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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL827-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:53:07 AM UTC 2026

% Result   : Unsatisfiable 12.03s 4.28s
% Output   : Refutation 13.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  386
% Syntax   : Number of formulae    :  773 ( 255 unt;   0 typ;   0 def)
%            Number of atoms       : 1523 ( 518 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 12640 ( 760   ~; 750   |;   0   &;11130   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   38 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   97 (  95 usr;  27 con; 0-5 aty)
%            Number of variables   : 1920 (   0   ^;1920   !;   0   ?;1920   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Oordered__idom_decl,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

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

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

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

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

thf(class_OrderedGroup_Omonoid__add_decl,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

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

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

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

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

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

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

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

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

thf(class_OrderedGroup_Ogroup__add_decl,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

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

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

thf(c_Lambda_OdB_OdB__size_decl,type,
    c_Lambda_OdB_OdB__size: $i > $i ).

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

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

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

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

thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

thf(class_Nat_Osemiring__char__0_decl,type,
    class_Nat_Osemiring__char__0: $i > $o ).

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

thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

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

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

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

thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

thf(class_OrderedGroup_Osemigroup__add_decl,type,
    class_OrderedGroup_Osemigroup__add: $i > $o ).

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

thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

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

thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

thf(class_Ring__and__Field_Osemiring__1_decl,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

thf(class_Ring__and__Field_Oidom_decl,type,
    class_Ring__and__Field_Oidom: $i > $o ).

thf(class_Int_Onumber__ring_decl,type,
    class_Int_Onumber__ring: $i > $o ).

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

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

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

thf(c_Type_Otype_Otype__size_decl,type,
    c_Type_Otype_Otype__size: $i > $i ).

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

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

thf(v_sko__local__XCons__1__1_decl,type,
    v_sko__local__XCons__1__1: $i > $i > $i > $i > $i ).

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

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

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

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

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

thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

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

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

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

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

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

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

thf(c_COMBS_decl,type,
    c_COMBS: $i > $i > $i > $i ).

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

thf(c_and_decl,type,
    c_and: $i ).

thf(c_All_decl,type,
    c_All: $i > $i ).

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

thf(c_implies_decl,type,
    c_implies: $i ).

thf(c_Ex_decl,type,
    c_Ex: $i > $i ).

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

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

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

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

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

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

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

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

thf(v_sko__local__XCons__Xhyps__1__1_decl,type,
    v_sko__local__XCons__Xhyps__1__1: $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xabs__typeE__1__1_decl,type,
    c_Type_Osko__Type__Xabs__typeE__1__1: $i > $i > $i ).

thf(c_Type_Osko__Type__Xabs__typeE__1__2_decl,type,
    c_Type_Osko__Type__Xabs__typeE__1__2: $i > $i > $i ).

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

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

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(223,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).

thf(941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(43,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(481,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)],[43]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

thf(1168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar @ c_Lambda_OdB_OdB__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).

thf(479,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar @ c_Lambda_OdB_OdB__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(962,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

thf(468,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(358,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( A @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).

thf(1200,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( A @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(333,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1142,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(1173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(62,axiom,
    tc_nat @ class_Nat_Osemiring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(523,plain,
    tc_nat @ class_Nat_Osemiring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(165,axiom,
    v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__1__1 ) ) ) @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_1) ).

thf(762,plain,
    v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__1__1 ) ) ) @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(156,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(741,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

thf(440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(614,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(128,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(677,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(861,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(1137,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(76,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(550,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

thf(797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(145,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( D @ ( E @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_Type_Otypings ) ) )
      | ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

thf(715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Otype @ ( tc_Type_Otype @ ( D @ ( E @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_Type_Otypings ) ) )
      | ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(39,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(472,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)],[39]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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(1260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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)],[384]) ).

thf(137,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(698,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)],[137]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ c_Suc @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) )
        = ( B @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).

thf(747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ c_Suc @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) )
        = ( B @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_Olift ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OdB__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).

thf(913,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OdB__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).

thf(1196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

thf(898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

thf(1243,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(142,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(709,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)],[142]) ).

thf(23,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(436,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)],[23]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(1254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(117,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(651,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)],[117]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(973,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

thf(885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).

thf(1046,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( C @ ( A @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( A @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Type_Otype_Otype__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Type_Otype_Otype__size @ ( A @ c_Type_Otype_Otype__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).

thf(719,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Type_Otype_Otype__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Type_Otype_Otype__size @ ( A @ c_Type_Otype_Otype__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(785,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(139,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(702,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)],[139]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_Lambda_Olift ) @ ( D @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).

thf(1059,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_Lambda_Olift ) @ ( D @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(294,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).

thf(1055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

thf(902,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

thf(1087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(1147,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(448,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).

thf(421,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

thf(870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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(969,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(99,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(606,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)],[99]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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(1013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

thf(881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(15,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(416,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)],[15]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

thf(492,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(26,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(443,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)],[26]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

thf(1109,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(115,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(646,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)],[115]) ).

thf(57,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(514,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)],[57]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Lambda_OdB_OAbs @ ( B @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Lambda_OdB_OAbs @ ( B @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__2 ) ) @ ( C @ ( B @ ( A @ c_Type_Osko__Type__Xtyping__elims__3__1 ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(1183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(905,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(45,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(485,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)],[45]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(834,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(278,axiom,
    v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__CHAINED__1 ) ) ) @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).

thf(1020,plain,
    v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__CHAINED__1 ) ) ) @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(86,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

thf(574,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(981,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(6,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(397,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)],[6]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Lambda_Olift ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Lambda_Olift ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OdB__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Lambda_OdB_OdB__size @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).

thf(998,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OdB__size )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( B @ c_Lambda_OdB_OdB__size @ ( A @ c_Lambda_OdB_OdB__size @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(314,axiom,
    v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

thf(1104,plain,
    v_u____ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(64,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(527,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)],[64]) ).

thf(234,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(920,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(56,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(512,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)],[56]) ).

thf(66,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(529,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)],[66]) ).

thf(121,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(661,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)],[121]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(546,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(236,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
      | ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).

thf(925,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ c_Type_Otypings ) ) )
      | ~ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( D @ ( C @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(1057,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(1163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(825,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(323,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1123,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

thf(598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(820,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

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

thf(424,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

thf(407,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(20,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(429,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)],[20]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) )
        = ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

thf(1238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(249,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(957,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).

thf(1223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(279,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Type_Otype @ ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Type_Otype @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Type_Otype @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).

thf(1021,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Type_Otype @ ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Type_Otype @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Type_Otype @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

thf(778,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(203,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

thf(847,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(205,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

thf(852,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

thf(665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(340,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(1159,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(130,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

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

thf(842,plain,
    v_T____ @ ( v_ua______ @ ( v_ea______ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(77,axiom,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

thf(551,plain,
    tc_nat @ class_OrderedGroup_Osemigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).

thf(1128,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).

thf(874,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
        = ( C @ ( D @ ( B @ c_Lambda_Olift ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).

thf(948,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
        = ( C @ ( D @ ( B @ c_Lambda_Olift ) @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(322,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( C @ ( D @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

thf(1121,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( C @ ( D @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).

thf(1064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(10,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(403,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)],[10]) ).

thf(272,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(1006,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( A @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(388,plain,
    ! [A: $i] :
      ( ~ ( A @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(94,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

thf(593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(101,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(610,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)],[101]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_Obeta @ c_ListOrder_Ostep1 ) ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).

thf(857,plain,
    ! [A: $i] :
      ( ~ ( A @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | v_thesis____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(60,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(519,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).

thf(578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(1089,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( v_a____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(1234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( v_a____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

thf(1111,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( v_a____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_I_0) ).

thf(1227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( v_a____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(174,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(783,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1118,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

thf(1028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(46,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(488,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)],[46]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).

thf(933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(161,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 ) ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(753,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 ) ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(70,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(537,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)],[70]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

thf(669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

thf(1075,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( E @ ( D @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(111,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(637,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(364,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(1214,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(338,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 @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

thf(1155,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 @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(1207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

thf(590,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).

thf(837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

thf(738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(372,axiom,
    v_n____ != v_i____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_False_0) ).

thf(1231,plain,
    v_n____ != v_i____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(328,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

thf(1131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

thf(1192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(230,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).

thf(911,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( B @ c_Nat_Osize__class_Osize ) @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).

thf(721,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(569,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(52,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(503,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(4,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(393,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)],[4]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(386,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ c_Lambda_Olift ) @ ( C @ ( B @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

thf(1263,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ c_Lambda_Olift ) @ ( C @ ( B @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(267,axiom,
    tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( v_i____ @ ( v_u____ @ ( c_Lambda_Osubst @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(997,plain,
    tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_as____ @ ( v_i____ @ ( v_u____ @ ( c_Lambda_Osubst @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_nat @ ( tc_Lambda_OdB @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ c_List_Omap ) ) ) @ ( c_InductTermi_OIT @ c_List_Olistsp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).

thf(1099,plain,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(985,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(336,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).

thf(1150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(380,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(1249,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(291,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).

thf(1050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xtyping__elims__2__1 ) ) ) @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(32,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(457,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)],[32]) ).

thf(242,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( B @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).

thf(938,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( G @ ( C @ ( B @ ( E @ ( F @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( F @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( v_T____
       != ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(184,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(805,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_fequal @ c_Predicate_Oconversep ) ) )
      = ( A @ c_fequal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).

thf(508,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_fequal @ c_Predicate_Oconversep ) ) )
      = ( A @ c_fequal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(765,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(352,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).

thf(1187,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(351,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__2 ) @ ( B @ ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__1 ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).

thf(1185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__2 ) @ ( B @ ( B @ ( A @ c_Type_Osko__Type__Xabs__typeE__1__1 ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

thf(888,plain,
    ! [A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( A @ c_Lambda_OdB_OAbs @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(301,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(1071,plain,
    ! [B: $i,A: $i] :
      ( ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(773,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[170]) ).

thf(179,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).

thf(794,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(91,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(586,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)],[91]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

thf(750,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(366,axiom,
    ! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

thf(1219,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ hAPP ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(745,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).

thf(601,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(330,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(1135,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(13,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_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(412,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_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(90,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(584,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(9,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(402,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).

thf(732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) @ ( B @ c_Lambda_OdB_OAbs @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(843,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

thf(1124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(73,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(545,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(3,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(391,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)],[3]) ).

thf(85,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(572,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)],[85]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

thf(713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(1107,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(126,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(672,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(27,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(445,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)],[27]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).

thf(936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(102,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(611,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(176,axiom,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

thf(787,plain,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(466,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(309,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).

thf(1092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).

thf(1194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(362,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(1209,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(226,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 @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(900,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 @ ( D @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

thf(831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(29,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(451,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(116,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(649,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)],[116]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

thf(1011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(17,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(419,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)],[17]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Lambda_Olift ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(1048,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Lambda_Olift ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(210,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).

thf(863,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

thf(1175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(222,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(890,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( 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_of__nat__0__less__iff_1) ).

thf(477,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( 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)],[41]) ).

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

thf(387,plain,
    ~ v_thesis____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

thf(631,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Olift ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

thf(758,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Olift ) )
      = ( tc_nat @ c_HOL_Oone__class_Oone @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

thf(552,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OVar @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).

thf(535,plain,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OVar @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

thf(483,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).

thf(700,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_ListOrder_Ostep1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(224,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(895,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

thf(964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeD__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(244,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

thf(943,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(124,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(668,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

thf(1177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(34,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(462,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)],[34]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(626,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(232,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(915,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(260,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).

thf(983,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(357,axiom,
    ! [A: $i] :
      ( A
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(1198,plain,
    ! [A: $i] :
      ( A
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(7,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(399,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).

thf(768,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(1015,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(100,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(608,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)],[100]) ).

thf(82,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(563,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).

thf(1000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(24,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(438,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(21,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(431,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)],[21]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

thf(653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(235,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(922,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OVar )
        = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

thf(685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OVar )
        = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
      = ( A @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

thf(521,plain,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
      = ( A @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(345,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(1171,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(288,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

thf(1044,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( B @ ( c_InductTermi_OIT @ c_List_Olistsp ) ) )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(378,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

thf(1066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(212,axiom,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).

thf(868,plain,
    ! [A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Predicate_Oconversep ) ) @ c_Wellfounded_Oaccp ) ) )
      | ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ 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_of__nat__less__iff_0) ).

thf(455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ 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)],[31]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(1166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(67,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(531,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(129,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(680,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)],[129]) ).

thf(122,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(663,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)],[122]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(927,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

thf(812,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

thf(1081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(823,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).

thf(836,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(47,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(490,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)],[47]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).

thf(675,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ c_Transitive__Closure_Ortranclp ) )
      = ( B @ ( A @ c_Transitive__Closure_Ortranclp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(359,axiom,
    v_T_Ha______ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_ia______ @ ( v_ea______ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).

thf(1203,plain,
    v_T_Ha______ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_ia______ @ ( v_ea______ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(92,axiom,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(589,plain,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(104,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(617,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)],[104]) ).

thf(58,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(516,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(334,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(1145,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 @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(1018,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(133,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(690,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(112,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(640,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)],[112]) ).

thf(281,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(1025,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(214,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 @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(872,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 @ ( C @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Lambda_OdB_OAbs ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).

thf(705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Lambda_OdB_OAbs ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
      = ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

thf(1225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ c_Lambda_Olift ) )
      = ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(971,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(143,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(712,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(270,axiom,
    v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).

thf(1003,plain,
    v_T_H____ @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( v_rs____ @ ( v_n____ @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(954,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

thf(1252,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_Type_Otype @ ( tc_Type_Otype @ ( C @ ( D @ ( B @ ( A @ ( C @ c_Type_Osko__Type__Xvar__app__typesE__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) @ ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(1053,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = 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(791,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(286,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = 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(1038,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

thf(717,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(51,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(502,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(385,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(1262,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) )
        = ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).

thf(463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldr ) ) ) ) )
        = ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_List_Ofoldl ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(38,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(470,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)],[38]) ).

thf(113,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(643,plain,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(1220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).

thf(808,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( D @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(1257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(292,axiom,
    v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__Xhyps__1__1 ) ) ) @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_Ohyps_I1_J_1) ).

thf(1052,plain,
    v_i____ @ ( v_e____ @ ( v_a____ @ ( v_T____ @ v_sko__local__XCons__Xhyps__1__1 ) ) ) @ ( v_a____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( v_a____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).

thf(727,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( v_a____ @ ( v_T____ @ ( B @ ( C @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( v_T____ @ ( A @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( v_a____ @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(273,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1008,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).

thf(859,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(119,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(656,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)],[119]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

thf(1023,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = E )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1094,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = E )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(258,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 ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(978,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 ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(1140,plain,
    ! [A: $i] :
      ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(49,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(497,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)],[49]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OAbs @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).

thf(876,plain,
    ! [A: $i] :
      ( ( tc_Lambda_OdB @ ( A @ c_Lambda_OdB_OAbs @ c_Nat_Osize__class_Osize ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_Lambda_OdB @ ( A @ c_Nat_Osize__class_Osize ) @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(376,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(1240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(264,axiom,
    tc_Lambda_OdB @ ( v_as____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ ( tc_Type_Otype @ c_Ex @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ ( c_InductTermi_OIT @ ( tc_nat @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( c_Type_Otyping @ ( tc_bool @ ( tc_Type_Otype @ ( tc_Lambda_OdB @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( tc_Type_Otype @ c_Type_Oshift @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ ( tc_nat @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_nat @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_nat @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBS ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ c_All @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ c_All @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_and @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(991,plain,
    tc_Lambda_OdB @ ( v_as____ @ ( v_T____ @ ( v_i____ @ ( v_e____ @ ( tc_Type_Otype @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ hAPP ) @ ( tc_Type_Otype @ c_Ex @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ ( c_InductTermi_OIT @ ( tc_nat @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( c_Type_Otyping @ ( tc_bool @ ( tc_Type_Otype @ ( tc_Lambda_OdB @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_InductTermi_OIT @ ( c_implies @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( v_T____ @ ( tc_Type_Otype @ c_Type_Oshift @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Type_Otyping @ ( tc_nat @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_implies @ ( tc_nat @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_nat @ c_COMBS ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_nat @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ c_COMBC ) ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_COMBS ) ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_nat @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_nat @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ c_All @ ( tc_Type_Otype @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Lambda_OdB @ tc_fun ) @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ c_All @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_Type_Otype @ tc_fun ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ c_All @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ ( tc_Type_Otype @ ( tc_nat @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( c_and @ ( tc_Lambda_OdB @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_Lambda_OdB @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).

thf(845,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(1084,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(1180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

thf(1157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(365,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(1216,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 )
       != ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
        = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).

thf(1189,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
        = C )
      | ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( C @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(976,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ 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 ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(688,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ 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 ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(63,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(524,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

thf(581,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_Lambda_OdB @ c_List_Olist_ONil ) )
      | ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
       != ( C @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(59,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(517,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).

thf(1062,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Wellfounded_Oaccp ) ) )
      | ( C @ ( B @ ( A @ c_Wellfounded_Oaccp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

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

thf(418,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

thf(781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( D @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( A @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ ( C @ c_Type_Osko__Type__Xlist__app__typeE__1__1 ) ) ) @ ( B @ ( A @ c_Type_Otypings ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).

thf(995,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(946,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(313,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

thf(1212,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(166,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ c_Suc @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).

thf(763,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ c_Suc @ ( E @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ c_Type_Oshift @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(75,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(549,plain,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(22,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(433,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)],[22]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).

thf(510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(341,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

thf(1161,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(181,axiom,
    v_T____ @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).

thf(800,plain,
    v_T____ @ ( v_u____ @ ( v_e____ @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).

thf(1116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(329,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).

thf(1133,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(105,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(620,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)],[105]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(1097,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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)],[311]) ).

thf(371,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).

thf(1229,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(818,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(11,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(405,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)],[11]) ).

thf(206,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(854,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(379,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

thf(1248,plain,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

thf(603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) )
     != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( C @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(83,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(564,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(53,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(506,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)],[53]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OAbs )
        = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

thf(474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Lambda_OdB_OAbs )
        = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Suc @ ( C @ ( B @ c_Lambda_Olift ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( C @ ( E @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).

thf(828,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( D @ ( B @ ( E @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Suc @ ( C @ ( B @ c_Lambda_Olift ) @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( C @ ( E @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

thf(960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ~ ( B @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL )
      | ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

thf(532,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(136,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(696,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)],[136]) ).

thf(14,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(415,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).

thf(918,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( c_Lambda_OdB_OApp @ hAPP ) @ hAPP ) @ ( tc_Lambda_OdB @ ( c_Lambda_Obeta @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).

thf(801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( B @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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(1033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(8,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(400,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)],[8]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( 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(1129,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(87,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(575,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)],[87]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Predicate_Oconversep ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).

thf(596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ ( A @ c_Predicate_Oconversep ) ) @ c_Predicate_Oconversep ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(65,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(528,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).

thf(644,plain,
    ! [A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
      = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ c_List_Olist_ONil @ ( A @ c_Lambda_OdB_OAbs @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(33,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(459,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)],[33]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(850,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

thf(1004,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ ( c_Lambda_Osubst @ hAPP ) @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(134,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(691,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(5,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(395,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)],[5]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(374,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).

thf(1236,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( E @ ( D @ ( A @ c_Predicate_Oconversep ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ 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(987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(908,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(265,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( C @ c_Type_Otypings ) ) )
      | ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Type_Otype @ ( tc_Type_Otype @ ( B @ ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).

thf(992,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( D @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( C @ c_Type_Otypings ) ) )
      | ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( F @ ( E @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( C @ ( c_Type_Otyping @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Type_Otype @ ( tc_Type_Otype @ ( B @ ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xvar__app__types__1__1 ) ) ) @ ( c_Type_Otype_OFun @ c_List_Ofoldr ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(803,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(240,axiom,
    v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

thf(935,plain,
    v_ua______ @ ( c_InductTermi_OIT @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(120,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(659,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)],[120]) ).

thf(72,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(543,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)],[72]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

thf(1204,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( C @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) @ ( c_Lambda_Obeta @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_Lambda_OdB @ ( tc_Lambda_OdB @ ( A @ ( C @ ( B @ c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 ) ) @ ( B @ c_Lambda_OdB_OVar @ ( c_Lambda_OdB_OApp @ c_List_Ofoldl ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(141,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(708,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

thf(775,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( c_Type_Otype_OFun @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(30,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(454,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)],[30]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(1069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(1267,plain,
    $false,
    inference(e,[status(thm)],[629,893,941,555,481,1168,760,479,1105,962,468,1200,1142,1173,523,762,741,1073,878,440,614,677,1041,861,1078,1137,550,797,715,472,930,1260,698,747,913,1196,898,1243,709,436,1254,651,973,885,1046,719,785,702,1059,1055,724,902,1087,1147,448,421,870,969,606,1013,770,881,416,492,756,443,1109,623,646,514,806,966,1183,905,485,834,1020,574,981,397,634,734,998,1104,527,920,512,529,661,546,925,810,1057,1163,825,1123,598,820,424,407,429,788,815,729,1238,957,1223,1021,778,847,852,665,1159,682,842,551,1128,874,948,1121,1064,403,1006,388,593,610,499,989,857,519,742,578,1089,1234,1111,1227,783,1118,1028,488,933,753,537,669,1075,637,1214,1155,1207,590,837,738,1231,1131,1192,911,721,569,503,393,1114,1263,997,1099,985,1150,1249,1050,457,938,805,508,765,1035,1187,1185,888,558,1071,773,794,586,750,1219,745,601,1135,412,584,694,402,732,843,1124,545,391,572,713,1107,540,672,445,936,611,787,466,1092,1194,1209,900,831,451,649,1011,419,1048,736,863,1175,890,477,387,631,758,552,535,483,700,895,964,943,668,1177,462,626,915,983,1198,399,768,1015,608,563,1000,438,431,653,922,685,521,1171,1044,1245,1066,868,455,883,1166,531,680,663,927,812,1081,823,836,490,675,1203,589,617,516,1145,1018,690,640,1025,872,705,1225,971,712,1003,954,1252,1053,791,1038,717,502,1262,463,470,643,1220,951,808,1257,1052,727,1008,859,656,1023,1094,978,1140,497,876,1240,991,845,1084,1180,1157,1216,1126,1189,976,688,524,581,517,1062,418,781,995,946,1101,1030,1212,763,549,433,510,1161,800,1116,1133,620,1097,1229,818,405,854,1248,865,603,564,506,474,828,960,532,696,415,918,801,1033,400,1129,575,1152,596,528,644,459,850,1004,691,395,839,1236,987,908,992,803,935,659,543,1204,708,775,560,454,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL827-1 : 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
% 0.15/0.40  % Computer : n026.cluster.edu
% 0.15/0.40  % Model    : x86_64 x86_64
% 0.15/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40  % Memory   : 8046.5625MB
% 0.15/0.40  % OS       : Linux 6.8.0-71-generic
% 0.15/0.40  % CPULimit : 300
% 0.15/0.40  % WCLimit  : 300
% 0.15/0.40  % DateTime : Fri Sep 25 23:41:55 UTC 2026
% 0.15/0.40  % CPUTime  : 
% 0.15/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.93/1.35  % [INFO] 	 Parsing done (353ms). 
% 1.93/1.36  % [INFO] 	 Running in sequential loop mode. 
% 3.08/1.74  % [INFO] 	 eprover registered as external prover. 
% 3.08/1.74  % [INFO] 	 Scanning for conjecture ... 
% 3.63/1.93  % [INFO] 	 Found a conjecture (or negated_conjecture) and 391 axioms. Running axiom selection ... 
% 4.12/2.12  % [INFO] 	 Axiom selection finished. Selected 384 axioms (removed 7 axioms). 
% 5.01/2.37  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.01/2.39  % [INFO] 	 Type checking passed. 
% 5.40/2.40  % [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 ... 
% 12.03/4.28  % External prover 'e' found a proof!
% 12.03/4.28  % [INFO] 	 Killing All external provers ... 
% 12.03/4.28  % Time passed: 3727ms (effective reasoning time: 2908ms)
% 12.03/4.28  % Axioms used in derivation (384): cls_Suc__pred_0, cls_not__one__less__zero_0, cls_less__iff__diff__less__0_0, cls_shift__commute_0, cls_add__0__left_0, cls_MI1_0, cls_subst__lt_0, cls_natgb_Oadd__r0__iff_1, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_apps__eq__Abs__conv_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_add__is__1_1, cls_zero__less__one_0, cls_of__nat__add_0, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_subst__App_0, cls_Suc__mono_0, cls_Var__eq__apps__conv_1, cls_of__nat__0_0, cls_subst__eq_0, cls_class__ringb_Oadd__r0__iff_1, cls_lift_Osimps_I2_J_0, cls_dB_Osimps_I8_J_0, cls_one__is__add_4, cls_termi__implies__IT_0, cls_nat__add__left__cancel__less_1, cls_diff__Suc__1_0, cls_typing__elims_I3_J_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_Cons_I1_J_1, cls_add__is__1_2, cls_add__strict__right__mono_0, cls_Cons_Ohyps_I1_J_1, cls_CHAINED_0, cls_less__add__Suc2_0, cls_of__nat__less__iff_0, cls_var__app__typesE_0, clsarity_fun__Orderings_Oorder, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_accp__downwards_0, cls_less__antisym_0, cls_conversepD_0, cls_MI2_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_termination__basic__simps_I1_J_0, cls_rtrancl__beta__Abs_0, cls_uIT_0, cls_add__is__0_0, cls_less__Suc__eq_2, cls_not__less__eq_1, cls_nat__add__left__cancel__less_0, cls_one__is__add_1, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_comm__monoid__add_Omult__1__right_0, cls_lift__subst__lt_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_of__nat__0__less__iff_0, cls_rtranclp__trans_0, cls_add__cancel__21_1, cls_add__left__cancel_0, cls_head__Var__reduction_1, cls_beta_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_add__gr__0_0, cls_Abs_0, cls_foldl__foldr1_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_gr0I_0, cls_lift__type_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_foldr_Osimps_I1_J_0, cls_nat__less__cases_0, cls_diff__diff__left_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_Var__apps__eq__Var__apps__conv_0, cls_gr__implies__not0_0, cls_order__less__asym_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_add__less__mono_0, cls_less__iff__diff__less__0_1, cls_subst__gt_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_type_Osize_I2_J_0, cls_shift__eq_0, cls_right__minus__eq_0, cls_Var_I2_J_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_dB_Osimps_I3_J_0, cls_foldl__absorb0_0, cls_type_Osize_I4_J_0, cls_add__Suc_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, clsarity_bool__Orderings_Oorder, cls_subst__Var_2, cls_diff__add__inverse2_0, cls_xt1_I10_J_0, cls_add__less__cancel__right_1, cls_nat__add__left__commute_0, cls_Var__apps__eq__Var__apps__conv_1, cls_lift__lift_0, cls_one__is__add_5, cls_typing__elims_I3_J_1, cls_class__semiring_Osemiring__rules_I6_J_0, cls_CHAINED_1, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_typing__elims_I2_J_0, cls_diff__Suc__Suc_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_CHAINED_0_01, cls_add__strict__left__mono_0, cls_App__eq__foldl__conv_0, cls_add__less__mono1_0, cls_type_Osimps_I2_J_1, cls_dB_Osimps_I4_J_0, cls_nat__diff__split_0, cls_Suc__diff__1_0, cls_of__nat__1_0, cls_typing__elims_I1_J_0, cls_class__semiring_Oadd__a_0, cls_var__app__types_0, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_subject__reduction_H_0, cls_add__is__1_0, cls_var__app__typesE_1, cls_dB_Osize_I5_J_0, cls_one__is__add_0, cls_less__add__Suc1_0, cls_Var__IT_0, cls_Var_I3_J_0, cls_converse__rtranclp__into__rtranclp_0, cls_list__app__typeD_1, cls_apps__preserves__betas_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_of__nat__eq__iff_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_comm__monoid__add_Omult__commute_0, cls_add__right__cancel_0, cls_App_0, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_nT_0, cls_nat__add__assoc_0, cls_head__Var__reduction_0, cls_One__nat__def_0, cls_less__add__one_0, cls_add__strict__mono_0, cls_Cons_I1_J_0, cls_lessI_0, cls_diff__Suc__eq__diff__pred_0, cls_zero__less__two_0, cls_of__nat__0__less__iff_1, cls_IT__implies__termi_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_apps__eq__Abs__conv_2, cls_add__cancel__21_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__Suc__eq__0__disj_3, cls_uT_0, cls_less__add__eq__less_0, cls_conversep__conversep_0, cls_lift_Osimps_I3_J_0, cls_dB_Osimps_I1_J_0, cls_Abs__App__neq__Var__apps_0, cls_rtrancl__beta__App_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_dB_Osize_I3_J_0, cls_subst__Var_1, clsarity_bool__Orderings_Opreorder, cls_rtrancl__beta__AppL_0, cls_natgb_Oadd__cancel_0, cls_Nitpick_Ortranclp__def_1, cls_diff__less_0, cls_diff__self_0, cls_less__imp__diff__less_0, cls_type_Osimps_I2_J_0, cls_zero__neq__one_0, cls_neq0__conv_1, cls_not__Nil__step1_0, cls_one__is__add_2, cls_apps__eq__Abs__conv_1, cls_dB_Osize_I4_J_0, cls_add__less__cancel__right_0, cls_add__diff__cancel_0, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_Var__apps__neq__Abs__apps_0, cls_subst__lemma_0, cls_foldl__assoc_0, clsarity_nat__Orderings_Opreorder, cls_nat__diff__split__asm_1, cls_less__not__refl_0, cls_conversep_Ointros_0, cls_gr0__conv__Suc_1, cls_class__ringb_Oadd__cancel_0, cls_accp__downwards__aux_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_lift__subst_0, cls_right__minus__eq_1, cls_foldl__foldr1__lemma_0, cls_diff__less__Suc_0, cls_nat__diff__split_1, cls_linorder__neqE__ordered__idom_0, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_dB_Osimps_I2_J_1, cls_var__app__types_1, cls_subst__subst_0, cls_less__diff__conv_1, cls_nat_Oinject_0, cls_add__lessD1_0, cls_even__less__0__iff_1, cls_False_0, cls_class__ringb_Oadd__r0__iff_0, cls_less__diff__conv_0, cls_less__SucE_0, cls_lift__preserves__beta_H_0, cls_list__app__typeD_0, cls_not__less__less__Suc__eq_1, cls_CHAINED_0_02, cls_rtranclp_Ortrancl__refl_0, cls_Nat_Oadd__0__right_0, cls_eq__eqI_0, cls_nat__neq__iff_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_lift_Osimps_I1_J_1, cls_Suc__lessD_0, cls_natgb_Oadd__r0__iff_0, cls_add__is__1_4, cls_add__is__1_5, cls_diff__self__eq__0_0, cls_add__neg__neg_0, cls_dB_Osize_I1_J_0, cls_add__eq__if_1, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_abs_0, cls_less__Suc0_0, cls_accp__downward_0, cls_Abs__eq__apps__conv_2, cls_diff__0__right_0, cls_rtranclp__idemp_0, cls_list__app__typeE_1, cls_typing_OVar_0, cls_diff__Suc__less_0, cls_lift__IT_0, cls_IT_OVar_0, cls_Var_I4_J_0, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_typing__elims_I2_J_1, cls_nat_Osimps_I3_J_0, cls_apps__preserves__beta2_0, cls_less__trans__Suc_0, cls_plus__nat_Oadd__0_0, cls_comm__monoid__add_Omult__1_0, cls_list__app__typeI_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_accp_Ocases_0, cls_diff__less__mono2_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_order__less__irrefl_0, cls_diff__0__eq__0_0, cls_eq__eqI_1, cls_class__semiring_Oadd__c_0, cls_Abs__eq__apps__conv_0, cls_zero__less__diff_1, cls_minus__nat_Odiff__0_0, cls_apps__preserves__beta_0, cls_shift__lt_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_App__eq__foldl__conv_4, cls_add__is__0_2, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_foldr__conv__foldl_0, cls_add__is__1_3, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_add__pos__pos_0, cls_Suc__eq__plus1_0, cls_n__not__Suc__n_0, cls_less__SucI_0, cls_not__less0_0, cls_diffs0__imp__equal_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_eq__iff__diff__eq__0_1, cls_add__less__cancel__left_0, cls_subst__Var__IT_0, cls_class__ringb_Osubr0__iff_1, cls_shift__gt_0, cls_one__is__add_3, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, cls_conversep__eq_0, cls_subst__Abs_0, cls_Lambda_0, cls_Suc__less__eq_0, cls_add__gr__0_2, cls_list__app__typeE_0, cls_lift_Osimps_I1_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_subst__Var_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_I_0, cls_foldl__Nil_0, cls_abs__typeE_0, cls_that_0, cls_Suc__pred_H_0, cls_add__gr__0_1, cls_less__Suc0_1, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, cls_Abs__eq__apps__conv_1, cls_subst__preserves__beta2_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_dB_Osize_I2_J_0, cls_diff__commute_0, cls_of__nat__Suc_0, cls_class__ringb_Osubr0__iff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, cls_dB_Osize_I6_J_0, cls_eq__iff__diff__eq__0_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_zero__less__Suc_0, cls_conversep__iff_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_subst__preserves__beta2_H_0, cls_rtranclp__converseD_0, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_conversep_Ocases_0, cls_even__less__0__iff_0, cls_rtranclp__converseI_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_of__nat__less__0__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0, cls_nat__add__commute_0, cls_double__induction__lemma_0, cls_add__diff__inverse_0, cls_rtrancl__beta__AppR_0
% 12.03/4.28  % No. of inferences in proof: 773
% 12.03/4.28  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3727 ms resp. 2908 ms w/o parsing
% 13.52/4.61  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.52/4.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------