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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT088-1 : 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 : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:27:13 AM UTC 2026

% Result   : Unsatisfiable 14.18s 4.98s
% Output   : Refutation 15.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  521
% Syntax   : Number of formulae    : 1043 ( 423 unt;   0 typ;   0 def)
%            Number of atoms       : 2041 ( 936 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 11310 ( 886   ~; 998   |;   0   &;9426   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   79 (  77 usr;  15 con; 0-5 aty)
%            Number of variables   : 2750 (   0   ^;2750   !;   0   ?;2750   :)

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

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

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

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

thf(v_d_____decl,type,
    v_d____: $i ).

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

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

thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

thf(c_HOL_Oplus__class_Oplus_decl,type,
    c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).

thf(c_Power_Opower__class_Opower_decl,type,
    c_Power_Opower__class_Opower: $i > $i > $i > $i ).

thf(c_HOL_Oone__class_Oone_decl,type,
    c_HOL_Oone__class_Oone: $i > $i ).

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

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

thf(class_Ring__and__Field_Osemiring__0_decl,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

thf(class_Ring__and__Field_Oordered__semidom_decl,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

thf(c_Divides_Odiv__class_Omod_decl,type,
    c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).

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

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

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

thf(class_Power_Opower_decl,type,
    class_Power_Opower: $i > $o ).

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

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

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

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

thf(c_Orderings_Oord__class_Omin_decl,type,
    c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).

thf(class_Int_Onumber_decl,type,
    class_Int_Onumber: $i > $o ).

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

thf(c_Int_Onumber__class_Onumber__of_decl,type,
    c_Int_Onumber__class_Onumber__of: $i > $i > $i ).

thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

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

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

thf(c_Nat_Osize__class_Osize_decl,type,
    c_Nat_Osize__class_Osize: $i > $i > $i ).

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

thf(tc_List_Olist_decl,type,
    tc_List_Olist: $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_List_Oappend_decl,type,
    c_List_Oappend: $i > $i > $i > $i ).

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

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

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

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

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

thf(c_List_Oreplicate_decl,type,
    c_List_Oreplicate: $i > $i > $i > $i ).

thf(c_List_Olast_decl,type,
    c_List_Olast: $i > $i > $i ).

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

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

thf(c_List_Obutlast_decl,type,
    c_List_Obutlast: $i > $i > $i ).

thf(c_List_OremoveAll_decl,type,
    c_List_OremoveAll: $i > $i > $i > $i ).

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

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

thf(c_List_Osko__List__XCons__eq__append__conv__1__1_decl,type,
    c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_decl,type,
    c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).

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

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

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

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

thf(c_Hilbert__Choice_Oinv__into_decl,type,
    c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i > $i ).

thf(c_Orderings_Otop__class_Otop_decl,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

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

thf(v_h_____decl,type,
    v_h____: $i ).

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

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

thf(c_List_Osko__List__Xneq__Nil__conv__1__1_decl,type,
    c_List_Osko__List__Xneq__Nil__conv__1__1: $i > $i > $i ).

thf(c_List_Osko__List__Xneq__Nil__conv__1__2_decl,type,
    c_List_Osko__List__Xneq__Nil__conv__1__2: $i > $i > $i ).

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

thf(v_sko__CHAINED__1_decl,type,
    v_sko__CHAINED__1: $i > $i > $i ).

thf(c_List_Osko__List__Xlist__Xexhaust__1__1_decl,type,
    c_List_Osko__List__Xlist__Xexhaust__1__1: $i > $i > $i ).

thf(c_List_Osko__List__Xlist__Xexhaust__1__2_decl,type,
    c_List_Osko__List__Xlist__Xexhaust__1__2: $i > $i > $i ).

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

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

thf(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1_decl,type,
    v_sko__Arrow__Order__Mirabelle__Xthird__alt__1: $i > $i > $i ).

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

thf(v_sko__Arrow__Order__Mirabelle__Xalt3__1_decl,type,
    v_sko__Arrow__Order__Mirabelle__Xalt3__1: $i ).

thf(v_sko__Arrow__Order__Mirabelle__Xalt3__2_decl,type,
    v_sko__Arrow__Order__Mirabelle__Xalt3__2: $i ).

thf(v_sko__Arrow__Order__Mirabelle__Xalt3__3_decl,type,
    v_sko__Arrow__Order__Mirabelle__Xalt3__3: $i ).

thf(c_List_Osko__List__Xlist__Xnchotomy__1__1_decl,type,
    c_List_Osko__List__Xlist__Xnchotomy__1__1: $i > $i > $i ).

thf(c_List_Osko__List__Xlist__Xnchotomy__1__2_decl,type,
    c_List_Osko__List__Xlist__Xnchotomy__1__2: $i > $i > $i ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(1036,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).

thf(1586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Odrop ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(404,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(1454,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)],[404]) ).

thf(481,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(1633,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)],[481]) ).

thf(518,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(1729,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)],[518]) ).

thf(223,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).

thf(1031,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(893,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(1315,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(245,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(1083,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(184,axiom,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

thf(941,plain,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OremoveAll ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( D @ ( B @ ( A @ c_List_OremoveAll ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll__append_0) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OremoveAll ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( D @ ( B @ ( A @ c_List_OremoveAll ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(501,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
        = E )
      | ( B
        = ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).

thf(1686,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
        = E )
      | ( B
        = ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(220,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(1024,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).

thf(1469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

thf(760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(448,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(1559,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)],[448]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(1105,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).

thf(1237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
        = C )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__list__update_0) ).

thf(846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
        = C )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(299,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1211,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
        = ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).

thf(1596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
        = ( C @ ( B @ ( A @ c_Suc @ c_List_Otake ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(1290,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

thf(1068,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(382,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(1401,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(452,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(1569,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)],[452]) ).

thf(97,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(741,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(443,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(1544,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)],[443]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(1142,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).

thf(677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( B @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Obutlast ) )
      = ( B @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__conv__take_0) ).

thf(1305,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Obutlast ) )
      = ( B @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Otl ) )
      = ( C @ ( C @ ( B @ c_List_Otl ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__take_0) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Otl ) )
      = ( C @ ( C @ ( B @ c_List_Otl ) @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_d____ @ c_List_Olist_OCons ) ) @ ( v_c____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(523,plain,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_d____ @ c_List_Olist_OCons ) ) @ ( v_c____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(107,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).

thf(762,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(1078,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(470,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(1608,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)],[470]) ).

thf(489,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(1655,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)],[489]) ).

thf(11,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(550,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).

thf(1327,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(77,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(698,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(406,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(1458,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).

thf(1164,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(797,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(357,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(1342,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__append_0) ).

thf(747,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(538,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(362,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(1354,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)],[362]) ).

thf(428,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(1507,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(179,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(930,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)],[179]) ).

thf(166,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(898,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)],[166]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
      = ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_Suc )
      = ( B @ tc_List_Olist @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(398,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(1441,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)],[398]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

thf(885,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(516,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Olast ) )
        = ( B @ ( A @ c_List_Ohd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).

thf(1724,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Olast ) )
        = ( B @ ( A @ c_List_Ohd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

thf(651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(477,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).

thf(1623,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(416,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(1482,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)],[416]) ).

thf(479,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(1628,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)],[479]) ).

thf(510,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(1709,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)],[510]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(570,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(491,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).

thf(1660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(122,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(802,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)],[122]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
       != B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).

thf(934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
       != B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
        = ( C @ ( B @ c_List_Olast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
        = ( C @ ( B @ c_List_Olast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(351,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(1330,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)],[351]) ).

thf(323,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(1264,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)],[323]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(1323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(43,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(619,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(430,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xthird__alt__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_third__alt_0) ).

thf(1511,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xthird__alt__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(751,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(128,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(817,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(431,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(1514,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)],[431]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).

thf(1147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(415,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
        = E )
      | ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
        = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).

thf(1479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
        = E )
      | ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
        = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
      = ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__drop_0) ).

thf(1115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
      = ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(483,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(1641,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)],[483]) ).

thf(422,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(1494,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)],[422]) ).

thf(309,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( C @ ( E @ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_1) ).

thf(1232,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( C @ ( E @ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(51,axiom,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(638,plain,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(853,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(508,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
        = E )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).

thf(1704,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
        = E )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).

thf(870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
        = ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).

thf(1347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
        = ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(419,axiom,
    tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( v_P____ @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).

thf(1489,plain,
    tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( v_P____ @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(409,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(1465,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)],[409]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(756,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).

thf(1714,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(402,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(266,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(1136,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(182,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(937,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(498,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(1677,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)],[498]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
      = ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

thf(1334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
      = ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

thf(646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(374,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(1383,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)],[374]) ).

thf(22,axiom,
    tc_nat @ class_Power_Opower,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(574,plain,
    tc_nat @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(457,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(1581,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)],[457]) ).

thf(194,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(966,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)],[194]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Otake ) ) )
        = ( C @ ( B @ ( A @ c_List_Otake ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__butlast_0) ).

thf(1183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Otake ) ) )
        = ( C @ ( B @ ( A @ c_List_Otake ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(1283,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

thf(687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(371,axiom,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_n____ @ ( v_h____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) ) @ ( v_P____ @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_d____ @ ( v_c____ @ c_Pair ) ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1377,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( v_n____ @ ( v_h____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) ) @ ( v_P____ @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_d____ @ ( v_c____ @ c_Pair ) ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(877,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(94,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).

thf(734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(152,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(866,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).

thf(1072,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(260,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(1119,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(435,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(1526,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(450,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(1564,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)],[450]) ).

thf(358,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(1345,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_expand__Suc_0) ).

thf(988,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).

thf(1242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).

thf(1206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(294,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(1199,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(125,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(810,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(355,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(1338,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(234,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(1057,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(1074,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(468,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).

thf(1604,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Osplice ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__splice_0) ).

thf(910,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Osplice ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(957,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B )
      | ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__id_0) ).

thf(825,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B )
      | ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(1255,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(862,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(282,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1174,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(33,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(598,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(493,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(1666,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)],[493]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).

thf(1487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).

thf(815,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
        = ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
      | ( C
       != ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
      | ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
       != A )
      | ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
       != D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).

thf(729,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
        = ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
      | ( C
       != ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
      | ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
       != A )
      | ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
       != D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__replicate_0) ).

thf(1021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
        = C )
      | ( A
       != ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).

thf(778,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
        = C )
      | ( A
       != ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(426,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(1502,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)],[426]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).

thf(820,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(116,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(788,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)],[116]) ).

thf(475,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(1619,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)],[475]) ).

thf(368,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).

thf(1370,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(391,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(1423,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)],[391]) ).

thf(173,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(916,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(18,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(566,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(467,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(1602,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)],[467]) ).

thf(366,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(1365,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)],[366]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

thf(625,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(446,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(1555,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)],[446]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(162,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(889,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)],[162]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).

thf(1159,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(551,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(141,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).

thf(842,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( A @ c_List_Olist_ONil @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(26,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(583,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

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

thf(522,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(134,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(830,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(292,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(1195,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)],[292]) ).

thf(384,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(1407,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)],[384]) ).

thf(454,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( 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_2) ).

thf(1573,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(198,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(974,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(441,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(1541,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)],[441]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).

thf(874,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(1259,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
        = ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I2_J_1) ).

thf(1534,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
        = ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(615,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(370,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).

thf(1375,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Orotate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).

thf(1111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Orotate ) ) @ ( A @ c_List_Orotate ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Orotate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__append_0) ).

thf(725,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(392,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(1425,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)],[392]) ).

thf(212,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(1006,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(514,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(1719,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)],[514]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

thf(610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Suc @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(115,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(783,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)],[115]) ).

thf(380,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(1397,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)],[380]) ).

thf(364,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
        = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).

thf(1360,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
        = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(463,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(1592,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(578,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__tl_0) ).

thf(980,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Otl ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(424,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(1498,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)],[424]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).

thf(1096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Otake ) ) )
        = ( D @ ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).

thf(1672,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(451,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(1567,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)],[451]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( ( C @ ( B @ ( A @ c_List_Oremove1 ) ) )
        = ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1__removeAll_0) ).

thf(1683,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( ( C @ ( B @ ( A @ c_List_Oremove1 ) ) )
        = ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Otl ) )
        = ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__replicate_0) ).

thf(1028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Otl ) )
        = ( C @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(335,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__butlast_0) ).

thf(1292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(554,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).

thf(669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

thf(642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
      = ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).

thf(1584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_List_Otake ) ) )
      = ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0L_0) ).

thf(1214,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(400,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(1446,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)],[400]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

thf(590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(484,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
      = ( B @ ( A @ c_List_Obutlast ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).

thf(1644,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
      = ( B @ ( A @ c_List_Obutlast ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(706,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(389,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(1419,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)],[389]) ).

thf(387,axiom,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_d____ @ c_List_Olist_OCons ) ) @ ( v_c____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).

thf(1414,plain,
    ! [A: $i] :
      ( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( v_d____ @ c_List_Olist_OCons ) ) @ ( v_c____ @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(472,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(1612,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)],[472]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(1039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(196,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

thf(970,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Obutlast ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__butlast_0) ).

thf(1155,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Obutlast ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(547,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).

thf(837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(337,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(1297,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

thf(1266,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).

thf(1131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(494,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(1668,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)],[494]) ).

thf(445,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(1552,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)],[445]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(1192,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).

thf(984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(461,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(1588,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)],[461]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

thf(1099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(440,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

thf(1539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(405,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).

thf(1456,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Oreplicate ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(236,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(1060,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)],[236]) ).

thf(231,axiom,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(1050,plain,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(466,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

thf(1599,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(315,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(1246,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(36,axiom,
    tc_nat @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

thf(605,plain,
    tc_nat @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(378,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(1393,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)],[378]) ).

thf(395,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).

thf(1434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B = D )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

thf(1318,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B = D )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Orev ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_List_Orev ) @ c_List_Olist__update ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__update_0) ).

thf(805,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Orev ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( A @ c_List_Orev ) @ c_List_Olist__update ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(505,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(1695,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)],[505]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).

thf(921,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

thf(541,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__drop_0) ).

thf(1170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).

thf(674,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(492,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(1663,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)],[492]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).

thf(1026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(87,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).

thf(718,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize__class_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__take_0) ).

thf(1202,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).

thf(792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(108,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(765,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)],[108]) ).

thf(511,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(1712,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)],[511]) ).

thf(233,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(1054,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__replicate_0) ).

thf(906,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(329,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).

thf(1278,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Odrop ) ) )
        = ( D @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(517,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(1727,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)],[517]) ).

thf(499,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(1680,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)],[499]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
        = ( D @ ( D @ ( D @ ( A @ ( B @ c_Suc @ c_List_Odrop ) ) @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ ( B @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).

thf(1219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
        = ( D @ ( D @ ( D @ ( A @ ( B @ c_Suc @ c_List_Odrop ) ) @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ ( B @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__replicate_0) ).

thf(1273,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(856,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).

thf(745,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Odrop ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(1301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(480,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(1631,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)],[480]) ).

thf(506,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).

thf(1698,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

thf(584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(487,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(1652,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)],[487]) ).

thf(376,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(1388,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)],[376]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).

thf(743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(507,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Ohd ) )
        = ( B @ ( A @ c_List_Olast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).

thf(1701,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Ohd ) )
        = ( B @ ( A @ c_List_Olast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(433,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ c_List_Olist_ONil ) )
      | ( B
        = ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).

thf(1520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( C @ c_List_Olist_ONil ) )
      | ( B
        = ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( A
        = ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oexhaust_0) ).

thf(1428,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( A
        = ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xexhaust__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(509,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(1707,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)],[509]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

thf(1271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).

thf(1312,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).

thf(713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).

thf(1058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(1239,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(1332,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(1090,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

thf(1675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(672,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(482,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(1638,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)],[482]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).

thf(831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(259,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1117,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(230,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(1048,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)],[230]) ).

thf(421,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(1492,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)],[421]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).

thf(567,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).

thf(1690,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(342,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(283,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

thf(1175,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__update ) ) ) )
      = ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

thf(1144,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(159,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(880,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)],[159]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(1043,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(453,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(1571,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)],[453]) ).

thf(397,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(1439,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)],[397]) ).

thf(412,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(1471,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Onull ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(6,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(535,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(519,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(1731,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)],[519]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(700,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(349,axiom,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(1325,plain,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
        = ( D @ ( C @ ( B @ ( D @ ( A @ c_List_Obutlast ) @ c_List_Olist__update ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_1) ).

thf(1149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
        = ( D @ ( C @ ( B @ ( D @ ( A @ c_List_Obutlast ) @ c_List_Olist__update ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(180,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(932,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__append_0) ).

thf(758,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
        = B )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

thf(1339,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
        = B )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(148,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(858,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(447,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(1557,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)],[447]) ).

thf(110,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(769,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).

thf(1460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_List_Oreplicate ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

thf(1177,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(373,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(1381,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)],[373]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
      = ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_0) ).

thf(1474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
      = ( C @ ( B @ ( A @ c_List_OremoveAll ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(464,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(1594,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)],[464]) ).

thf(191,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(959,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( B = D )
      | ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

thf(695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( B = D )
      | ( ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( C @ c_Suc @ ( D @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(1015,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(608,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).

thf(986,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(210,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

thf(1000,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(423,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(1496,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(145,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(851,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_HOL_Oord )
      | ~ ( A @ class_Int_Onumber ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__number__of_1) ).

thf(653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_HOL_Oord )
      | ~ ( A @ class_Int_Onumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ c_List_Olist_ONil ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).

thf(1528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) @ c_List_Otake ) ) )
        = ( D @ c_List_Olist_ONil ) )
      | ( ( tc_nat @ ( A @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).

thf(868,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(257,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(1113,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)],[257]) ).

thf(16,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(563,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).

thf(1076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(224,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

thf(1034,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(458,axiom,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__3 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__2 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__1 @ c_List_Olist_OCons ) ) @ c_List_Odistinct ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_alt3_0) ).

thf(1583,plain,
    tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__3 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__2 @ c_List_Olist_OCons ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xalt3__1 @ c_List_Olist_OCons ) ) @ c_List_Odistinct ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(1208,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(410,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(1467,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)],[410]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(178,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).

thf(927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

thf(648,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(429,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).

thf(1509,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(101,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(749,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)],[101]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(617,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(939,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(217,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(1018,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

thf(754,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).

thf(795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff_0) ).

thf(680,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Orderings_Oord__class_Omin ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(968,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(286,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(1181,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(739,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(437,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(1531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osize_I4_J_0) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(444,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(1547,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)],[444]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

thf(776,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).

thf(1070,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(155,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(872,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).

thf(954,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(1230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(417,axiom,
    v_c____ != v_d____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(1484,plain,
    v_c____ != v_d____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(513,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
        = ( C @ ( B @ c_List_Olast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).

thf(1716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
        = ( C @ ( B @ c_List_Olast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OremoveAll ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I1_J_0) ).

thf(1452,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OremoveAll ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ c_List_Olist_ONil ) )
      | ( B
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
        = ( D @ ( A @ c_List_Olast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__list__update_1) ).

thf(1186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ c_List_Olist_ONil ) )
      | ( B
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olast ) )
        = ( D @ ( A @ c_List_Olast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(140,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(840,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)],[140]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(1285,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(1336,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(544,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(322,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(1262,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).

thf(1235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

thf(1085,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(490,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(1658,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)],[490]) ).

thf(188,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(951,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).

thf(808,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__CHAINED__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1404,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( B @ ( A @ v_sko__CHAINED__1 ) @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(442,axiom,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_0) ).

thf(1543,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

thf(1257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

thf(600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(232,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(1052,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__drop_0) ).

thf(864,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Otake ) ) )
      = ( D @ ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Otake ) ) @ ( B @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(200,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(978,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(495,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(1670,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)],[495]) ).

thf(213,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(1008,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(612,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(157,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(876,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

thf(859,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(427,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
        = ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).

thf(1504,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
        = ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(369,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( A
        = ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).

thf(1372,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( A
        = ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

thf(595,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).

thf(991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(474,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(1617,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)],[474]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).

thf(1421,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_List_Otake ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

thf(627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(486,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
        = E )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).

thf(1649,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
        = E )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(432,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_1) ).

thf(1517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OremoveAll ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_OremoveAll ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(255,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append1_0) ).

thf(1108,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

thf(1157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).

thf(1321,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

thf(976,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

thf(903,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(488,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(1654,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(386,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(1412,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)],[386]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(1216,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(163,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(891,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(401,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(1448,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)],[401]) ).

thf(289,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(1189,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(1010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(455,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(1575,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)],[455]) ).

thf(520,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( A
        = ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Onchotomy_0) ).

thf(1734,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( A
        = ( B @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xlist__Xnchotomy__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(111,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(771,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(485,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(1646,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)],[485]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(963,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(414,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(1476,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(165,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).

thf(896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_HOL_Oord )
      | ~ ( A @ class_Int_Onumber ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__number__of_0) ).

thf(632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_HOL_Oord )
      | ~ ( A @ class_Int_Onumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(314,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(1244,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)],[314]) ).

thf(434,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(1523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(114,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(781,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).

thf(995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( B @ c_List_Orev ) @ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rev_0) ).

thf(1276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Orotate ) ) )
      = ( C @ ( C @ ( B @ ( tc_nat @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(462,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(1590,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)],[462]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(78,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(699,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Olast ) )
        = ( C @ ( B @ c_List_Olast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__drop_0) ).

thf(946,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Olast ) )
        = ( C @ ( B @ c_List_Olast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(1101,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(502,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(1689,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)],[502]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(914,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(300,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(1212,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)],[300]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(1309,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(399,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(1444,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)],[399]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).

thf(1045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(667,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(276,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(1161,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(473,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(1614,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)],[473]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(1133,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(456,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( A
        = ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).

thf(1578,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( A
        = ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).

thf(833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(137,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(835,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)],[137]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).

thf(818,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).

thf(1303,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(379,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(1395,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)],[379]) ).

thf(478,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(1625,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)],[478]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Oreplicate ) ) )
      = ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).

thf(1248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_List_Oreplicate ) ) )
      = ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( D @ ( C @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

thf(790,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(564,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(396,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).

thf(1436,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(174,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(918,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(365,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(1363,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)],[365]) ).

thf(504,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(1693,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)],[504]) ).

thf(449,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(1561,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)],[449]) ).

thf(133,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(828,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(471,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(1610,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)],[471]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
      = ( B @ ( A @ c_List_Obutlast ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_0) ).

thf(1172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_List_Olist__update ) ) ) @ c_List_Obutlast ) )
      = ( B @ ( A @ c_List_Obutlast ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(385,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(1410,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)],[385]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(333,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(1288,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)],[333]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(192,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(960,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(1065,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(361,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(1352,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)],[361]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(439,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
      = ( B @ ( A @ c_List_Olast ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).

thf(1537,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
      = ( B @ ( A @ c_List_Olast ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(372,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( A
        = ( B @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_0) ).

thf(1378,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( A
        = ( B @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__2 ) @ ( B @ ( A @ c_List_Osko__List__Xneq__Nil__conv__1__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Orderings_Oord__class_Omin ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__take_0) ).

thf(1019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_Orderings_Oord__class_Omin ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(644,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(363,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(1357,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)],[363]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(822,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).

thf(1299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Oord__class_Omin ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

thf(1093,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(139,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(839,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).

thf(1268,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
       != ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).

thf(575,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(425,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(1500,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(89,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(723,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)],[89]) ).

thf(202,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(982,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(394,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(1431,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)],[394]) ).

thf(381,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(1399,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)],[381]) ).

thf(476,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(1621,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omember ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(469,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(1606,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)],[469]) ).

thf(367,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(1367,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)],[367]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(659,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(388,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(1416,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)],[388]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

thf(639,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

thf(1088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1204,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).

thf(592,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).

thf(708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Orderings_Oord__class_Omin ) ) @ ( B @ c_Orderings_Oord__class_Omin ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Orderings_Oord__class_Omin ) ) @ ( C @ c_Orderings_Oord__class_Omin ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(197,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(972,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)],[197]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(521,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(1737,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(420,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(1490,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)],[420]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(560,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1744,plain,
    $false,
    inference(e,[status(thm)],[1036,1586,629,1190,1454,1633,1729,1031,893,1315,1083,941,1179,1686,1024,1469,1168,760,1559,1105,1237,846,1211,1596,1290,1068,1401,1569,741,1544,1142,677,1305,1041,523,762,1078,1608,1655,550,715,1327,698,1458,1164,797,1342,747,538,1354,1507,1222,930,898,1391,1441,885,1386,1724,651,1228,1623,1482,1628,1709,570,1660,802,934,1462,949,1330,1264,1323,619,1511,702,751,817,1514,1147,1479,1115,1641,1494,1232,638,853,1704,870,606,1347,1489,1465,756,1714,1450,623,1136,937,1677,1334,646,1383,574,1581,966,1183,1283,602,687,1377,877,734,866,1072,1119,1526,1564,1345,988,1242,849,1206,529,661,925,1199,810,1338,1057,1074,1604,910,957,825,1255,862,1174,598,1666,1487,693,815,729,1021,778,1502,820,788,1619,1370,1423,916,566,1602,1365,625,1555,665,889,1159,551,1281,842,1012,583,522,830,682,1195,1407,1573,974,1541,874,1259,1534,615,1375,1111,725,1425,1006,1719,610,783,1397,1360,1350,1592,578,980,1498,1096,1672,1567,1683,1028,1292,554,669,642,1584,1214,1446,590,1644,706,1419,1414,526,1612,1039,970,1155,547,837,997,1297,1266,1131,1668,1552,1192,984,1588,1099,1539,1456,1060,1050,1599,1246,605,1393,1434,1318,805,1695,921,541,1170,674,1663,1026,586,718,1202,792,765,1712,1054,906,1278,1727,1680,1219,1273,856,745,1301,689,1631,1698,1103,584,732,1652,1388,743,711,1701,1520,1124,1226,1428,1139,572,1707,1271,1312,713,1058,1239,1332,1090,704,1675,672,1638,1224,831,1117,1048,1492,567,737,1690,1307,1175,1722,1144,880,1043,1571,1439,1471,535,1731,799,700,1325,1149,943,932,758,1339,858,1557,769,1460,1177,1381,1474,1594,959,695,1015,608,986,1000,1250,1496,851,653,912,685,1528,868,1113,563,1076,1034,1583,1166,1208,1467,663,927,648,1509,749,617,939,1018,754,795,680,968,1181,580,887,739,1531,993,1547,776,557,1003,1070,872,954,1252,1230,1484,1716,1452,1186,840,1285,1336,544,1262,1235,1085,1658,951,808,1404,1543,1257,656,600,1052,864,978,1670,1008,612,876,859,1504,727,1372,595,991,1617,1421,627,1649,1517,1126,844,1108,1157,1321,976,903,1654,1412,1216,891,1448,1189,1010,1575,1734,771,1646,813,963,1476,896,1062,632,1244,1523,781,995,1276,1590,588,699,946,1101,1689,914,1212,1309,1444,1045,667,1294,1161,1614,1133,620,1578,833,835,818,1303,1395,1625,1248,790,564,1436,918,1363,1693,1561,828,720,1610,1172,1410,767,1288,1197,960,635,532,1065,1352,1129,1152,1537,1378,1019,644,1357,908,822,1299,691,1093,839,1268,575,1500,723,982,1431,1399,1621,1606,1367,659,1416,639,1088,1204,592,708,972,923,1737,1490,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT088-1 : 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
% 0.15/0.61  % Computer : n020.cluster.edu
% 0.15/0.61  % Model    : x86_64 x86_64
% 0.15/0.61  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.61  % Memory   : 8046.5625MB
% 0.15/0.61  % OS       : Linux 6.8.0-71-generic
% 0.15/0.62  % CPULimit : 300
% 0.15/0.62  % WCLimit  : 300
% 0.15/0.62  % DateTime : Sat Sep 26 06:27:34 UTC 2026
% 0.15/0.62  % CPUTime  : 
% 0.15/0.62  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
% 1.03/1.29  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.11/1.66  % [INFO] 	 Parsing done (371ms). 
% 2.11/1.68  % [INFO] 	 Running in sequential loop mode. 
% 3.25/2.07  % [INFO] 	 eprover registered as external prover. 
% 3.25/2.07  % [INFO] 	 Scanning for conjecture ... 
% 3.68/2.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 672 axioms. Running axiom selection ... 
% 4.79/2.50  % [INFO] 	 Axiom selection finished. Selected 519 axioms (removed 153 axioms). 
% 5.54/2.73  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.54/2.76  % [INFO] 	 Type checking passed. 
% 5.54/2.76  % [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 ... 
% 14.18/4.97  % External prover 'e' found a proof!
% 14.18/4.97  % [INFO] 	 Killing All external provers ... 
% 14.18/4.97  % Time passed: 4159ms (effective reasoning time: 3289ms)
% 14.18/4.98  % Axioms used in derivation (519): clsarity_nat__HOL_Oord, cls_Nil__is__rev__conv_1, cls_not__one__less__zero_0, cls_last_Osimps_0, cls_min__max_Oinf__commute_0, cls_linorder__antisym__conv2_1, cls_power__0_0, cls_natgb_Oadd__r0__iff_1, cls_min__max_Ole__infE_0, cls_length__0__conv_1, cls_take__eq__Nil_0, cls_take__take_0, cls_butlast__snoc_0, cls_Suc__pred_0, cls_last__drop_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_rev__swap_1, cls_add__is__1_1, cls_last_Osimps_1, cls_zero__less__one_0, cls_Cons__eq__append__conv_2, cls_Suc__inject_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_remove1_Osimps_I2_J_0, cls_list__update__overwrite_0, cls_splice_Osimps_I2_J_1, cls_xt1_I12_J_0, cls_append__self__conv_0, cls_Suc__n__not__n_0, cls_min__max_Oinf__le1_0, cls_zero__le__one_0, cls_take__tl_0, cls_butlast_Osimps_I1_J_0, cls_one__is__add_4, cls_drop__append_0, cls_min__less__iff__conj_0, cls_distinct__remove1__removeAll_0, cls_nat__add__left__cancel__less_1, cls_splice__Cons__Cons_0, cls_take__0_0, cls_diff__Suc__1_0, cls_list_Oinject_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_tl_Osimps_I1_J_0, cls_linorder__neqE_0, cls_less__antisym_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_min__0R_0, cls_replicate__empty_0, cls_take__Cons_H_0, clsarity_fun__Orderings_Oorder, cls_rev__singleton__conv_1, cls_pos__add__strict_0, cls_termination__basic__simps_I1_J_0, cls_add__is__0_0, cls_not__Cons__self2_0, cls_Suc__lessI_0, cls_diff__cancel_0, cls_removeAll_Osimps_I2_J_0, cls_min__less__iff__disj_2, cls_not__less__eq_1, cls_rev__is__rev__conv_0, cls_one__is__add_1, clsarity_nat__Orderings_Olinorder, cls_list__update__append_1, cls_less__Suc__eq_2, cls_nat__add__left__cancel__less_0, cls_min__less__iff__disj_0, cls_distinct__rev_1, cls_append__eq__append__conv__if_6, cls_list__update__nonempty_1, cls_eq__Nil__appendI_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_alt3_0, cls_power__less__imp__less__exp_0, cls_length__splice_0, cls_drop__0_0, cls_power__gt1_0, cls_append__eq__Cons__conv_4, cls_List_Omember_Osimps_I2_J_0, cls_same__append__eq_0, cls_take__Cons__number__of_1, cls_append__Cons_0, cls_butlast_Osimps_I2_J_1, cls_gr0I_0, cls_rotate__conv__mod_0, cls_length__butlast_0, cls_add__gr__0_0, cls_hd__append_0, cls_drop__Cons__number__of_0, clsarity_bool__HOL_Oord, cls_replicate__eq__replicate_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_diff__diff__left_0, cls_append__eq__Cons__conv_0, cls_min__max_Oless__infI2_0, cls_min__number__of_1, cls_one__le__power_0, cls_tl__replicate_0, cls_gr__implies__not0_0, cls_sorted_Osimps_I3_J_1, cls_linorder__not__less_0, cls_list_Osize_I4_J_0, cls_add__less__mono_0, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_min__max_Ole__inf__iff_1, cls_order__less__asym_0, cls_butlast__list__update_0, cls_mod__if_1, cls_append1__eq__conv_1, cls_order__eq__refl_0, cls_neq__Nil__conv_0, cls_order__le__less_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_splice_Osimps_I2_J_0, cls_linorder__antisym__conv2_0, cls_distinct_Osimps_I1_J_0, cls_linorder__antisym__conv1_0, cls_sorted__take_0, cls_distinct_Osimps_I2_J_1, cls_length__greater__0__conv_1, cls_empty__null_0, cls_min__max_Ole__infE_1, cls_length__remdups__eq_0, cls_replicate__append__same_0, cls_rev_Osimps_I2_J_0, cls_add__Suc_0, cls_hd__append_1, cls_list__update__append1_0, cls_distinct__remove1_0, clsarity_bool__Orderings_Oorder, cls_take__1__Cons_0, cls_drop__Suc__Cons_0, cls_rev__singleton__conv_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_less__le__not__le_2, cls_diff__add__inverse2_0, cls_xt1_I10_J_0, cls_append__Nil2_0, cls_rotate__rev_0, cls_nat__add__left__commute_0, cls_not__less__iff__gr__or__eq_0, cls_diff__Suc__Suc_0, cls_append__self__conv2_0, cls_remdups__id__iff__distinct_0, cls_one__is__add_5, cls_class__semiring_Osemiring__rules_I6_J_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_drop__tl_0, cls_CHAINED_0_01, cls_distinct__append_0, cls_power__0__Suc_0, clsarity_fun__HOL_Oord, cls_remdups__eq__nil__iff_1, cls_Cons__eq__append__conv_3, cls_self__append__conv2_1, cls_sorted__drop_0, cls_rotate__rotate_0, cls_sorted_Osimps_I3_J_2, cls_Suc__diff__1_0, cls_removeAll__append_0, cls_length__0__conv_0, cls_mod__Suc_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_min__max_Ole__infI2_0, cls_append__is__Nil__conv_2, cls_append__Nil_0, cls_one__is__add_0, cls_append__eq__append__conv2_5, cls_list_Oexhaust_0, cls_less__add__Suc1_0, cls_rev__update_0, cls_take__Cons_H_1, cls_append__eq__Cons__conv_5, cls_replicate__Suc_0, cls_List_Omember_Osimps_I2_J_1, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_length__list__update_0, cls_add__is__1_0, cls_length__take_0, cls_class__semiring_Oadd__a_0, cls_last__append_1, cls_min__max_Ole__iff__inf_1, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_xt1_I8_J_0, cls_drop__Cons__number__of_1, cls_List_Omember_Osimps_I1_J_0, cls_min__max_Oinf__assoc_0, cls_rev__is__Nil__conv_0, cls_distinct__rev_0, cls_butlast__conv__take_0, cls_min__max_Oinf__idem_0, cls_class__semiring_Oadd__0_0, cls_min__max_Ole__inf__iff_0, cls_butlast__list__update_1, cls_last__list__update_1, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_take__hd__drop_0, cls_length__remdups__eq_1, cls_distinct__rotate_1, cls_replicate__app__Cons__same_0, cls_power__strict__mono_0, cls_min__max_Oinf__left__idem_0, cls_rotate__simps_0, cls_replicate__eq__replicate_1, cls_One__nat__def_0, cls_lessI_0, cls_power__strict__decreasing_0, cls_drop__1__Cons_0, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_diff__Suc__eq__diff__pred_0, cls_zero__less__two_0, cls_less__add__one_0, cls_not__leE_0, cls_min__le__iff__disj_0, cls_append__eq__Cons__conv_1, cls_list__update__append_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_splice__Nil2_0, cls_zero__less__power_0, cls_order__antisym_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_butlast__append_0, cls_less__add__eq__less_0, cls_list__update__code_I2_J_0, cls_le__number__of__eq__not__less_1, cls_self__append__conv_1, cls_take__append_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_append__eq__conv__conj_2, cls_less__Suc__eq__0__disj_3, cls_rotate1__is__Nil__conv_0, cls_rotate1__rotate__swap_0, cls_not__Cons__self_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_linorder__antisym__conv1_1, cls_length__greater__0__conv_0, cls_append__same__eq_0, cls_last__snoc_0, cls_append__take__drop__id_0, clsarity_bool__Orderings_Opreorder, cls_splice_Osimps_I1_J_0, cls_last__append_0, cls_zero__neq__one_0, cls_list__update__swap_0, cls_length__rev_0, cls_append__eq__conv__conj_0, cls_rotate__drop__take_0, cls_butlast__drop_0, cls_less__imp__diff__less_0, cls_natgb_Oadd__cancel_0, cls_drop__Cons_H_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_diff__less_0, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_linorder__not__le_1, cls_append__assoc_0, cls_one__is__add_2, cls_not__less__less__Suc__eq_0, cls_butlast__append_1, cls_tl__take_0, cls_mod__Suc_1, cls_drop__Nil_0, cls_neq0__conv_1, cls_add__Suc__right_0, cls_not__less__iff__gr__or__eq_1, cls_Cons__eq__append__conv_0, cls_drop__butlast_0, cls_Nitpick_Olist__size__simp_I2_J_1, cls_nat__add__right__cancel_0, cls_mod__1_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, clsarity_nat__Int_Onumber, cls_order__le__neq__trans_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_diff__less__Suc_0, cls_less__not__refl_0, cls_linorder__antisym__conv3_0, cls_last__rev_0, cls_min__max_Oinf__greatest_0, cls_rotate__Suc_0, cls_removeAll_Osimps_I1_J_0, cls_gr0__conv__Suc_1, cls_list_Onchotomy_0, cls_less__le__not__le_1, cls_take__eq__Nil_2, cls_distinct__append_1, cls_last__list__update_0, cls_order__eq__iff_2, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_sorted__remdups_0, cls_less__diff__conv_1, cls_rotate__id_0, cls_less__diff__conv_0, cls_order__antisym__conv_0, cls_rev__replicate_0, cls_less__SucE_0, cls_order__neq__le__trans_0, cls_power__eq__imp__eq__base_0, cls_distinct__remdups__id_0, cls_empty__replicate_0, cls_remdups__eq__nil__right__iff_1, cls_append__eq__Cons__conv_2, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_replicate__add_0, cls_sorted_Osimps_I1_J_0, cls_tl__append2_0, cls_nat_Oinject_0, cls_add__lessD1_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_List_Onull_Osimps_I2_J_0, cls_drop__drop_0, cls_rev__eq__Cons__iff_1, cls_hd__replicate_0, cls_power__le__imp__le__base_0, cls_not__less__less__Suc__eq_1, clsarity_nat__Power_Opower, cls_drop__replicate_0, cls_CHAINED_0_02, cls_rotate__is__Nil__conv_1, cls_Nat_Oadd__0__right_0, cls_min__max_Ole__infI1_0, cls_power__strict__increasing__iff_1, cls_sorted__append_0, cls_linorder__less__linear_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_Suc__lessD_0, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_drop__Suc_0, cls_Suc__length__conv_2, cls_add__is__1_4, cls_add__is__1_5, cls_rotate1__hd__tl_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_append__eq__conv__conj_1, cls_xt1_I11_J_0, cls_one__neq__zero_0, cls_add__eq__if_1, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_rev__is__Nil__conv_1, cls_natgb_Oadd__r0__iff_0, cls_min__Suc__Suc_0, cls_length__append_0, cls_last__replicate_0, cls_length__rotate1_0, cls_diff__self__eq__0_0, cls_take__Suc__Cons_0, cls_less__Suc0_0, cls_length__rotate_0, cls_min__max_Ole__inf__iff_2, cls_xt1_I6_J_0, cls_diff__Suc__less_0, cls_min__max_Oinf__le2_0, cls_replicate__eq__replicate_2, cls_min__less__iff__conj_2, cls_distinct__rotate_0, cls_take__butlast_0, cls_append__is__Nil__conv_1, cls_take__replicate_0, cls_nat_Osimps_I3_J_0, cls_plus__nat_Oadd__0_0, cls_length__drop_0, cls_min__max_Oinf__absorb2_0, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, cls_min__max_Oinf__left__commute_0, cls_diff__less__mono2_0, cls_length__tl_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_less__trans__Suc_0, cls_Nil__is__rev__conv_0, cls_order__less__irrefl_0, cls_Cons__eq__append__conv_4, cls_append__is__Nil__conv_0, cls_add__is__0_2, cls_distinct__take_0, cls_class__semiring_Oadd__c_0, cls_singleton__rev__conv_1, cls_append__eq__appendI_0, cls_one__less__power_0, cls_power__Suc__less__one_0, cls_nat__add__left__cancel_0, cls_minus__nat_Odiff__0_0, cls_butlast_Osimps_I2_J_0, cls_add__is__1_3, cls_length__Suc__conv_2, cls_diff__0__eq__0_0, cls_list_Oinject_1, cls_zero__less__diff_1, cls_distinct__remdups_0, cls_add__eq__self__zero_0, cls_power__less__imp__less__base_0, cls_hd_Osimps_0, cls_mod__less__divisor_0, cls_Suc__eq__plus1_0, cls_rev__append_0, cls_n__not__Suc__n_0, cls_min__le__iff__disj_1, cls_Cons__eq__append__conv_1, cls_take__Cons__number__of_0, clsarity_fun__Orderings_Opreorder, cls_min__le__iff__disj_2, cls_remove1_Osimps_I2_J_1, cls_power__inject__base_0, cls_min__max_Ole__infI_0, cls_less__SucI_0, cls_drop__take_0, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_not__less0_0, cls_hd__rev_0, cls_diffs0__imp__equal_0, cls_expand__Suc_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_rev__swap_0, cls_tl__drop_0, cls_min__max_Ole__iff__inf_0, cls_replicate__empty_1, cls_one__is__add_3, cls_sorted_Osimps_I2_J_0, cls_List_Omember_Osimps_I2_J_2, cls_diff__add__inverse_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_tl_Osimps_I2_J_0, cls_Suc__less__eq_0, cls_length__replicate_0, cls_add__gr__0_2, cls_zero__le__power_0, cls_third__alt_0, cls_take__drop_0, cls_order__less__imp__le_0, cls_take__Suc_0, cls_distinct__drop_0, cls_min__number__of_0, cls_class__semiring_Opwr__0_0, cls_CHAINED_0_03, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_that_0, cls_Suc__pred_H_0, cls_add__gr__0_1, cls_diff__commute_0, cls_power__strict__increasing__iff_0, cls_mod__if_0, cls_less__Suc0_1, cls_termination__basic__simps_I2_J_0, cls_Suc__eq__plus1__left_0, cls_append__eq__Cons__conv_3, cls_list__update__code_I3_J_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_remdups__eq__nil__iff_0, cls_linorder__not__less_1, cls_removeAll_Osimps_I2_J_1, cls_nat__less__le_1, cls_min__diff_0, cls_upd__conv__take__nth__drop_0, cls_rev__rev__ident_0, cls_distinct1__rotate_1, cls_empty__replicate_1, cls_sorted_Osimps_I3_J_0, cls_min__less__iff__conj_1, cls_xt1_I7_J_0, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_drop__Cons_H_1, cls_not__one__le__zero_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_min__less__iff__disj_1, cls_min__0L_0, cls_power__0__left_1, cls_mod__Suc__eq__Suc__mod_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_le__number__of__eq__not__less_0, cls_list__update__nonempty_0, cls_power__mono_0, cls_add__diff__inverse_0, cls_empty__null_1
% 14.18/4.98  % No. of inferences in proof: 1043
% 14.18/4.98  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4159 ms resp. 3289 ms w/o parsing
% 15.95/5.31  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.95/5.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------