xconcat__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(11,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).

thf(348,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).

thf(687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).

thf(734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Oremdups ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).

thf(956,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Oremdups ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).

thf(849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).

thf(602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ v_sko__List__Xzip__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).

thf(766,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ v_sko__List__Xzip__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(56,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).

thf(452,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).

thf(920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(546,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(24,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(381,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)],[24]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( E @ ( C @ c_List_Oappend ) ) @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).

thf(534,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( E @ ( C @ c_List_Oappend ) ) @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).

thf(714,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(324,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( F @ c_List_Oappend ) ) @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).

thf(1057,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( F @ c_List_Oappend ) ) @ ( E @ ( E @ ( E @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
      = ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).

thf(942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
      = ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).

thf(439,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(3,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(334,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(184,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( E @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( F @ ( E @ ( D @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).

thf(746,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( E @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( F @ ( E @ ( D @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(45,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
      = ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).

thf(429,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
      = ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).

thf(788,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(215,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).

thf(815,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).

thf(407,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(131,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_Olist_Olist__case ) ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).

thf(630,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_Olist_Olist__case ) ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).

thf(916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).

thf(435,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
      = ( A @ ( B @ c_List_Ohd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).

thf(757,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
      = ( A @ ( B @ c_List_Ohd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(97,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(551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).

thf(710,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(288,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orotate1 ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).

thf(974,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orotate1 ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_3) ).

thf(847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(566,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_2) ).

thf(522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).

thf(830,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__take_0) ).

thf(650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(125,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).

thf(615,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ v_sko__List__Xtake__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_1) ).

thf(1064,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ v_sko__List__Xtake__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(175,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(725,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)],[175]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).

thf(356,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(114,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(593,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)],[114]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(869,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(294,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).

thf(989,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).

thf(857,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).

thf(980,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).

thf(403,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(62,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).

thf(471,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_0) ).

thf(884,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).

thf(1028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(85,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).

thf(526,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).

thf(637,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).

thf(489,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).

thf(554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(187,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xdrop__Xinduct__2 @ ( A @ v_sko__List__Xdrop__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop_Oinduct_1) ).

thf(753,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xdrop__Xinduct__2 @ ( A @ v_sko__List__Xdrop__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__rev_1) ).

thf(679,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_1) ).

thf(1039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinducts__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
      = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__filter_0) ).

thf(393,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
      = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(181,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orotate1 ) )
        = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orotate1 ) )
        = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(142,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(654,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)],[142]) ).

thf(105,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(569,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)],[105]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xrev__Xinduct__2 @ ( A @ v_sko__List__Xrev__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Oinduct_1) ).

thf(779,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xrev__Xinduct__2 @ ( A @ v_sko__List__Xrev__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ v_sko__List__XdropWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).

thf(1060,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ v_sko__List__XdropWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(321,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

thf(1050,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(292,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).

thf(984,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(259,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(911,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)],[259]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_0) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
        = ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).

thf(360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
        = ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( A @ ( B @ c_List_Olistsp ) ) )
      | ( A
        = ( t_a @ c_List_Olist_ONil ) )
      | ( A
        = ( t_a @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_0) ).

thf(805,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ ( A @ ( B @ c_List_Olistsp ) ) )
      | ( A
        = ( t_a @ c_List_Olist_ONil ) )
      | ( A
        = ( t_a @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlistsp__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__take_0) ).

thf(541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(323,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(1054,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).

thf(398,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(100,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(558,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)],[100]) ).

thf(310,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(1026,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(196,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xrev__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Oinduct_0) ).

thf(773,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xrev__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(206,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(794,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)],[206]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).

thf(662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).

thf(718,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Oinduct_0) ).

thf(888,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).

thf(906,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).

thf(412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

thf(425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(79,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(513,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(824,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(159,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).

thf(689,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).

thf(965,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(750,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).

thf(819,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Odrop ) ) )
      = ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc_0) ).

thf(423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Odrop ) ) )
      = ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xdrop__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop_Oinduct_0) ).

thf(732,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xdrop__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Oinduct_0) ).

thf(843,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ v_sko__List__XtakeWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_1) ).

thf(1007,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ v_sko__List__XtakeWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(244,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
      | ( C = D )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).

thf(875,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( D @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( F @ ( F @ ( F @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( E @ c_ListOrder_Ostep1 ) ) ) )
      | ( C = D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).

thf(826,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(28,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
      = ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).

thf(391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
      = ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(122,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(611,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(73,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(498,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)],[73]) ).

thf(4,axiom,
    tc_nat @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(335,plain,
    tc_nat @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).

thf(350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(151,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(672,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_List_Omember ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).

thf(445,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_List_Omember ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).

thf(936,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(900,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(155,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
      | ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).

thf(681,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
      | ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
      = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

thf(784,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
      = ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(40,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ c_List_Orev ) @ ( D @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).

thf(419,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ c_List_Orev ) @ ( D @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

thf(863,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_0) ).

thf(764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).

thf(604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Suc @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(320,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_0) ).

thf(1048,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(180,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(736,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)],[180]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(377,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) )
        = ( C @ c_List_Olist_ONil ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sort__key_Osimps_I1_J_0) ).

thf(996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) )
        = ( C @ c_List_Olist_ONil ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(250,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(890,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)],[250]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).

thf(799,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).

thf(621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).

thf(895,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xfoldl__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl_Oinduct_0) ).

thf(1022,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xfoldl__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(1,negated_conjecture,
    ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(330,plain,
    ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).

thf(700,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(82,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ ( E @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( E @ ( D @ ( C @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).

thf(520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ ( E @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( E @ ( D @ ( C @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(462,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

thf(932,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(281,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(959,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(768,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(318,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(1044,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)],[318]) ).

thf(328,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).

thf(1066,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
      | ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

thf(455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(305,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).

thf(1015,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
        = ( C @ ( A @ c_List_Ohd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).

thf(986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
        = ( C @ ( A @ c_List_Ohd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(563,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(232,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(851,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)],[232]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(431,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(264,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Lambda_Olift ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(922,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Lambda_Olift ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(144,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).

thf(658,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ c_Suc @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( C @ ( E @ ( D @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Osublist ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__sublistI_0) ).

thf(473,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Osublist ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

thf(722,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).

thf(1034,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).

thf(675,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( C @ ( D @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).

thf(589,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( E @ ( D @ c_List_Orev ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( C @ ( D @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ v_sko__List__Xlist__update__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Oinduct_1) ).

thf(944,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ v_sko__List__Xlist__update__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).

thf(927,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(342,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xremdups__Xinduct__2 @ ( A @ v_sko__List__Xremdups__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Oinduct_1) ).

thf(1018,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xremdups__Xinduct__2 @ ( A @ v_sko__List__Xremdups__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Onull ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_1) ).

thf(836,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Onull ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(139,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(648,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)],[139]) ).

thf(69,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(487,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)],[69]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).

thf(617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
      = ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).

thf(516,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
      = ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).

thf(414,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).

thf(712,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).

thf(1003,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(580,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(234,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).

thf(855,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
        = ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).

thf(791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
        = ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__filter_0) ).

thf(441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) @ c_List_Otl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__tl_0) ).

thf(338,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Otake ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) @ c_List_Otl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(107,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).

thf(576,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(94,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).

thf(544,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Orev ) )
      = ( D @ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_0) ).

thf(585,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Orev ) )
      = ( D @ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
      = ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__drop_0) ).

thf(370,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
      = ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(278,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xsplice__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Oinduct_0) ).

thf(951,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xsplice__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xtl__Xinduct__2 @ ( A @ v_sko__List__Xtl__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Oinduct_1) ).

thf(744,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xtl__Xinduct__2 @ ( A @ v_sko__List__Xtl__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(5,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(336,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)],[5]) ).

thf(165,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Odrop ) ) @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).

thf(703,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Odrop ) ) @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( D @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).

thf(656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ ( A @ c_ListOrder_Ostep1 ) ) ) )
      | ( D @ ( D @ ( E @ ( B @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(124,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).

thf(613,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_List_Odistinct ) )
      | ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) @ c_List_Odistinct ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__sort_1) ).

thf(600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_List_Odistinct ) )
      | ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Osort__key ) ) ) @ c_List_Odistinct ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(322,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xhd__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Oinduct_0) ).

thf(1052,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xhd__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(26,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
        = ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).

thf(386,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
        = ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(123,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(612,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(72,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(497,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(859,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(295,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( F @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_ListOrder_Ostep1 ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).

thf(991,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( F @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( D @ ( D @ ( D @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( C @ c_ListOrder_Ostep1 ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_ListOrder_Ostep1 ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).

thf(845,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

thf(450,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
      | ( D @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).

thf(482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
      | ( D @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).

thf(671,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
        = ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).

thf(903,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
        = ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(524,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__Xinducts__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinducts_0) ).

thf(759,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__Xinducts__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

thf(771,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).

thf(363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

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

thf(556,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(268,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(931,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).

thf(539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__1 ) @ c_List_Olist_OCons ) ) @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ c_List_Oappend ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_1) ).

thf(748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__1 ) @ c_List_Olist_OCons ) ) @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ c_List_Oappend ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(326,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).

thf(1062,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).

thf(946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_List_Omember ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).

thf(632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omember ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_List_Omember ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_3) ).

thf(786,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).

thf(961,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(104,axiom,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).

thf(568,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

thf(914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(47,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(433,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)],[47]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).

thf(478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(383,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
      = ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).

thf(832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
      = ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(10,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_Olist_Olist__rec ) ) ) ) )
      = ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).

thf(346,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_Olist_Olist__rec ) ) ) ) )
      = ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(96,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).

thf(549,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(90,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(536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(716,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(298,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xsplice__Xinduct__2 @ ( A @ v_sko__List__Xsplice__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Oinduct_1) ).

thf(999,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xsplice__Xinduct__2 @ ( A @ v_sko__List__Xsplice__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
        = ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).

thf(447,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
        = ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(36,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__tl_0) ).

thf(410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__rev_0) ).

thf(405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(204,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).

thf(790,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(240,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(867,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)],[240]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinducts__2 @ ( A @ v_sko__List__Xlist__Xinducts__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinducts_1) ).

thf(865,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinducts__2 @ ( A @ v_sko__List__Xlist__Xinducts__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(76,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(506,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__drop_0) ).

thf(358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(49,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oconcat__map ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Oconcat__map ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).

thf(437,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oconcat__map ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Oconcat__map ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(253,axiom,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_0) ).

thf(897,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(147,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Odrop ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__map_0) ).

thf(664,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Odrop ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(400,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(221,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(828,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)],[221]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).

thf(635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).

thf(696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xtl__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Oinduct_0) ).

thf(720,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xtl__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

thf(796,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(886,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).

thf(918,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xhd__Xinduct__2 @ ( A @ v_sko__List__Xhd__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Oinduct_1) ).

thf(801,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xhd__Xinduct__2 @ ( A @ v_sko__List__Xhd__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Oinduct_0) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(332,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__map_0) ).

thf(427,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(115,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).

thf(596,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( C @ ( B @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) @ c_List_Odistinct ) )
      | ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__sort_0) ).

thf(528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( C @ ( B @ ( D @ c_List_Olinorder__class_Osort__key ) ) ) @ c_List_Odistinct ) )
      | ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(137,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).

thf(644,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ v_sko__List__Xlistsum__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Oinduct_1) ).

thf(982,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ v_sko__List__Xlistsum__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(160,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(691,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)],[160]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osublist ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sublist__nil_0) ).

thf(871,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osublist ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(501,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
        = ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set_Oinduct_0) ).

thf(839,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__drop_0) ).

thf(354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(303,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(1009,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)],[303]) ).

thf(93,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(543,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all__append_0) ).

thf(639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(188,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).

thf(755,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xremdups__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Oinduct_0) ).

thf(708,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ v_sko__List__Xremdups__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(287,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ v_sko__List__Xlistset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).

thf(972,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ v_sko__List__Xlistset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(61,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).

thf(469,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(273,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).

thf(940,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_1) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( B @ ( C @ c_List_Olistsp ) ) )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( A @ ( C @ v_sko__List__Xlistsp__Xinduct__2 ) @ ( C @ c_List_Olistsp ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).

thf(775,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(1069,plain,
    $false,
    inference(e,[status(thm)],[645,1036,1024,365,893,518,962,777,666,352,628,1031,977,1005,683,730,1068,994,741,873,379,677,878,511,1041,861,698,340,898,1001,841,1046,389,372,504,344,934,949,460,587,619,817,853,421,606,881,416,492,591,443,623,834,821,480,475,924,574,1020,348,687,734,956,660,849,602,766,452,920,546,761,810,381,534,714,1057,942,439,334,746,598,429,788,815,407,630,916,435,757,551,710,974,1012,847,566,484,522,830,578,650,615,1064,725,356,593,869,989,857,980,403,471,884,1028,526,637,489,554,753,679,1039,970,393,738,654,569,779,1060,1050,984,911,938,360,805,541,1054,398,558,1026,530,953,773,794,662,718,888,906,412,425,513,824,689,965,750,819,423,732,843,1007,694,875,826,641,391,611,498,335,350,672,445,936,900,681,784,419,509,863,764,604,1048,736,377,996,890,609,799,621,895,1022,668,330,700,520,462,932,685,959,768,1044,1066,455,1015,986,563,851,431,922,658,473,722,1034,675,589,944,927,342,1018,968,836,648,487,617,516,705,414,712,1003,580,855,791,441,338,576,544,585,370,951,808,744,336,703,656,613,600,1052,386,612,497,859,991,845,450,482,671,903,524,759,771,363,556,931,539,748,1062,946,652,632,786,781,961,813,568,914,433,929,478,383,832,346,549,536,716,999,447,410,405,790,867,865,506,358,437,897,664,400,828,635,532,696,720,796,886,918,801,728,464,332,427,596,528,644,908,982,691,871,501,395,839,803,354,1009,543,639,755,708,972,469,940,1037,775,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL764-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42  % Computer : n009.cluster.edu
% 0.15/0.42  % Model    : x86_64 x86_64
% 0.15/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42  % Memory   : 8046.5625MB
% 0.15/0.42  % OS       : Linux 6.8.0-71-generic
% 0.15/0.42  % CPULimit : 300
% 0.15/0.42  % WCLimit  : 300
% 0.15/0.42  % DateTime : Fri Sep 25 23:30:59 UTC 2026
% 0.15/0.42  % CPUTime  : 
% 0.15/0.42  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
% 0.90/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.90/1.35  % [INFO] 	 Parsing done (338ms). 
% 1.90/1.36  % [INFO] 	 Running in sequential loop mode. 
% 2.83/1.75  % [INFO] 	 eprover registered as external prover. 
% 2.83/1.76  % [INFO] 	 Scanning for conjecture ... 
% 3.32/1.91  % [INFO] 	 Found a conjecture (or negated_conjecture) and 328 axioms. Running axiom selection ... 
% 3.77/2.08  % [INFO] 	 Axiom selection finished. Selected 328 axioms (removed 0 axioms). 
% 4.55/2.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.90/2.30  % [INFO] 	 Type checking passed. 
% 4.90/2.30  % [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 ... 
% 11.30/4.01  % External prover 'e' found a proof!
% 11.30/4.01  % [INFO] 	 Killing All external provers ... 
% 11.30/4.01  % Time passed: 3452ms (effective reasoning time: 2643ms)
% 11.30/4.02  % Axioms used in derivation (328): clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_list_Orecs_I1_J_0, cls_listsp_Oinduct_0, cls_concat_Oinduct_1, cls_rev__swap_1, cls_takeWhile_Oinduct_1, cls_distinct_Oinduct_0, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_dropWhile_Osimps_I1_J_0, cls_Suc__inject_0, cls_Cons__step1__Cons_0, cls_Cons__eq__append__conv_5, cls_remove1_Osimps_I2_J_0, cls_listrelp_OCons_0, cls_list__all__append_1, cls_list__all2__Cons_2, cls_listsum_Oinduct_0, cls_list__update__overwrite_0, cls_list__all_Osimps_I2_J_1, cls_splice_Osimps_I2_J_1, cls_list__all2__eq_1, cls_append__self__conv_0, cls_Suc__n__not__n_0, cls_splice__Cons__Cons_0, cls_take__tl_0, cls_append__step1I_0, clsarity_bool__Lattices_Olower__semilattice, cls_tl_Osimps_I1_J_0, cls_rev__induct_0, cls_map_Oinduct_1, cls_distinct__sort_0, cls_rotate__map_0, cls_rev__singleton__conv_1, cls_drop_Oinduct_1, cls_listsp_Oinduct_3, cls_list_Oinject_0, cls_Cons__eq__map__conv_3, cls_listsp__infI_0, cls_distinct__filter_0, cls_Snoc__step1__SnocD_2, cls_not__Cons__self2_0, cls_remove1__filter__not_0, cls_rev__is__rev__conv_0, cls_not__step1__Nil_0, cls_distinct__rev_1, clsarity_nat__Orderings_Olinorder, cls_list__update__nonempty_1, cls_filter__eq__ConsD_2, cls_zip_Oinduct_0, cls_Cons__step1__Cons_5, cls_list_Osimps_I5_J_0, cls_inf__left__commute_0, cls_sort__key_Osimps_I1_J_0, cls_listsp_ONil_0, cls_inf1E_1, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_list__update_Oinduct_1, cls_eq__Nil__appendI_0, cls_list_Oinduct_1, cls_self__append__conv_0, cls_distinct__sort_1, cls_List_Omember_Osimps_I2_J_0, cls_same__append__eq_0, cls_list__all_Osimps_I2_J_0, cls_inf__commute_0, cls_hd__append_0, cls_filter_Osimps_I2_J_0, cls_append__Cons_0, cls_listset_Oinduct_1, cls_Nil__is__map__conv_0, cls_drop__map_0, cls_foldr_Osimps_I1_J_0, cls_append__eq__append__conv2_4, cls_rev_Oinduct_1, cls_sorted_Osimps_I3_J_1, cls_list__all__rev_0, cls_append1__eq__conv_1, cls_list__all2__rev_1, cls_filter__append_0, cls_splice_Osimps_I2_J_0, cls_sorted__take_0, cls_distinct_Osimps_I2_J_1, cls_list__all2__rev_0, cls_list__all2__Cons_1, cls_distinct_Osimps_I1_J_0, cls_empty__null_0, cls_concat_Oinduct_0, cls_dB_Osimps_I3_J_0, cls_listsp_Oinducts_1, cls_rev__map_0, cls_hd__append_1, cls_filter_Osimps_I1_J_0, cls_rev__induct_1, cls_drop__Suc__Cons_0, cls_hd_Oinduct_1, cls_last_Oinduct_1, cls_takeWhile_Oinduct_0, cls_listsp_Ocases_0, cls_listset_Oinduct_0, cls_rev_Osimps_I2_J_0, cls_distinct__remove1_0, cls_list_Osimps_I4_J_0, cls_removeAll_Oinduct_0, cls_rev__singleton__conv_0, cls_remdups_Oinduct_1, cls_listrelp_ONil_0, cls_append__self__conv2_0, cls_remdups__id__iff__distinct_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_list__all__append_2, cls_dropWhile__eq__Cons__conv_1, cls_append__Nil2_0, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_distinct__map_0, cls_drop__tl_0, cls_listsp_Ocases_2, cls_distinct__append_0, cls_remdups__eq__nil__iff_1, cls_map__eq__Cons__conv_3, cls_remove1_Oinduct_0, cls_self__append__conv2_1, cls_sorted__drop_0, cls_Cons__step1__Cons_1, cls_map__update_0, cls_List_Omember_Osimps_I2_J_1, cls_append__is__Nil__conv_2, cls_list_Osplit_0, cls_append__Nil_0, cls_sorted__sort__key_0, cls_map__is__Nil__conv_0, cls_append__in__listsp__conv_0, cls_append__eq__append__conv2_5, cls_Cons__step1__Cons_3, cls_singleton__rev__conv_0, cls_rev_Oinduct_0, cls_append__eq__Cons__conv_5, cls_take__map_0, cls_append__in__listsp__conv_1, cls_list__all__rev_1, clsarity_nat__Lattices_Olower__semilattice, cls_zip_Oinduct_1, cls_List_Omember_Osimps_I1_J_0, cls_Snoc__step1__SnocD_3, cls_map__upds__Nil2_0, cls_foldl__Cons_0, cls_rev__is__Nil__conv_0, cls_list__all2__Cons_0, cls_inf__sup__aci_I3_J_0, cls_distinct__rev_0, cls_list__ex_Osimps_I1_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_hd__dropWhile_0, cls_distinct__rotate_1, clsarity_fun__Lattices_Olattice, cls_rotate__simps_0, cls_distinct__sublistI_0, cls_list__update_Osimps_I1_J_0, cls_rotate1__is__Nil__conv_0, cls_take_Oinduct_1, cls_list__all2__appendI_0, cls_sublist__nil_0, cls_self__append__conv_1, cls_rev__filter_0, cls_Int__assoc_0, cls_splice__Nil2_0, cls_append__step1I_1, cls_list__all2__Nil_1, cls_rotate1__rotate__swap_0, cls_not__Cons__self_0, cls_listsp_Oinduct_1, cls_append__same__eq_0, cls_splice_Oinduct_1, cls_append__take__drop__id_0, cls_list__all2__rev1_1, cls_hd_Oinduct_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__swap_0, cls_Cons__step1__Cons_2, cls_splice_Osimps_I1_J_0, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_drop__Nil_0, cls_append__assoc_0, cls_inf__sup__aci_I1_J_0, cls_not__Nil__step1_0, cls_foldr_Osimps_I2_J_0, cls_Int__commute_0, cls_concat__map_Osimps_I2_J_0, cls_map__upds__Nil1_0, cls_list__all2__Nil2_0, cls_remove1_Osimps_I1_J_0, cls_remove1_Oinduct_1, clsarity_nat__Lattices_Olattice, cls_tl_Oinduct_0, cls_Cons__step1__Cons_4, cls_Int__absorb_0, cls_inf__assoc_0, cls_append__in__listsp__conv_2, cls_map__append_0, cls_rotate__Suc_0, cls_remdups_Oinduct_0, cls_list__all2__dropI_0, cls_take__eq__Nil_2, cls_distinct__append_1, cls_take_Oinduct_0, cls_listsp_Oinducts_2, cls_Int__left__absorb_0, cls_sorted__remdups_0, cls_distinct__remdups__id_0, cls_remdups__eq__nil__right__iff_1, cls_set_Oinduct_0, cls_foldr__append_0, cls_sorted_Osimps_I1_J_0, cls_tl__append2_0, cls_nat_Oinject_0, cls_list__all2__Nil_0, cls_in__listsp__conv__set_2, cls_sorted__remove1_0, cls_rotate__simps_1, cls_List_Onull_Osimps_I2_J_0, cls_foldl_Oinduct_1, cls_rev__eq__Cons__iff_1, cls_list_Osplit__asm_1, cls_distinct__dropWhile_0, clsarity_bool__Lattices_Olattice, cls_sorted__append_0, cls_listsp_Oinducts_0, cls_rotate__is__Nil__conv_1, cls_map__is__Nil__conv_1, cls_list_Osimps_I3_J_0, cls_tl_Oinduct_1, cls_drop_Oinduct_0, cls_list_Orecs_I2_J_0, cls_drop__Suc_0, cls_inf1I_0, cls_rotate1__hd__tl_0, cls_listsp_Ocases_1, cls_inf__idem_0, cls_list__ex_Osimps_I2_J_1, cls_rev__is__Nil__conv_1, cls_list__all2__Cons1_3, cls_Int__left__commute_0, cls_map_Osimps_I2_J_0, cls_take__Suc__Cons_0, cls_listsum_Oinduct_1, cls_distinct__rotate_0, cls_append__is__Nil__conv_1, cls_lift__IT_0, cls_inf__sup__aci_I4_J_0, cls_Snoc__step1__SnocD_0, cls_dropWhile_Osimps_I2_J_1, cls_list__all2__takeI_0, cls_list_Oinducts_0, cls_dropWhile_Oinduct_0, cls_Nil__is__rev__conv_0, cls_Cons__eq__appendI_0, cls_Cons__eq__append__conv_4, cls_append__is__Nil__conv_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_distinct__take_0, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_listsp_Oinduct_2, cls_splice_Oinduct_0, cls_append__eq__appendI_0, cls_list__all_Osimps_I2_J_2, cls_remove1_Osimps_I2_J_1, cls_list__update_Oinduct_0, cls_list__all_Osimps_I1_J_0, cls_hd_Osimps_0, cls_rev__append_0, cls_n__not__Suc__n_0, cls_listsp_Oinducts_3, cls_map_Oinduct_0, cls_foldl__append_0, cls_distinct__remdups_0, cls_Nil__is__append__conv_2, cls_list_Osplit_1, cls_List_Omember_Osimps_I2_J_2, cls_list_Oinducts_1, cls_list__all2__eq_0, cls_tl__drop_0, cls_inf__left__idem_0, cls_rev__swap_0, cls_concat__map_Osimps_I1_J_0, cls_sorted_Osimps_I2_J_0, cls_filtermap_Osimps_I1_J_0, cls_tl_Osimps_I2_J_0, cls_foldl__Nil_0, cls_distinct__drop_0, cls_Lambda_0, cls_last_Oinduct_0, cls_take__Suc_0, cls_list_Oinduct_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_list__ex_Osimps_I2_J_0, cls_list__ex_Osimps_I2_J_2, cls_set_Oinduct_1, cls_list__update__code_I3_J_0, cls_remdups__eq__nil__iff_0, cls_filter_Osimps_I2_J_1, cls_rev__rev__ident_0, cls_distinct1__rotate_1, cls_Snoc__step1__SnocD_1, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_sorted__dropWhile_0, cls_dropWhile_Oinduct_1, cls_distinct_Oinduct_1, cls_Cons__eq__filterD_2, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_removeAll_Oinduct_1, cls_dropWhile_Osimps_I2_J_0, cls_list__all__append_0, cls_foldl_Oinduct_0, cls_inf1E_0, cls_list__update__nonempty_0, cls_empty__null_1, cls_list__all2__rev1_0
% 11.30/4.02  % No. of inferences in proof: 659
% 11.30/4.02  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3452 ms resp. 2643 ms w/o parsing
% 12.54/4.28  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.54/4.29  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------