TSTP Solution File: SWV926-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV926-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n001.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:19:27 EDT 2023

% Result   : Unsatisfiable 15.63s 4.88s
% Output   : Refutation 17.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  571
% Syntax   : Number of formulae    : 1066 ( 509 unt;  77 typ;   0 def)
%            Number of atoms       : 1633 ( 724 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 52248 ( 942   ~; 644   |;   0   &;50662   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  146 ( 146   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   79 (  77 usr;  22 con; 0-5 aty)
%            Number of variables   : 4944 (   0   ^;4944   !;   0   ?;4944   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(v_ad_type,type,
    v_ad: $i ).

thf(v_ab_type,type,
    v_ab: $i ).

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

thf(tc_List_Olist_type,type,
    tc_List_Olist: $i > $i ).

thf(tc_String_Ochar_type,type,
    tc_String_Ochar: $i ).

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

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

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

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

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

thf(tc_Expr_Oexp_type,type,
    tc_Expr_Oexp: $i > $i ).

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

thf(tc_Option_Ooption_type,type,
    tc_Option_Ooption: $i > $i ).

thf(tc_Value_Oval_type,type,
    tc_Value_Oval: $i ).

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

thf(v_ea_type,type,
    v_ea: $i ).

thf(v_a_type,type,
    v_a: $i ).

thf(v_b_type,type,
    v_b: $i ).

thf(v_e_Ha_type,type,
    v_e_Ha: $i ).

thf(v_aa_type,type,
    v_aa: $i ).

thf(v_ba_type,type,
    v_ba: $i ).

thf(c_SmallStep_Ored_type,type,
    c_SmallStep_Ored: $i > $i ).

thf(v_P_type,type,
    v_P: $i ).

thf(c_DefAss_O_092_060A_062_type,type,
    c_DefAss_O_092_060A_062: $i > $i > $i ).

thf(c_Option_Ooption_OSome_type,type,
    c_Option_Ooption_OSome: $i > $i ).

thf(v_ac_type,type,
    v_ac: $i ).

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

thf(c_Map_Odom_type,type,
    c_Map_Odom: $i > $i > $i > $i ).

thf(v_ae_type,type,
    v_ae: $i ).

thf(v_e_092_060_094isub_0622_type,type,
    v_e_092_060_094isub_0622: $i ).

thf(v_x_type,type,
    v_x: $i ).

thf(c_Expr_Oexp_OFAcc_type,type,
    c_Expr_Oexp_OFAcc: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OCond_type,type,
    c_Expr_Oexp_OCond: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OBlock_type,type,
    c_Expr_Oexp_OBlock: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OLAss_type,type,
    c_Expr_Oexp_OLAss: $i > $i > $i > $i ).

thf(c_Expr_Oexp_OVal_type,type,
    c_Expr_Oexp_OVal: $i > $i > $i ).

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

thf(c_Expr_Oexp_OFAss_type,type,
    c_Expr_Oexp_OFAss: $i > $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OTryCatch_type,type,
    c_Expr_Oexp_OTryCatch: $i > $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OBinOp_type,type,
    c_Expr_Oexp_OBinOp: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_Othrow_type,type,
    c_Expr_Oexp_Othrow: $i > $i > $i ).

thf(c_Expr_Oexp_OCall_type,type,
    c_Expr_Oexp_OCall: $i > $i > $i > $i > $i ).

thf(c_Expr_Oexp_OSeq_type,type,
    c_Expr_Oexp_OSeq: $i > $i > $i > $i ).

thf(c_Expr_Oexp_OWhile_type,type,
    c_Expr_Oexp_OWhile: $i > $i > $i > $i ).

thf(c_Expr_Oexp_OCast_type,type,
    c_Expr_Oexp_OCast: $i > $i > $i > $i ).

thf(c_Value_Oval_OAddr_type,type,
    c_Value_Oval_OAddr: $i > $i ).

thf(c_Value_Oval_ONull_type,type,
    c_Value_Oval_ONull: $i ).

thf(c_BigStep_Ofinal_type,type,
    c_BigStep_Ofinal: $i > $i > $o ).

thf(c_Objects_Ohext_type,type,
    c_Objects_Ohext: $i > $i > $o ).

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

thf(c_Fun_Ofun__upd_type,type,
    c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).

thf(c_Map_Omap__add_type,type,
    c_Map_Omap__add: $i > $i > $i > $i > $i ).

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

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

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

thf(c_BigStep_Oeval_type,type,
    c_BigStep_Oeval: $i > $i > $i > $i > $i > $o ).

thf(c_Map_Orestrict__map_type,type,
    c_Map_Orestrict__map: $i > $i > $i > $i > $i ).

thf(c_Expr_Ofv_type,type,
    c_Expr_Ofv: $i > $i ).

thf(c_WellForm_Owf__prog_type,type,
    c_WellForm_Owf__prog: $i > $i > $i > $o ).

thf(c_WWellForm_Owwf__J__mdecl_type,type,
    c_WWellForm_Owwf__J__mdecl: $i ).

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

thf(class_Orderings_Obot_type,type,
    class_Orderings_Obot: $i > $o ).

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

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

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

thf(c_BigStep_Oevals_type,type,
    c_BigStep_Oevals: $i > $i > $i > $i > $i > $o ).

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

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

thf(c_Option_Ooption_Ooption__case_type,type,
    c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).

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

thf(c_Recdef_Osame__fst_type,type,
    c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).

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

thf(c_Expr_Ofvs_type,type,
    c_Expr_Ofvs: $i > $i ).

thf(c_Wellfounded_Olex__prod_type,type,
    c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).

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

thf(c_Map_Osko__Map__XdomD__1__1_type,type,
    c_Map_Osko__Map__XdomD__1__1: $i > $i > $i > $i > $i ).

thf(463,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(1665,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(339,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow1_0) ).

thf(1411,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).

thf(629,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(234,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).

thf(1190,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(448,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).

thf(1633,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(199,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).

thf(1105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(176,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).

thf(1031,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(229,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

thf(1179,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(97,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

thf(777,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(60,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).

thf(666,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(406,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofvs @ ( c_List_Olist_OCons @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofvs @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I17_J_0) ).

thf(1549,plain,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofvs @ ( c_List_Olist_OCons @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofvs @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(472,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow2_0) ).

thf(1686,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(1586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(384,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBlockThrow_0) ).

thf(1501,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

thf(809,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

thf(1718,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(192,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

thf(1083,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(154,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).

thf(962,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(1200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(440,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1618,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(164,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).

thf(994,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(335,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(1401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(126,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).

thf(873,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(289,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOp2Reds_0) ).

thf(1305,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(353,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( c_BigStep_Oeval @ C @ D @ ( c_Pair @ E @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__lcl__incr_0) ).

thf(1437,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( c_BigStep_Oeval @ C @ D @ ( c_Pair @ E @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(226,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

thf(1173,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(1158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(92,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

thf(762,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(430,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OLAssThrow_0) ).

thf(1596,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(1406,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(42,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).

thf(614,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(466,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ D @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ G @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Reds__dom__lcl_0) ).

thf(1671,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ D @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ G @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OWhile @ A @ B @ C ) @ C )
      = ( c_DefAss_O_092_060A_062 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I13_J_0) ).

thf(1655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OWhile @ A @ B @ C ) @ C )
      = ( c_DefAss_O_092_060A_062 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(209,axiom,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1137,plain,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(17,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

thf(533,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(22,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I208_J_0) ).

thf(550,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(3,negated_conjecture,
    ( ( c_DefAss_O_092_060A_062 @ v_e_Ha @ ( tc_List_Olist @ tc_String_Ochar ) )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ v_ac ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(500,plain,
    ( ( c_DefAss_O_092_060A_062 @ v_e_Ha @ ( tc_List_Olist @ tc_String_Ochar ) )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ v_ac ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(222,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssRedsThrow_0) ).

thf(1164,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(76,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

thf(715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(186,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).

thf(1063,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(312,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(1354,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(144,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(930,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(381,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

thf(1497,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_COMBC @ ( c_in @ A ) @ B @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_COMBC @ ( c_in @ A ) @ C @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).

thf(1705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_COMBC @ ( c_in @ A ) @ B @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_COMBC @ ( c_in @ A ) @ C @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(267,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ E @ I @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow2_0) ).

thf(1260,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ E @ I @ ( c_Expr_Oexp_Othrow @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).

thf(698,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(306,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(1342,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(87,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).

thf(747,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(236,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqRedsThrow_0) ).

thf(1196,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(134,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).

thf(898,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(259,axiom,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1243,plain,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(355,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).

thf(1441,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(130,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).

thf(885,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(456,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(1650,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ B @ C @ D ) @ ( c_Map_Odom @ A @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__map__add_0) ).

thf(1366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ B @ C @ D ) @ ( c_Map_Odom @ A @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).

thf(829,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(196,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

thf(1095,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(331,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
       != A )
      | ( ( hAPP @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(1391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
       != A )
      | ( ( hAPP @ A @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Expr_Ofv @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I7_J_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Expr_Ofv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(432,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow1_0) ).

thf(1601,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(328,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(1386,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(350,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ D @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Red__dom__lcl_0) ).

thf(1430,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ D @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(297,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(1323,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(140,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).

thf(917,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(150,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
      = ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(949,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
      = ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(338,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CastReds_0) ).

thf(1409,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(79,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).

thf(724,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(461,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1660,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(286,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).

thf(1298,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(1330,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(269,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oevals @ A @ ( c_List_Olist_OCons @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D @ ( c_List_Olist_OCons @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G )
      | ~ ( c_BigStep_Oevals @ A @ C @ H @ F @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OCons_0) ).

thf(1264,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oevals @ A @ ( c_List_Olist_OCons @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D @ ( c_List_Olist_OCons @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ G )
      | ~ ( c_BigStep_Oevals @ A @ C @ H @ F @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_OVal @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(293,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(1313,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(277,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_TryRedsVal_0) ).

thf(1279,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(638,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ThrowRedsThrow_0) ).

thf(1379,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(391,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Ofinal @ D @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_small__by__big_0) ).

thf(1514,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Ofinal @ D @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(1147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(1247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1319,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

thf(1013,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(416,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ A @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).

thf(1568,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ A @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(452,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).

thf(1641,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1232,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedCastNull_0) ).

thf(1479,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(436,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).

thf(1609,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(156,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I200_J_0) ).

thf(969,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1347,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(377,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(1489,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(90,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

thf(756,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(360,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).

thf(1450,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(179,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).

thf(1040,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(215,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

thf(1151,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(423,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).

thf(1581,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(111,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(821,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(136,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

thf(905,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(343,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1418,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).

thf(1020,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(29,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

thf(574,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(224,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

thf(1169,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(124,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).

thf(866,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(189,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).

thf(1072,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(332,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_BigStep_Oevals @ C @ D @ ( c_Pair @ A @ E @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ B @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evals__hext_0) ).

thf(1394,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_BigStep_Oevals @ C @ D @ ( c_Pair @ A @ E @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ B @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(394,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( c_BigStep_Oevals @ C @ D @ ( c_Pair @ E @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evals__lcl__incr_0) ).

thf(1521,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( c_BigStep_Oevals @ C @ D @ ( c_Pair @ E @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(15,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

thf(527,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(414,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ A @ B ) @ ( c_Pair @ C @ E @ A @ B ) @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Wellfounded_Olex__prod @ F @ G @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ D @ E @ B @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_3) ).

thf(1564,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ A @ B ) @ ( c_Pair @ C @ E @ A @ B ) @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Wellfounded_Olex__prod @ F @ G @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ D @ E @ B @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(442,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(96,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).

thf(774,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(1345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(162,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).

thf(988,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(477,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_BigStep_Oeval @ C @ D @ ( c_Pair @ A @ E @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ B @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__hext_0) ).

thf(1697,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_BigStep_Oeval @ C @ D @ ( c_Pair @ A @ E @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ B @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(119,axiom,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OAddr @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I16_J_0) ).

thf(849,plain,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OAddr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(434,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAccReds_0) ).

thf(1604,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(1206,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(141,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).

thf(920,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(64,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).

thf(678,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(1470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(292,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I13_J_0) ).

thf(1311,plain,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

thf(1636,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(10,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).

thf(512,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(148,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

thf(942,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I89_J_0) ).

thf(1047,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).

thf(1730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(1274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(491,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

thf(1723,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(1223,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(393,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ A @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ B @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

thf(1519,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ A @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ B @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1355,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(37,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

thf(598,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(385,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Oeval @ A @ F @ G @ D @ E )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extend__1__eval_0) ).

thf(1502,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Oeval @ A @ F @ G @ D @ E )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(25,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).

thf(561,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(376,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1487,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(109,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).

thf(815,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).

thf(729,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(257,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oevals @ A @ ( c_List_Olist_OCons @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D @ ( c_List_Olist_OCons @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ConsThrow_0) ).

thf(1238,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oevals @ A @ ( c_List_Olist_OCons @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ D @ ( c_List_Olist_OCons @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(412,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

thf(1560,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(112,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(825,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1619,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(320,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1370,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I12_J_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(433,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(128,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).

thf(879,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(120,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

thf(852,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(59,axiom,
    ! [B: $i,A: $i] : ( c_BigStep_Ofinal @ ( c_Expr_Oexp_OVal @ A @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_final__def_1) ).

thf(665,plain,
    ! [B: $i,A: $i] : ( c_BigStep_Ofinal @ ( c_Expr_Oexp_OVal @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(473,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_DefAss_O_092_060A_062 @ A @ ( tc_List_Olist @ tc_String_Ochar ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ B ) )
      | ( c_lessequals @ B @ ( c_Expr_Ofv @ A ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__fv_0) ).

thf(1687,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_DefAss_O_092_060A_062 @ A @ ( tc_List_Olist @ tc_String_Ochar ) )
       != ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ B ) )
      | ( c_lessequals @ B @ ( c_Expr_Ofv @ A ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(443,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

thf(1624,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(243,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

thf(1210,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(191,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

thf(1079,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(206,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).

thf(1128,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_1) ).

thf(1281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(117,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).

thf(842,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(418,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
      | ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(1573,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
      | ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(32,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).

thf(583,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(522,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(315,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(1360,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(1270,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(54,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I65_J_0) ).

thf(650,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(171,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).

thf(1017,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(299,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOpRedsThrow1_0) ).

thf(1328,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(201,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).

thf(1111,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(382,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(1498,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Expr_Ofv @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I14_J_0) ).

thf(1425,plain,
    ! [A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Expr_Ofv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(125,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).

thf(869,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(99,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).

thf(783,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(7,negated_conjecture,
    ( ( c_DefAss_O_092_060A_062 @ v_e_092_060_094isub_0622 @ ( tc_List_Olist @ tc_String_Ochar ) )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ v_x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(499,plain,
    ( ( c_DefAss_O_092_060A_062 @ v_e_092_060_094isub_0622 @ ( tc_List_Olist @ tc_String_Ochar ) )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ v_x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).

thf(519,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(428,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1592,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(70,axiom,
    ! [B: $i,A: $i] : ( c_BigStep_Ofinal @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ A ) @ B ) @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_final__def_2) ).

thf(697,plain,
    ! [B: $i,A: $i] : ( c_BigStep_Ofinal @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ A ) @ B ) @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(194,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).

thf(1089,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(255,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssReds2_0) ).

thf(1234,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(402,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1540,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(168,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

thf(1006,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(210,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).

thf(1138,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(488,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1719,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1493,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I4_J_0) ).

thf(1160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(175,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

thf(1028,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(316,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(1361,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(89,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

thf(753,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I221_J_0) ).

thf(669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Othrow @ A @ B )
       != ( c_Expr_Oexp_Othrow @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

thf(901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Othrow @ A @ B )
       != ( c_Expr_Oexp_Othrow @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(479,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).

thf(1700,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(358,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CondReds_0) ).

thf(1446,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(453,axiom,
    ! [B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OVal @ A @ B ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I3_J_0) ).

thf(1644,plain,
    ! [B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OVal @ A @ B ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(437,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OCastThrow_0) ).

thf(1612,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(21,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

thf(547,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(344,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAccRedsThrow_0) ).

thf(1419,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(283,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ ( c_Pair @ C @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ A @ ( c_Pair @ E @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ G @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Red__fv_0) ).

thf(1292,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ ( c_Pair @ C @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ A @ ( c_Pair @ E @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ G @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(145,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

thf(933,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(364,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ D @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRedsThrow2_0) ).

thf(1461,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ D @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(18,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

thf(537,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(202,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).

thf(1114,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(72,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).

thf(701,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(1249,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(285,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1297,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(84,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).

thf(738,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CastRedsThrow_0) ).

thf(1530,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(270,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

thf(1266,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(207,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).

thf(1131,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(464,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(138,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).

thf(911,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(78,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

thf(721,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(486,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).

thf(1715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(489,axiom,
    class_HOL_Oord @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(1720,plain,
    class_HOL_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(53,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).

thf(647,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(165,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).

thf(997,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(426,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(161,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).

thf(985,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(185,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I205_J_0) ).

thf(1060,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(182,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

thf(1050,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(445,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ t_a @ C ) @ v_x )
      = ( c_Option_Ooption_Ooption__case @ ( hAPP @ A @ v_x ) @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ B @ v_x ) @ ( tc_Option_Ooption @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__def_0) ).

thf(1627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ t_a @ C ) @ v_x )
      = ( c_Option_Ooption_Ooption__case @ ( hAPP @ A @ v_x ) @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ B @ v_x ) @ ( tc_Option_Ooption @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(396,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1525,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(302,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).

thf(1333,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).

thf(1086,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(93,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).

thf(765,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1286,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(366,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_TryReds_0) ).

thf(1466,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(439,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).

thf(1616,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(16,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).

thf(530,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(33,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).

thf(586,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).

thf(926,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(239,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Oeval @ A @ F @ G @ D @ E )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extend__eval_0) ).

thf(1202,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Oeval @ A @ F @ G @ D @ E )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(102,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

thf(792,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(58,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I50_J_0) ).

thf(662,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(77,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I64_J_0) ).

thf(718,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).

thf(888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1648,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1483,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(322,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssReds1_0) ).

thf(1374,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(38,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).

thf(601,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(155,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(965,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(88,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

thf(750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(493,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(389,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOp1Reds_0) ).

thf(1510,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(217,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

thf(1154,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(69,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I215_J_0) ).

thf(694,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(82,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I191_J_0) ).

thf(732,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(457,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(1652,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(329,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ A @ B ) @ ( c_Pair @ C @ E @ A @ B ) @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Recdef_Osame__fst @ F @ G @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ D @ E @ B @ B ) ) @ ( hAPP @ G @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ F @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__fstI_0) ).

thf(1388,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ A @ B ) @ ( c_Pair @ C @ E @ A @ B ) @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Recdef_Osame__fst @ F @ G @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ D @ E @ B @ B ) ) @ ( hAPP @ G @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ F @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(30,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

thf(577,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(400,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(1535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(153,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).

thf(958,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(480,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(205,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

thf(1124,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(265,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OThrowThrow_0) ).

thf(1256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(251,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

thf(1226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

thf(936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(483,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(41,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

thf(611,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(2,negated_conjecture,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ v_ea @ ( c_Pair @ v_a @ v_b @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_e_Ha @ ( c_Pair @ v_aa @ v_ba @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ v_P ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(498,plain,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ v_ea @ ( c_Pair @ v_a @ v_b @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_e_Ha @ ( c_Pair @ v_aa @ v_ba @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ v_P ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(301,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).

thf(1332,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(195,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).

thf(1092,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(468,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1675,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(62,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).

thf(672,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(51,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I222_J_0) ).

thf(641,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(349,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
      | ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1428,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
      | ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(266,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(73,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).

thf(704,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(65,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).

thf(681,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(203,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

thf(1117,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(1349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(403,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallRedsObj_0) ).

thf(1542,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(212,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).

thf(1144,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(474,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Red__lcl__add_0) ).

thf(1690,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(290,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).

thf(1307,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(159,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

thf(979,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(39,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

thf(604,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(9,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).

thf(509,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(180,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

thf(1043,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(417,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ D @ H @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow2_0) ).

thf(1571,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ D @ H @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(323,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallObjThrow_0) ).

thf(1376,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(354,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CastNull_0) ).

thf(1439,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ C @ D @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).

thf(863,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(1175,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(298,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ A @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).

thf(1325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ A @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(133,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).

thf(895,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_COMBC @ ( c_in @ C ) @ A @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_COMBC @ ( c_in @ C ) @ B @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_COMBC @ ( c_in @ C ) @ A @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_COMBC @ ( c_in @ C ) @ B @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(104,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

thf(799,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(1162,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(1177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(326,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Ofv @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) )
      | ~ ( c_BigStep_Oeval @ B @ A @ ( c_Pair @ C @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ( G = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__closed__lcl__unchanged_0) ).

thf(1381,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Ofv @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) )
      | ~ ( c_BigStep_Oeval @ B @ A @ ( c_Pair @ C @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ( G = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(94,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(768,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I11_J_0) ).

thf(1245,plain,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ B ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(187,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I165_J_0) ).

thf(1066,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(98,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).

thf(780,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(40,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).

thf(608,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(166,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).

thf(1000,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(371,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1477,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(198,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).

thf(1102,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(55,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).

thf(653,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(476,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ G @ ( tc_Option_Ooption @ C ) ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).

thf(1694,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ G @ ( tc_Option_Ooption @ C ) ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(413,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ A @ B ) @ ( c_Pair @ E @ F @ A @ B ) @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Wellfounded_Olex__prod @ G @ H @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ E @ A @ A ) ) @ G ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_2) ).

thf(1562,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ A @ B ) @ ( c_Pair @ E @ F @ A @ B ) @ ( tc_prod @ A @ B ) @ ( tc_prod @ A @ B ) ) ) @ ( c_Wellfounded_Olex__prod @ G @ H @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ E @ A @ A ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(66,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(685,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(1171,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(237,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BinOpRedsThrow2_0) ).

thf(1198,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(1396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofvs @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I9_J_0) ).

thf(1594,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofvs @ C ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(1699,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(317,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1364,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Val_0) ).

thf(1626,plain,
    ! [C: $i,B: $i,A: $i] : ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_OVal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(177,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

thf(1034,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ A @ E @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).

thf(1166,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ A @ E @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(471,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(276,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(1277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(208,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(108,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).

thf(812,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(23,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).

thf(553,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(1181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

thf(1413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(190,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).

thf(1076,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(63,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

thf(675,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(424,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).

thf(1583,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_BigStep_Oeval @ C @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(242,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed2_0) ).

thf(1208,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_ONull ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I17_J_0) ).

thf(589,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_ONull ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(43,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).

thf(617,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(11,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

thf(516,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(147,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

thf(939,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1340,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(115,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).

thf(836,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(407,axiom,
    ! [A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I3_J_0) ).

thf(1551,plain,
    ! [A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(405,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ F @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ B @ F @ D ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd_0) ).

thf(1547,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ F @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ B @ F @ D ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(174,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).

thf(1025,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(218,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ ( c_Pair @ C @ ( c_Map_Orestrict__map @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ ( c_Map_Orestrict__map @ H @ E @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_lessequals @ ( c_Expr_Ofv @ B ) @ E @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( c_BigStep_Oeval @ A @ B @ ( c_Pair @ C @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__restrict__lcl_0) ).

thf(1156,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ ( c_Pair @ C @ ( c_Map_Orestrict__map @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ ( c_Map_Orestrict__map @ H @ E @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_lessequals @ ( c_Expr_Ofv @ B ) @ E @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( c_BigStep_Oeval @ A @ B @ ( c_Pair @ C @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ F @ ( c_Pair @ G @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(250,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1225,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(415,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1368,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

thf(1267,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(253,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WhileCondThrow_0) ).

thf(1230,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OWhile @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

thf(1098,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

thf(712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(24,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

thf(557,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(167,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

thf(1003,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(31,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I178_J_0) ).

thf(580,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(121,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

thf(855,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1516,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(1598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(183,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I149_J_0) ).

thf(1053,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ D ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I8_J_0) ).

thf(1432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Expr_Ofv @ A ) @ ( c_Expr_Ofv @ D ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ B @ C )
      | ~ ( c_BigStep_Ofinal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__finalId_0) ).

thf(1637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ B @ C )
      | ~ ( c_BigStep_Ofinal @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(4,negated_conjecture,
    ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ v_ac @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    = v_ab ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(502,plain,
    ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ v_ac @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    = v_ab ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_COMBC @ ( c_in @ t_a ) @ A @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_COMBC @ ( c_in @ t_a ) @ B @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).

thf(1679,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_COMBC @ ( c_in @ t_a ) @ A @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_COMBC @ ( c_in @ t_a ) @ B @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(1579,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(247,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ThrowReds_0) ).

thf(1218,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

thf(1336,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(248,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ F @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ F @ E @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).

thf(1220,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ F @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ F @ E @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(20,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I105_J_0) ).

thf(544,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(233,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CastRedsNull_0) ).

thf(1188,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(1186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(336,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed1_0) ).

thf(1404,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(86,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

thf(744,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(211,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

thf(1141,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(348,axiom,
    class_Orderings_Obot @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(1427,plain,
    class_Orderings_Obot @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(465,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1670,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(28,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).

thf(571,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(122,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(859,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(56,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(173,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

thf(1023,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(375,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqReds_0) ).

thf(1485,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(387,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LAssReds_0) ).

thf(1506,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(386,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

thf(1504,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(321,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Try_0) ).

thf(1372,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_BigStep_Oeval @ A @ B @ F @ ( c_Expr_Oexp_OVal @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(36,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).

thf(595,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(6,negated_conjecture,
    ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_b @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ v_ae @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    = v_ad ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(497,plain,
    ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_b @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ v_ae @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    = v_ad ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(127,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).

thf(876,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(258,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ C @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ ( c_Expr_Ofv @ D ) ) )
      | ~ ( c_BigStep_Oeval @ E @ D @ ( c_Pair @ F @ C @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G @ ( c_Pair @ H @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__notfree__unchanged_0) ).

thf(1240,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ C @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ ( c_Expr_Ofv @ D ) ) )
      | ~ ( c_BigStep_Oeval @ E @ D @ ( c_Pair @ F @ C @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ G @ ( c_Pair @ H @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(163,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).

thf(991,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(118,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(845,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(345,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Expr_Ofv @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fv__fvs_Osimps_I2_J_0) ).

thf(1421,plain,
    ! [B: $i,A: $i] :
      ( ( c_Expr_Ofv @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) )
      = ( c_Expr_Ofv @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(408,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1553,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(296,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CallRedsThrowObj_0) ).

thf(1321,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(14,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

thf(524,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(5,negated_conjecture,
    ( ( c_DefAss_O_092_060A_062 @ v_ea @ ( tc_List_Olist @ tc_String_Ochar ) )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ v_ae ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(495,plain,
    ( ( c_DefAss_O_092_060A_062 @ v_ea @ ( tc_List_Olist @ tc_String_Ochar ) )
    = ( hAPP @ ( c_Option_Ooption_OSome @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ v_ae ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(91,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).

thf(759,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(359,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(361,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OBinOpThrow1_0) ).

thf(1453,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OBinOp @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(95,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).

thf(771,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(200,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

thf(1108,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(158,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).

thf(976,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(67,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).

thf(688,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(246,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OSeqThrow_0) ).

thf(1216,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(132,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).

thf(891,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(169,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).

thf(1010,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(330,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1390,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(419,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1575,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(427,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SeqReds2_0) ).

thf(1590,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(454,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

thf(1646,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(264,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__in_0) ).

thf(1253,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(490,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1721,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(451,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OCast @ A @ B @ C ) @ C )
      = ( c_DefAss_O_092_060A_062 @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I2_J_0) ).

thf(1639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OCast @ A @ B @ C ) @ C )
      = ( c_DefAss_O_092_060A_062 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(388,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1508,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(149,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).

thf(946,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(48,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).

thf(632,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(411,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ F @ G @ E @ E ) ) @ H ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ E @ A ) @ ( tc_prod @ E @ A ) ) ) @ ( c_Pair @ ( c_Pair @ F @ B @ E @ A ) @ ( c_Pair @ G @ C @ E @ A ) @ ( tc_prod @ E @ A ) @ ( tc_prod @ E @ A ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ D @ E @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_1) ).

thf(1558,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ F @ G @ E @ E ) ) @ H ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ E @ A ) @ ( tc_prod @ E @ A ) ) ) @ ( c_Pair @ ( c_Pair @ F @ B @ E @ A ) @ ( c_Pair @ G @ C @ E @ A ) @ ( tc_prod @ E @ A ) @ ( tc_prod @ E @ A ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ D @ E @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(27,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).

thf(568,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(139,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).

thf(914,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_COMBC @ ( c_in @ A ) @ B @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool )
       != ( c_COMBC @ ( c_in @ A ) @ C @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).

thf(1294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_COMBC @ ( c_in @ A ) @ B @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool )
       != ( c_COMBC @ ( c_in @ A ) @ C @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(291,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).

thf(1308,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(235,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(244,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__lcl__add_0) ).

thf(1212,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(114,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

thf(832,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(438,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OCondThrow_0) ).

thf(1614,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(357,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Ofinal @ A @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( c_BigStep_Oeval @ B @ C @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__final_0) ).

thf(1444,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Ofinal @ A @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( c_BigStep_Oeval @ B @ C @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(356,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WhileRedsThrow_0) ).

thf(1442,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(44,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).

thf(620,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(492,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_BigStep_Oeval @ E @ A @ B @ C @ D )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ E @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_big__by__small_0) ).

thf(1725,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_BigStep_Oeval @ E @ A @ B @ C @ D )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ E @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(421,axiom,
    class_Lattices_Olattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(1578,plain,
    class_Lattices_Olattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(252,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(1229,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).

thf(818,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Ofinal @ D @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_big__iff__small_2) ).

thf(1303,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ B @ C @ D @ E )
      | ~ ( c_BigStep_Ofinal @ D @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(83,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).

thf(735,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(397,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(1527,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(467,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).

thf(1673,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(26,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).

thf(564,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(380,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ G @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Seq_0) ).

thf(1495,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ C @ G @ E @ F )
      | ~ ( c_BigStep_Oeval @ A @ B @ D @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(459,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(1657,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(184,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

thf(1056,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(152,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).

thf(955,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(103,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

thf(796,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(281,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Ofinal @ A @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( c_BigStep_Oeval @ B @ C @ D @ A @ E )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_big__iff__small_1) ).

thf(1288,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Ofinal @ A @ ( tc_List_Olist @ tc_String_Ochar ) )
      | ~ ( c_BigStep_Oeval @ B @ C @ D @ A @ E )
      | ~ ( c_WellForm_Owf__prog @ c_WWellForm_Owwf__J__mdecl @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(484,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( c_Map_Osko__Map__XdomD__1__1 @ B @ A @ D @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domD_0) ).

thf(1710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( c_Map_Osko__Map__XdomD__1__1 @ B @ A @ D @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(49,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

thf(635,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(369,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

thf(1473,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(116,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).

thf(839,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(1236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D ) @ D )
      = ( c_DefAss_O_092_060A_062 @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060A_062___092_060A_062s_Osimps_I7_J_0) ).

thf(1352,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_DefAss_O_092_060A_062 @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D ) @ D )
      = ( c_DefAss_O_092_060A_062 @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(272,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Throw_0) ).

thf(1268,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_BigStep_Oeval @ A @ B @ C @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(216,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(1152,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1378,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(52,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).

thf(644,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(314,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).

thf(1357,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(137,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).

thf(908,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(383,axiom,
    class_Lattices_Oupper__semilattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(1500,plain,
    class_Lattices_Oupper__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(485,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAccThrow_0) ).

thf(1713,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_BigStep_Oeval @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_BigStep_Oeval @ A @ B @ E @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(160,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).

thf(982,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(68,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I111_J_0) ).

thf(691,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(204,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).

thf(1120,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(8,negated_conjecture,
    ( ~ ( c_lessequals @ v_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ v_ac @ v_x @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    | ~ ( c_lessequals @ v_ae @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ v_ac @ v_x @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    | ~ ( c_lessequals @ ( c_Map_Odom @ v_b @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ v_ac @ v_x @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(501,plain,
    ( ~ ( c_lessequals @ v_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ v_ac @ v_x @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    | ~ ( c_lessequals @ v_ae @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ v_ac @ v_x @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
    | ~ ( c_lessequals @ ( c_Map_Odom @ v_b @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ v_ba @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ v_ac @ v_x @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(327,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CondRedsThrow_0) ).

thf(1384,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1606,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(105,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).

thf(803,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(142,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).

thf(923,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(178,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).

thf(1037,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(342,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRedsThrow1_0) ).

thf(1416,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(240,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ D @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__lcl__incr_0) ).

thf(1204,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Map_Odom @ A @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( c_Map_Odom @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ D @ A @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ B @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OAddr @ A )
       != ( c_Value_Oval_OAddr @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).

thf(708,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OAddr @ A )
       != ( c_Value_Oval_OAddr @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(129,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

thf(882,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(157,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

thf(972,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(470,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ C @ E ) @ ( tc_prod @ C @ E ) ) ) @ ( c_Pair @ ( c_Pair @ A @ F @ C @ E ) @ ( c_Pair @ B @ G @ C @ E ) @ ( tc_prod @ C @ E ) @ ( tc_prod @ C @ E ) ) ) @ ( c_Wellfounded_Olex__prod @ D @ H @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lex__prod_0) ).

thf(1681,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ ( tc_prod @ C @ E ) @ ( tc_prod @ C @ E ) ) ) @ ( c_Pair @ ( c_Pair @ A @ F @ C @ E ) @ ( c_Pair @ B @ G @ C @ E ) @ ( tc_prod @ C @ E ) @ ( tc_prod @ C @ E ) ) ) @ ( c_Wellfounded_Olex__prod @ D @ H @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(1184,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(57,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).

thf(659,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

thf(592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1468,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(1,negated_conjecture,
    c_lessequals @ v_ad @ v_ab @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(496,plain,
    c_lessequals @ v_ad @ v_ab @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(188,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(1069,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(1733,plain,
    $false,
    inference(e,[status(thm)],[1665,1411,629,1190,1633,1105,1031,1179,777,666,1549,1554,1686,1586,1501,809,1337,1718,1083,962,1200,1290,1618,994,1401,741,1544,873,1305,1437,1173,1158,762,1596,1406,614,1692,1671,1655,1137,533,550,500,1164,715,1063,1354,930,1458,1497,1705,1260,698,1342,747,1196,898,1243,1441,885,1650,1366,1703,829,1095,1391,1576,1601,1386,1430,1323,917,1455,949,1409,724,1660,1298,1330,1264,1313,1279,638,1379,1514,1147,1247,1319,1013,1568,1641,1232,1479,1609,969,1347,1489,756,789,1450,1040,1151,806,1581,1283,821,905,1418,623,1020,574,1169,866,1072,1394,1521,527,1564,1622,774,1345,988,1697,849,1604,1206,920,678,1470,1311,1636,512,942,1047,1730,1274,1723,1223,1519,1355,598,1502,561,1487,815,729,1238,1560,825,1343,1619,1370,1423,1602,879,852,665,1687,1624,1210,1079,1128,1281,842,1573,583,522,1360,1270,650,1017,1328,1111,1498,1425,869,783,499,519,1592,697,1089,1234,1540,1006,1138,1719,1493,1160,1028,1361,753,669,901,1414,1700,1214,1446,1644,1612,547,1419,1292,933,1461,537,1114,701,1249,1297,738,1530,1266,1131,1668,911,721,1715,1720,647,997,1588,985,1060,1050,1627,1525,1333,1434,1086,541,765,1286,1466,1616,530,586,926,1202,792,662,718,888,1648,1483,1301,1374,1631,601,965,750,1727,1510,1154,694,732,1652,1388,577,1535,958,1701,1124,1256,1226,936,1707,611,498,1332,1092,1675,672,641,1428,1258,704,681,1117,1349,1492,1542,1144,1690,1307,979,604,509,1043,1571,1376,1439,863,1175,1325,895,1149,626,1556,799,1162,1177,1381,1474,768,1245,1066,780,608,1000,1477,1102,653,1694,1562,685,1171,1198,1396,1594,1699,1364,1250,1626,1034,1662,1166,1684,1277,1134,812,553,1181,1413,1076,675,1583,1208,589,617,516,939,1340,836,1551,1547,1025,1156,1225,1566,1368,1267,1230,1098,712,557,1003,580,855,1516,1598,1053,1432,1637,502,1262,1317,1658,951,1679,1579,1218,1336,1220,544,1188,1186,1404,744,1141,1427,1670,571,1272,859,656,1023,1485,1506,1504,727,1372,595,497,876,1240,991,845,1421,1553,1321,524,495,759,1448,1453,771,1108,976,688,1216,891,1010,1390,1575,1590,1646,1253,1721,1639,1508,946,1629,632,1523,786,1558,568,914,1294,1308,1193,1212,832,1614,1444,1442,620,1512,1725,1578,1229,818,1303,1480,735,1527,1673,564,1495,1657,1056,955,796,1288,1710,635,1473,839,1236,1352,1268,1152,1532,1378,644,1357,908,1500,1713,982,691,1399,1120,501,1384,1537,1606,803,923,1037,1416,1204,708,882,972,1681,1184,1463,659,592,1468,496,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV926-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n001.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Fri May 19 02:47:52 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.82/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.59/1.07  % [INFO] 	 Parsing done (239ms). 
% 1.87/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.33/1.27  % [INFO] 	 eprover registered as external prover. 
% 2.33/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 2.33/1.27  % [INFO] 	 Scanning for conjecture ... 
% 2.89/1.46  % [INFO] 	 Found a conjecture and 488 axioms. Running axiom selection ... 
% 3.67/1.65  % [INFO] 	 Axiom selection finished. Selected 486 axioms (removed 2 axioms). 
% 4.53/1.92  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.53/1.94  % [INFO] 	 Type checking passed. 
% 4.53/1.94  % [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 ... 
% 15.51/4.87  % External prover 'e' found a proof!
% 15.51/4.87  % [INFO] 	 Killing All external provers ... 
% 15.63/4.87  % Time passed: 4355ms (effective reasoning time: 3786ms)
% 15.63/4.87  % Solved by 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)>
% 15.63/4.87  % Axioms used in derivation (486): cls_option_Oinject_0, cls_red__lcl__add_0, cls_exp_Osimps_I56_J_0, cls_red__reds_OInitBlockThrow_0, cls_CallObjThrow_0, cls_red__reds_OLAssThrow_0, cls_bot__fun__eq_0, cls_exp_Osimps_I184_J_0, clsarity_nat__HOL_Oord, cls_red__reds_ORedInitBlock_0, cls_map__upd__eqD1_0, cls_exp_Osimps_I156_J_0, cls_val_Osimps_I3_J_0, cls_exp_Osimps_I9_J_1, cls_rtrancl__idemp_0, cls_exp_Osimps_I92_J_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_sup__ge1_0, cls_red__reds_OFAssRed2_0, cls_Un__subset__iff_0, cls_CallRedsThrowObj_0, cls_order__eq__iff_0, cls_equalityI_0, cls_exp_Osimps_I218_J_0, cls_exp_Osimps_I213_J_0, cls_fv__fvs_Osimps_I3_J_0, cls_red__reds_OFAssRed1_0, cls_COMBC__def_0, cls_map__add__assoc_0, cls_eval__evals_OFAssThrow2_0, cls_Un__empty__left_0, cls_fun__upd__apply_1, cls_map__upd__Some__unfold_4, cls_le__funD_0, cls_subset__empty_1, cls_eval__cases_I1_J_1, cls_exp_Osimps_I193_J_0, cls_CastReds_0, cls_exp_Osimps_I10_J_1, cls_exp_Osimps_I225_J_0, cls_exp_Osimps_I138_J_0, cls_exp_Osimps_I81_J_0, cls_exp_Osimps_I137_J_0, cls_BinOpRedsThrow2_0, cls_sup__bot__right_0, cls_exp_Osimps_I165_J_0, cls_exp_Osimps_I7_J_2, cls_fv__fvs_Osimps_I11_J_0, cls_list_Oinject_0, cls_exp_Osimps_I204_J_0, cls_CallRedsObj_0, cls_exp_Osimps_I219_J_0, cls_exp_Osimps_I149_J_0, cls_eval__final_0, cls_extend__eval_0, cls_fv__fvs_Osimps_I17_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_exp_Osimps_I190_J_0, clsarity_fun__Orderings_Oorder, cls_exp_Osimps_I221_J_0, cls_big__iff__small_2, cls_exp_Osimps_I11_J_0, cls_UnCI_1, cls_exp_Osimps_I15_J_1, cls_BinOpRedsThrow1_0, cls_map__upd__Some__unfold_3, cls_inf__sup__aci_I6_J_0, cls_eval__evals_OCondThrow_0, cls_exp_Osimps_I115_J_0, cls_exp_Osimps_I211_J_0, cls_rtrancl__trans_0, cls_mem__def_1, cls_BinOp2Reds_0, clsarity_nat__Orderings_Olinorder, cls_empty__iff_0, cls_not__Cons__self2_0, cls_FAssReds2_0, cls_exp_Osimps_I13_J_0, cls_exp_Osimps_I154_J_0, cls_exp_Osimps_I199_J_0, cls_LAssReds_0, cls_exp_Osimps_I185_J_0, cls_SeqReds2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_exp_Osimps_I141_J_0, cls_le__sup__iff_0, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I208_J_0, cls_red__reds_OFAssThrow2_0, cls_exp_Osimps_I188_J_0, cls_set__rev__mp_0, cls_exp_Osimps_I109_J_0, cls_pred__equals__eq_0, cls_exp_Osimps_I212_J_0, cls_exp_Osimps_I178_J_0, cls__092_060A_062___092_060A_062s_Osimps_I7_J_0, cls_exp_Osimps_I2_J_1, cls_Un__left__commute_0, cls_exp_Osimps_I8_J_3, cls_in__lex__prod_1, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_exp_Osimps_I194_J_0, cls_exp_Osimps_I113_J_0, cls_exp_Osimps_I223_J_0, cls_exp_Osimps_I11_J_1, cls_exp_Osimps_I4_J_1, cls_le__supI_0, cls_Un__subset__iff_1, cls_exp_Osimps_I171_J_0, cls_red__reds_OCallThrowObj_0, cls_red__reds_OLAssRed_0, cls_exp_Osimps_I157_J_0, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_order__eq__refl_0, cls_eval__evals_OSeqThrow_0, cls_exp_Osimps_I67_J_0, cls_converse__rtrancl__into__rtrancl_0, cls_exp_Osimps_I4_J_0, cls_CondReds_0, cls_map__upd__Some__unfold_0, cls_exp_Osimps_I160_J_0, cls_le__iff__sup_0, clsarity_fun__Orderings_Obot, cls_hext__trans_0, cls_le__supE_1, cls_fun__upd__other_0, cls_exp_Osimps_I84_J_0, cls_exp_Osimps_I209_J_0, cls_hext__refl_0, cls_big__iff__small_1, cls_Red__dom__lcl_0, cls_exp_Osimps_I142_J_0, cls_exp_Osimps_I74_J_0, cls_Un__absorb2_0, cls_exp_Osimps_I205_J_0, cls_inf__sup__aci_I8_J_0, cls_red__reds_OCallObj_0, cls_Un__empty__right_0, cls__092_060A_062___092_060A_062s_Osimps_I13_J_0, cls__092_060A_062___092_060A_062s_Osimps_I2_J_0, cls_WhileRedsThrow_0, cls_map__add__upd__left_0, cls_exp_Osimps_I110_J_0, clsarity_bool__Orderings_Oorder, cls_red__reds_OThrowThrow_0, cls_bot__least_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_eval__evals_OBinOpThrow2_0, cls_eval__evals_OFAccThrow_0, cls_exp_Osimps_I143_J_0, cls_sup__eq__bot__eq2_0, cls_refl__on__def_1, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_UnCI_0, cls_Un__upper2_0, cls_exp_Osimps_I148_J_0, cls_map__add__dom__app__simps_I2_J_0, cls_red__reds_OBinOpThrow1_0, cls_WhileCondThrow_0, cls_exp_Osimps_I172_J_0, cls_exp_Osimps_I139_J_0, cls_exp_Osimps_I10_J_2, cls_exp_Osimps_I176_J_0, cls_eval__notfree__unchanged_0, cls_fv__fvs_Osimps_I7_J_0, cls_ThrowReds_0, cls_ConsThrow_0, cls_exp_Osimps_I46_J_0, cls_Reds__dom__lcl_0, clsarity_fun__HOL_Oord, cls_exp_Osimps_I99_J_0, cls_subset__empty_0, cls_fv__fvs_Osimps_I12_J_0, cls_subset__iff_0, cls_eval__evals_OFAssThrow1_0, cls_rev__predicate1D_0, cls_red__reds_OTryRed_0, cls_exp_Osimps_I69_J_0, cls_in__lex__prod_2, cls_fv__fvs_Osimps_I8_J_0, clsarity_bool__Lattices_Oupper__semilattice, cls_exp_Osimps_I180_J_0, cls_red__reds_ORedBlock_0, cls_FAccReds_0, cls_exp_Osimps_I77_J_0, cls_map__add__dom__app__simps_I3_J_0, cls_exp_Osimps_I98_J_0, cls_exp_Osimps_I61_J_0, cls_exp_Osimps_I15_J_0, cls_exp_Osimps_I183_J_0, cls_exp_Osimps_I207_J_0, cls_fun__upd__triv_0, cls_exp_Osimps_I2_J_0, cls_exp_Osimps_I12_J_2, cls_exp_Osimps_I8_J_2, cls_set__eq__subset_2, cls_Un__mono_0, cls_Seq_0, clsarity_nat__Orderings_Obot, cls_exp_Osimps_I83_J_0, cls_ex__in__conv_0, cls_exp_Osimps_I76_J_0, cls_exp_Osimps_I70_J_0, cls_sup__commute_0, cls_exp_Osimps_I177_J_0, cls_FAssRedsThrow2_0, cls__092_060A_062___092_060A_062s_Osimps_I3_J_0, cls_CastRedsNull_0, cls_exp_Osimps_I89_J_0, cls_exp_Osimps_I159_J_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_exp_Osimps_I62_J_0, cls_red__reds_OBinOpRed2_0, cls_linorder__linear_0, cls_Un__empty_0, cls_TryReds_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_exp_Osimps_I105_J_0, cls_exp_Osimps_I220_J_0, cls_order__antisym_0, cls_exp_Osimps_I158_J_0, cls_dom__map__add_0, cls_fv__fvs_Osimps_I13_J_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I60_J_0, cls_sup__Un__eq_0, cls_exp_Osimps_I162_J_0, cls_CondRedsThrow_0, cls_subset__trans_0, cls_not__Cons__self_0, cls_refl__onD2_0, cls_val_Osimps_I16_J_0, cls_order__trans_0, cls_exp_Osimps_I15_J_3, cls_exp_Osimps_I201_J_0, cls_exp_Osimps_I166_J_0, cls_map__upd__Some__unfold_1, cls_red__reds_OFAssThrow1_0, cls_le__supE_0, cls_exp_Osimps_I47_J_0, cls_exp_Osimps_I7_J_1, cls_red__reds_OBlockThrow_0, cls_sup__assoc_0, cls_exp_Osimps_I189_J_0, cls_exp_Osimps_I224_J_0, cls_eval__evals_OThrowThrow_0, cls_red__reds_OBinOpRed1_0, cls_exp_Osimps_I169_J_0, cls_map__upd__triv_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, clsarity_bool__Orderings_Opreorder, cls_TryRedsVal_0, cls_rtrancl__eq__or__trancl_1, cls_exp_Osimps_I55_J_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_CastRedsThrow_0, cls_exp_Osimps_I75_J_0, cls_empty__subsetI_0, cls_red__reds_OSeqRed_0, cls_sup1E_0, cls_refl__onD_0, cls_sup__least_0, cls_subset__refl_0, cls_CastNull_0, cls_exp_Osimps_I145_J_0, cls_Pair__eq_0, cls_fun__upd__twist_0, cls_SeqRedsThrow_0, cls_Un__absorb1_0, cls_exp_Osimps_I80_J_0, cls_in__lex__prod_3, cls_exp_Osimps_I59_J_0, clsarity_nat__Orderings_Opreorder, clsarity_nat__Lattices_Olattice, cls_final__def_1, cls_sup1CI_1, cls_exp_Osimps_I182_J_0, cls_fun__upd__apply_0, cls_LAssRedsThrow_0, cls_pred__subset__eq_1, cls_exp_Osimps_I68_J_0, cls_restrict__in_0, cls_exp_Osimps_I4_J_2, cls_exp_Osimps_I114_J_0, cls_order__eq__iff_2, cls_bot1E_0, cls_exp_Osimps_I216_J_0, cls_exp_Osimps_I203_J_0, cls_Un__assoc_0, cls_red__reds_OCastThrow_0, cls_exp_Osimps_I191_J_0, cls_option_Osplit_1, cls_evals__hext_0, cls_domI_0, cls_le__supI2_0, cls_fv__fvs_Osimps_I2_J_0, cls_extend__1__eval_0, cls_exp_Osimps_I57_J_0, cls_bex__empty_0, cls_eval__evals_OCons_0, cls_UnE_0, cls_exp_Osimps_I215_J_0, cls_inf__sup__ord_I4_J_0, cls_eval__evals_OCastThrow_0, cls_exp_Osimps_I93_J_0, cls_SeqReds_0, cls_exp_Osimps_I53_J_0, cls_Un__absorb_0, cls_exp_Osimps_I152_J_0, cls_eval__evals_OLAssThrow_0, cls_exp_Osimps_I50_J_0, cls_eval__restrict__lcl_0, cls_order__antisym__conv_0, cls_red__reds_OThrowRed_0, cls_val_Osimps_I17_J_0, cls_red__reds_OFAccRed_0, cls_exp_Osimps_I54_J_0, cls_exp_Osimps_I86_J_0, cls_bot__empty__eq_0, cls_map__add__upd_0, cls_fv__fvs_Osimps_I9_J_0, cls_refl__onD1_0, cls_exp_Osimps_I179_J_0, clsarity_bool__Lattices_Olattice, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_exp_Osimps_I8_J_1, cls_exp_Osimps_I58_J_0, cls_exp_Osimps_I106_J_0, cls_le__supI1_0, cls_sup__left__idem_0, cls_exp_Osimps_I66_J_0, cls_exp_Osimps_I6_J_0, cls_exp_Osimps_I108_J_0, cls_exp_Osimps_I222_J_0, cls_final__def_2, cls_red__reds_OBinOpThrow2_0, cls_le__sup__iff_2, cls_subsetD_0, cls_fv__fvs_Osimps_I14_J_0, cls_exp_Osimps_I90_J_0, clsarity_fun__Lattices_Obounded__lattice, cls_fun__upd__idem_0, cls_FAssRedsThrow1_0, cls_xt1_I6_J_0, cls_eval__cases_I1_J_0, cls_red__reds_OCondThrow_0, cls_exp_Osimps_I12_J_1, cls_eval__evals_OBinOpThrow1_0, cls_fun__upd__idem__iff_0, cls_sup__fun__eq_0, cls_FAccRedsThrow_0, cls_exp_Osimps_I155_J_0, cls_domD_0, cls_rtrancl_Ortrancl__refl_0, cls_exp_Osimps_I71_J_0, cls_option_Osplit__asm_1, cls_exp_Osimps_I82_J_0, cls_exp_Osimps_I14_J_0, cls_exp_Osimps_I107_J_0, cls_exp_Osimps_I167_J_0, cls_exp_Osimps_I161_J_0, cls_Un__left__absorb_0, cls_exp_Osimps_I9_J_2, cls_red__reds_ORedCastNull_0, cls_sup__idem_0, cls_exp_Osimps_I217_J_0, cls_inf__sup__aci_I5_J_0, cls_sup__eq__bot__eq1_0, cls_A__fv_0, cls_list_Oinject_1, cls_exp_Osimps_I45_J_0, cls_Red__fv_0, cls_exp_Osimps_I8_J_0, cls_exp_Osimps_I44_J_0, cls_ThrowRedsThrow_0, cls_exp_Osimps_I192_J_0, cls_Un__empty_1, clsarity_nat__Lattices_Oupper__semilattice, cls_exp_Osimps_I7_J_0, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_exp_Osimps_I151_J_0, cls_same__fstI_0, cls_map__add__dom__app__simps_I1_J_0, cls_exp_Osimps_I153_J_0, cls_red__lcl__incr_0, cls_map__upd__Some__unfold_2, cls_eval__lcl__incr_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_sup__ge2_0, cls_exp_Osimps_I6_J_1, cls_red__reds_OSeqThrow_0, cls_exp_Osimps_I65_J_0, cls_Try_0, cls_exp_Osimps_I51_J_0, cls_Un__least_0, cls_BinOp1Reds_0, cls_red__hext__incr_0, cls_sup1CI_0, cls_restrict__fun__upd_1, clsarity_fun__Orderings_Opreorder, cls_exp_Osimps_I164_J_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_exp_Osimps_I111_J_0, cls_exp_Osimps_I52_J_0, cls_red__reds_OCastRed_0, cls_Val_0, cls_exp_Osimps_I187_J_0, cls_exp_Osimps_I15_J_2, cls_r__into__rtrancl_0, cls_small__by__big_0, cls_red__reds_OFAccThrow_0, cls_exp_Osimps_I10_J_0, cls_eval__hext_0, cls_exp_Osimps_I64_J_0, cls_exp_Osimps_I88_J_0, cls_FAssReds1_0, cls_pred__subset__eq_0, cls_exp_Osimps_I96_J_0, cls_map__add__find__right_0, cls_exp_Osimps_I196_J_0, cls_fv__fvs_Osimps_I4_J_0, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I200_J_0, cls_exp_Osimps_I63_J_0, cls_map__add__Some__iff_2, cls_exp_Osimps_I214_J_0, cls_exp_Osimps_I168_J_0, cls_Throw_0, cls_exp_Osimps_I181_J_0, cls_sup__bot__left_0, cls_red__reds_OCondRed_0, cls_fun__upd__upd_0, cls_map__add__SomeD_1, cls_exp_Osimps_I140_J_0, cls_eval__closed__lcl__unchanged_0, cls_Red__lcl__add_0, cls_exp_Osimps_I87_J_0, cls_exp_Osimps_I198_J_0, cls_exp_Osimps_I202_J_0, cls_exp_Osimps_I12_J_0, cls_Pair__eq_1, cls_exp_Osimps_I173_J_0, cls_big__by__small_0, cls_sup__absorb1_0, cls_exp_Osimps_I104_J_0, cls_eval__finalId_0, cls_exp_Osimps_I78_J_0, clsarity_nat__Orderings_Oorder, cls_exp_Osimps_I100_J_0, cls_option_Osimps_I5_J_0, cls_equalityE_0, cls_exp_Osimps_I163_J_0, cls_red__reds_ORedSeq_0, cls_ball__empty_0, cls_in__lex__prod_0, cls_exp_Osimps_I147_J_0, cls_exp_Osimps_I3_J_0, cls_map__add__def_0, cls_red__reds_ORedTry_0, cls_predicate1D_0, cls_exp_Osimps_I197_J_0, cls_evals__lcl__incr_0, cls_exp_Osimps_I13_J_1, cls_fun__upd__idem__iff_1
% 15.63/4.87  % No. of inferences in proof: 989
% 15.63/4.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4355 ms resp. 3786 ms w/o parsing
% 17.03/5.30  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.03/5.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------