TSTP Solution File: SWV939-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV939-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 12:19:29 EDT 2023

% Result   : Unsatisfiable 13.55s 4.07s
% Output   : Refutation 14.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  779
% Syntax   : Number of formulae    : 1446 ( 615 unt; 113 typ;   0 def)
%            Number of atoms       : 2990 (1479 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 33369 (1470   ~;1657   |;   0   &;30242   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   42 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  262 ( 262   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  115 ( 113 usr;  32 con; 0-8 aty)
%            Number of variables   : 7226 (   0   ^;7226   !;   0   ?;7226   :)

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

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

thf(c_TypeRel_Owiden_type,type,
    c_TypeRel_Owiden: $i > $i > $i ).

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

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

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

thf(c_WellTypeRT_OWTrt_type,type,
    c_WellTypeRT_OWTrt: $i > $i > $i > $i > $i > $o ).

thf(v_ha_____type,type,
    v_ha____: $i ).

thf(v_E_____type,type,
    v_E____: $i ).

thf(c_SmallStep_Oblocks_type,type,
    c_SmallStep_Oblocks: $i > $i ).

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

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

thf(c_Type_Othis_type,type,
    c_Type_Othis: $i ).

thf(v_pns_____type,type,
    v_pns____: $i ).

thf(c_Type_Oty_OClass_type,type,
    c_Type_Oty_OClass: $i > $i ).

thf(v_D_____type,type,
    v_D____: $i ).

thf(v_Ts_____type,type,
    v_Ts____: $i ).

thf(tc_Type_Oty_type,type,
    tc_Type_Oty: $i ).

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

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

thf(v_vs_____type,type,
    v_vs____: $i ).

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

thf(v_body_____type,type,
    v_body____: $i ).

thf(c_Type_Oty_OBoolean_type,type,
    c_Type_Oty_OBoolean: $i ).

thf(c_Type_Oty_OVoid_type,type,
    c_Type_Oty_OVoid: $i ).

thf(c_Type_Oty_Oty__case_type,type,
    c_Type_Oty_Oty__case: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xty__Xcase__cong__1__1_type,type,
    c_Type_Osko__Type__Xty__Xcase__cong__1__1: $i > $i > $i > $i > $i ).

thf(c_Type_Oty_ONT_type,type,
    c_Type_Oty_ONT: $i ).

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

thf(c_Expr_Oexp_Onew_type,type,
    c_Expr_Oexp_Onew: $i > $i > $i ).

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

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

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

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

thf(c_List_OtakeWhile_type,type,
    c_List_OtakeWhile: $i > $i > $i > $i ).

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

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

thf(c_Option_Ooption_ONone_type,type,
    c_Option_Ooption_ONone: $i > $i ).

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

thf(c_COMBI_type,type,
    c_COMBI: $i > $i > $i ).

thf(c_Map_Omap__le_type,type,
    c_Map_Omap__le: $i > $i > $i > $i > $o ).

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

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

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

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

thf(c_Type_Oty_OInteger_type,type,
    c_Type_Oty_OInteger: $i ).

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

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

thf(c_Value_Oval_OIntg_type,type,
    c_Value_Oval_OIntg: $i > $i ).

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

thf(c_Value_Oval_Oval__rec_type,type,
    c_Value_Oval_Oval__rec: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_Value_Oval_OUnit_type,type,
    c_Value_Oval_OUnit: $i ).

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

thf(c_List_Oremove1_type,type,
    c_List_Oremove1: $i > $i > $i > $i ).

thf(tc_Int_Oint_type,type,
    tc_Int_Oint: $i ).

thf(c_List_Olist__all2_type,type,
    c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).

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

thf(c_Type_Oty_Oty__rec_type,type,
    c_Type_Oty_Oty__rec: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_Type_Ois__refT_type,type,
    c_Type_Ois__refT: $i > $o ).

thf(c_Decl_Ois__class_type,type,
    c_Decl_Ois__class: $i > $i > $i > $o ).

thf(c_TypeRel_OMethod_type,type,
    c_TypeRel_OMethod: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

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

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

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

thf(c_COMBK_type,type,
    c_COMBK: $i > $i > $i > $i ).

thf(c_WellTypeRT_OWTrts_type,type,
    c_WellTypeRT_OWTrts: $i > $i > $i > $i > $i > $o ).

thf(c_Progress_OWTrts_H_type,type,
    c_Progress_OWTrts_H: $i > $i > $i > $i > $i > $o ).

thf(c_Value_Oval_Oval__case_type,type,
    c_Value_Oval_Oval__case: $i > $i > $i > $i > $i > $i > $i > $i ).

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

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

thf(c_WellType_OWTs_type,type,
    c_WellType_OWTs: $i > $i > $i > $i > $o ).

thf(c_Progress_OWTrt_H_type,type,
    c_Progress_OWTrt_H: $i > $i > $i > $i > $i > $o ).

thf(c_WellType_OWT_type,type,
    c_WellType_OWT: $i > $i > $i > $i > $o ).

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

thf(v_sko__Type__Xty__Xsplit__asm__1_type,type,
    v_sko__Type__Xty__Xsplit__asm__1: $i > $i > $i > $i ).

thf(v_sko__Type__Xty__Xsplit__1_type,type,
    v_sko__Type__Xty__Xsplit__1: $i > $i > $i > $i ).

thf(c_SmallStep_Oredp_type,type,
    c_SmallStep_Oredp: $i > $i > $i > $i > $i > $o ).

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

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

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

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

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

thf(c_Value_Othe__Addr_type,type,
    c_Value_Othe__Addr: $i > $i ).

thf(v_sko__TypeRel__Xwiden__Xcases__2_type,type,
    v_sko__TypeRel__Xwiden__Xcases__2: $i > $i > $i > $i ).

thf(v_sko__TypeRel__Xwiden__Xcases__1_type,type,
    v_sko__TypeRel__Xwiden__Xcases__1: $i > $i > $i > $i ).

thf(c_Objects_Otypeof__h_type,type,
    c_Objects_Otypeof__h: $i > $i > $i ).

thf(c_Conform_Oconf_type,type,
    c_Conform_Oconf: $i > $i > $i > $i ).

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

thf(c_State_Ohp_type,type,
    c_State_Ohp: $i > $i ).

thf(v_la_____type,type,
    v_la____: $i ).

thf(v_C_____type,type,
    v_C____: $i ).

thf(v_fs_____type,type,
    v_fs____: $i ).

thf(c_TypeRel_Ohas__field_type,type,
    c_TypeRel_Ohas__field: $i > $i > $i > $i > $i > $i > $o ).

thf(v_sko__TypeSafe__Mirabelle__Xwt__blocks__1_type,type,
    v_sko__TypeSafe__Mirabelle__Xwt__blocks__1: $i > $i > $i > $i > $i ).

thf(c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1_type,type,
    c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1: $i > $i > $i > $i > $i ).

thf(c_List_OListMem_type,type,
    c_List_OListMem: $i > $i > $i > $o ).

thf(v_Ts_H_____type,type,
    v_Ts_H____: $i ).

thf(c_TypeRel_Osko__TypeRel__XClass__widen__1__1_type,type,
    c_TypeRel_Osko__TypeRel__XClass__widen__1__1: $i > $i ).

thf(c_TypeSafe__Mirabelle_Osconf_type,type,
    c_TypeSafe__Mirabelle_Osconf: $i > $i > $i > $o ).

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

thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2_type,type,
    c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2: $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1_type,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(v_sko__TypeRel__Xwiden__Xcases__3_type,type,
    v_sko__TypeRel__Xwiden__Xcases__3: $i > $i ).

thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1_type,type,
    c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1: $i > $i > $i > $i > $i > $i ).

thf(v_T_H_H_____type,type,
    v_T_H_H____: $i ).

thf(v_M_____type,type,
    v_M____: $i ).

thf(551,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) @ 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

thf(2094,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) @ 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(128,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I17_J_0) ).

thf(1024,plain,
    c_Type_Oty_ONT != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(177,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1168,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(359,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ J @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_19) ).

thf(1633,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ J @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(626,axiom,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E____ @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_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_RedCall_I5_J_0) ).

thf(2263,plain,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E____ @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_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)],[626]) ).

thf(327,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_8) ).

thf(1559,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(399,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ D )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( c_State_Ohp @ D ) @ B @ E @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ 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 @ G @ 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 @ A ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__preserves__sconf_0) ).

thf(1729,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ D )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( c_State_Ohp @ D ) @ B @ E @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ 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 @ G @ 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 @ A ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(471,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OIntg @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ E @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit__asm_3) ).

thf(1899,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OIntg @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ E @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(447,axiom,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_OVoid ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I9_J_0) ).

thf(1840,plain,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_OVoid ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(99,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
     != ( c_COMBK @ ( c_Option_Ooption_ONone @ D ) @ ( tc_Option_Ooption @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).

thf(941,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
     != ( c_COMBK @ ( c_Option_Ooption_ONone @ D ) @ ( tc_Option_Ooption @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(655,axiom,
    ( ( c_Nat_Osize__class_Osize @ v_vs____ @ ( tc_List_Olist @ tc_Value_Oval ) )
    = ( c_Nat_Osize__class_Osize @ v_pns____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RedCall_I3_J_0) ).

thf(2331,plain,
    ( ( c_Nat_Osize__class_Osize @ v_vs____ @ ( tc_List_Olist @ tc_Value_Oval ) )
    = ( c_Nat_Osize__class_Osize @ v_pns____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(492,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_0) ).

thf(1950,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(580,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_OBoolean @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_1) ).

thf(2163,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_OBoolean @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(81,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ A @ F @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ B @ J @ K @ L @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_0) ).

thf(892,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ A @ F @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ B @ J @ K @ L @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(558,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBlock @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ E @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtBlock_0) ).

thf(2109,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBlock @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ E @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(567,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ E ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ F @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ H @ E @ D @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_1) ).

thf(2131,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ E ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ F @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ H @ E @ D @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(525,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__3 @ A ) ) )
      | ( B
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__1 @ C @ B @ A ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ t_a ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_1) ).

thf(2031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__3 @ A ) ) )
      | ( B
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__1 @ C @ B @ A ) ) )
      | ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ t_a ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(542,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OInteger
     != ( c_Type_Oty_OClass @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I18_J_0) ).

thf(2072,plain,
    ! [A: $i] :
      ( c_Type_Oty_OInteger
     != ( c_Type_Oty_OClass @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(415,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCastRed_0) ).

thf(1767,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(148,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(1083,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)],[148]) ).

thf(107,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(962,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)],[107]) ).

thf(504,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Value_Oval_OIntg @ A )
     != ( c_Value_Oval_OAddr @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I22_J_0) ).

thf(1982,plain,
    ! [B: $i,A: $i] :
      ( ( c_Value_Oval_OIntg @ A )
     != ( c_Value_Oval_OAddr @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(544,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).

thf(2077,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(112,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(977,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(310,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_34) ).

thf(1522,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(118,axiom,
    c_Value_Oval_ONull != c_Value_Oval_OUnit,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I5_J_0) ).

thf(994,plain,
    c_Value_Oval_ONull != c_Value_Oval_OUnit,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(270,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ H @ I @ E @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_18) ).

thf(1422,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ H @ I @ E @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Value_Oval_ONull ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Value_Oval_ONull ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedCastNull_0) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Value_Oval_ONull ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Value_Oval_ONull ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(190,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_OBoolean @ F )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I2_J_0) ).

thf(1205,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_OBoolean @ F )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(315,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I13_J_0) ).

thf(1533,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(134,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(1041,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)],[134]) ).

thf(482,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
       != ( c_Option_Ooption_OSome @ G @ D ) )
      | ( ( hAPP @ A @ F )
        = ( c_Option_Ooption_OSome @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).

thf(1924,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
       != ( c_Option_Ooption_OSome @ G @ D ) )
      | ( ( hAPP @ A @ F )
        = ( c_Option_Ooption_OSome @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(122,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(1005,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)],[122]) ).

thf(602,axiom,
    ! [A: $i] :
      ( ( c_Objects_Otypeof__h @ A @ c_Value_Oval_ONull )
      = ( c_Option_Ooption_OSome @ c_Type_Oty_ONT @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typeof__h_Osimps_I2_J_0) ).

thf(2210,plain,
    ! [A: $i] :
      ( ( c_Objects_Otypeof__h @ A @ c_Value_Oval_ONull )
      = ( c_Option_Ooption_OSome @ c_Type_Oty_ONT @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(278,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ B @ C @ H @ I @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ I @ G ) ) )
      | ( F = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_28) ).

thf(1443,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ B @ C @ H @ I @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ I @ G ) ) )
      | ( F = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(433,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_Progress_OWTrt_H @ D @ A @ E @ ( c_Expr_Oexp_OBlock @ F @ G @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ F @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I )
      | ~ ( c_Progress_OWTrt_H @ D @ A @ ( c_Fun_Ofun__upd @ E @ F @ ( c_Option_Ooption_OSome @ G @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ H @ I )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ G ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I16_J_0) ).

thf(1808,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_Progress_OWTrt_H @ D @ A @ E @ ( c_Expr_Oexp_OBlock @ F @ G @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ F @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I )
      | ~ ( c_Progress_OWTrt_H @ D @ A @ ( c_Fun_Ofun__upd @ E @ F @ ( c_Option_Ooption_OSome @ G @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ H @ I )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(553,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_TypeRel_Ohas__field @ A @ H @ E @ G @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ H ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAcc_0) ).

thf(2099,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_TypeRel_Ohas__field @ A @ H @ E @ G @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(635,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_19) ).

thf(2282,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(560,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_2) ).

thf(2114,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(168,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ ( c_Map_Omap__upds @ F @ B @ C @ D @ E ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__upds_0) ).

thf(1142,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__upds @ A @ B @ C @ D @ E ) @ ( c_Map_Omap__upds @ F @ B @ C @ D @ E ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(375,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OTryCatch @ D @ B @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_2) ).

thf(1671,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OTryCatch @ D @ B @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(347,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).

thf(1608,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(511,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_21) ).

thf(1999,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(572,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).

thf(2141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(202,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(1233,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)],[202]) ).

thf(54,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(814,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)],[54]) ).

thf(480,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(1919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OIntg @ A )
     != c_Value_Oval_ONull ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I15_J_0) ).

thf(913,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OIntg @ A )
     != c_Value_Oval_ONull ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(242,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Onew @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I17_J_0) ).

thf(1354,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Onew @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(95,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I27_J_0) ).

thf(930,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(300,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( 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 ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OBlockThrow_0) ).

thf(1497,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( 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 ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(389,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

thf(1705,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(583,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

thf(2168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(12,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(698,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)],[12]) ).

thf(83,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(898,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)],[83]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ c_Value_Oval_ONull ) @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__NT_1) ).

thf(1835,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ c_Value_Oval_ONull ) @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(662,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(2348,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(478,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ D @ A @ E ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typeof__conf_0) ).

thf(1914,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ D @ A @ E ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(422,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ G @ J @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_13) ).

thf(1782,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ G @ J @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(334,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ J @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_11) ).

thf(1576,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ J @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(277,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

thf(1441,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(516,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_34) ).

thf(2010,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(365,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_23) ).

thf(1650,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_Onew @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I41_J_0) ).

thf(1359,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_Onew @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(253,axiom,
    ! [B: $i,A: $i] : ( c_List_Olist__all @ A @ ( c_List_Olist_ONil @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).

thf(1386,plain,
    ! [B: $i,A: $i] : ( c_List_Olist__all @ A @ ( c_List_Olist_ONil @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(546,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( c_WellTypeRT_OWTrt @ D @ E @ ( c_Map_Omap__upds @ F @ C @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty ) @ G @ H )
      | ~ ( c_WellTypeRT_OWTrt @ D @ E @ F @ ( c_SmallStep_Oblocks @ ( c_Pair @ C @ ( c_Pair @ B @ ( c_Pair @ A @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__blocks_0) ).

thf(2082,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( c_WellTypeRT_OWTrt @ D @ E @ ( c_Map_Omap__upds @ F @ C @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty ) @ G @ H )
      | ~ ( c_WellTypeRT_OWTrt @ D @ E @ F @ ( c_SmallStep_Oblocks @ ( c_Pair @ C @ ( c_Pair @ B @ ( c_Pair @ A @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(313,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ c_Value_Oval_OUnit @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit_0) ).

thf(1529,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ c_Value_Oval_OUnit @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(431,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      = ( c_Map_Omap__upds @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ E @ G ) @ D @ ( tc_Option_Ooption @ G ) ) @ C @ F @ D @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Cons_0) ).

thf(1803,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      = ( c_Map_Omap__upds @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ E @ G ) @ D @ ( tc_Option_Ooption @ G ) ) @ C @ F @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(466,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ D @ A @ E ) @ B ) @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ E ) @ C ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__def_2) ).

thf(1887,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ D @ A @ E ) @ B ) @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ E ) @ C ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(397,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_10) ).

thf(1724,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_ONil @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_ONil @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_ONil @ tc_Value_Oval ) @ A @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocks_Osimps_I2_J_0) ).

thf(1475,plain,
    ! [A: $i] :
      ( ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_ONil @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_ONil @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_ONil @ tc_Value_Oval ) @ A @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

thf(1904,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(212,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I32_J_0) ).

thf(1265,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(200,axiom,
    ! [A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( c_Type_Ois__refT @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__refTE_0) ).

thf(1228,plain,
    ! [A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( c_Type_Ois__refT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(294,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_25) ).

thf(1482,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(654,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_12) ).

thf(2328,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(426,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ E @ C @ A @ F @ G @ D @ H @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_0) ).

thf(1792,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ E @ C @ A @ F @ G @ D @ H @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ C @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedSeq_0) ).

thf(1985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(659,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_32) ).

thf(2339,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(475,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__3 @ A ) ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__2 @ B @ C @ A ) ) )
      | ( A = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ B @ t_a ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_3) ).

thf(1907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__3 @ A ) ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__2 @ B @ C @ A ) ) )
      | ( A = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ B @ t_a ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(606,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_13) ).

thf(2217,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(231,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ A @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ B @ K @ L @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_1) ).

thf(1323,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ A @ G @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ B @ K @ L @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ A @ D @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).

thf(802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ A @ D @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(217,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(1279,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)],[217]) ).

thf(590,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

thf(2185,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(185,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(1191,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)],[185]) ).

thf(565,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

thf(2126,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(140,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(1059,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)],[140]) ).

thf(665,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_29) ).

thf(2356,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).

thf(724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
      = ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(264,axiom,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1409,plain,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(412,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ E @ F @ G @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed2_0) ).

thf(1760,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ E @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OLAssThrow_0) ).

thf(1660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(306,axiom,
    ! [A: $i] :
      ( ( c_Objects_Otypeof__h @ A @ c_Value_Oval_OUnit )
      = ( c_Option_Ooption_OSome @ c_Type_Oty_OVoid @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typeof__h_Osimps_I1_J_0) ).

thf(1511,plain,
    ! [A: $i] :
      ( ( c_Objects_Otypeof__h @ A @ c_Value_Oval_OUnit )
      = ( c_Option_Ooption_OSome @ c_Type_Oty_OVoid @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(631,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) ) ) ) @ ( c_Pair @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Value_Oval_ONull ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedCastNull_0) ).

thf(2274,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) ) ) ) @ ( c_Pair @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Value_Oval_ONull ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(322,axiom,
    ( ( hAPP @ ( c_State_Ohp @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ v_a____ )
    = ( c_Option_Ooption_OSome @ ( c_Pair @ v_C____ @ v_fs____ @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hp_0) ).

thf(1545,plain,
    ( ( hAPP @ ( c_State_Ohp @ ( c_Pair @ v_ha____ @ v_la____ @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ v_a____ )
    = ( c_Option_Ooption_OSome @ ( c_Pair @ v_C____ @ v_fs____ @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(68,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(853,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)],[68]) ).

thf(170,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(1147,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)],[170]) ).

thf(467,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I9_J_0) ).

thf(1890,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(293,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OLAss @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I1_J_0) ).

thf(1479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OLAss @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(239,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(1347,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)],[239]) ).

thf(36,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ J @ K @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_17) ).

thf(770,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ J @ K @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(331,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_32) ).

thf(1568,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(245,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I42_J_0) ).

thf(1362,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(450,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_ONT @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_3) ).

thf(1847,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_ONT @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(481,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ ( c_Type_Oty_OClass @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I5_J_0) ).

thf(1922,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ ( c_Type_Oty_OClass @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(55,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(817,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)],[55]) ).

thf(468,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).

thf(1892,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(1379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(405,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ I @ E @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_10) ).

thf(1741,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ I @ E @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(881,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(643,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ F @ C ) @ D ) @ E ) )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__hext_0) ).

thf(2301,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ F @ C ) @ D ) @ E ) )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(1815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(461,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

thf(1875,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(420,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ D @ F @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_3) ).

thf(1778,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ D @ F @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(587,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ B @ C @ A @ D @ E @ F @ G @ H ) ) @ D ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ H @ C @ ( c_Expr_Oexp_OTryCatch @ F @ B @ E @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_2) ).

thf(2178,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ B @ C @ A @ D @ E @ F @ G @ H ) ) @ D ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ H @ C @ ( c_Expr_Oexp_OTryCatch @ F @ B @ E @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(92,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(924,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)],[92]) ).

thf(287,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ A @ E ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( c_Option_Ooption_OSome @ B @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).

thf(1465,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ A @ E ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( c_Option_Ooption_OSome @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( c_TypeRel_Osko__TypeRel__XClass__widen__1__1 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ B @ C ) @ ( c_Type_Oty_OClass @ D ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Class__widen_0) ).

thf(1714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( c_TypeRel_Osko__TypeRel__XClass__widen__1__1 @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ B @ C ) @ ( c_Type_Oty_OClass @ D ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).

thf(789,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(549,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ F ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedInitBlock_0) ).

thf(2090,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(249,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(1373,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)],[249]) ).

thf(477,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_15) ).

thf(1911,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(380,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ G @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_7) ).

thf(1682,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ G @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(526,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed1_0) ).

thf(2034,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OFAss @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(50,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_ONT @ F )
      = D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I25_J_0) ).

thf(806,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_ONT @ F )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(31,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ c_Value_Oval_OUnit @ F )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Orecs_I1_J_0) ).

thf(756,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ c_Value_Oval_OUnit @ F )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_Onew @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( 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_WTrtNew_0) ).

thf(1664,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_Onew @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( 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)],[371]) ).

thf(556,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(2105,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(434,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ ( c_Type_Oty_OClass @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I26_J_0) ).

thf(1811,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ ( c_Type_Oty_OClass @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(281,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( c_Type_Oty_OClass @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I8_J_0) ).

thf(1450,plain,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( c_Type_Oty_OClass @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).

thf(1828,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(502,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_OListMem @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert_0) ).

thf(1978,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_OListMem @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(638,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ C @ tc_Type_Oty @ tc_Type_Oty ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__refl_0) ).

thf(2291,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ C @ tc_Type_Oty @ tc_Type_Oty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(127,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(1020,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)],[127]) ).

thf(621,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(2254,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(336,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWTs @ A @ B @ ( c_List_Olist_OCons @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) )
      | ~ ( c_WellType_OWTs @ A @ B @ D @ F )
      | ~ ( c_WellType_OWT @ A @ B @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCons_0) ).

thf(1581,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWTs @ A @ B @ ( c_List_Olist_OCons @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) )
      | ~ ( c_WellType_OWTs @ A @ B @ D @ F )
      | ~ ( c_WellType_OWT @ A @ B @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(657,axiom,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_OInteger ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I19_J_0) ).

thf(2335,plain,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_OInteger ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(114,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(981,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)],[114]) ).

thf(634,axiom,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_T_H_H____ ) @ v_T____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_H_HsubT_0) ).

thf(2281,plain,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_T_H_H____ ) @ v_T____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(161,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I31_J_0) ).

thf(1119,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(570,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWT @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).

thf(2137,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWT @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(512,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_0) ).

thf(2002,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(274,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ H @ D @ E @ I @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ I @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_22) ).

thf(1433,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ H @ D @ E @ I @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ I @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(188,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_ONT @ F )
      = D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I4_J_0) ).

thf(1201,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_ONT @ F )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(577,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

thf(2154,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(600,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ ( c_Value_Oval_OAddr @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Orecs_I5_J_0) ).

thf(2205,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ ( c_Value_Oval_OAddr @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(448,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ C @ H @ E @ I @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ I @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_26) ).

thf(1843,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ C @ H @ E @ I @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ I @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(536,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).

thf(2058,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(178,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I7_J_0) ).

thf(1169,plain,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(470,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_27) ).

thf(1896,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(877,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(10,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I13_J_0) ).

thf(692,plain,
    c_Type_Oty_ONT != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(428,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OBoolean
     != ( c_Type_Oty_OClass @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I14_J_0) ).

thf(1796,plain,
    ! [A: $i] :
      ( c_Type_Oty_OBoolean
     != ( c_Type_Oty_OClass @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(145,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(1072,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)],[145]) ).

thf(615,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).

thf(2242,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(116,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ K @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_3) ).

thf(988,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ K @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(555,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ E @ F @ tc_Value_Oval ) @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) )
      = ( c_Expr_Oexp_OBlock @ A @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_SmallStep_Oblocks @ ( c_Pair @ B @ ( c_Pair @ D @ ( c_Pair @ F @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_blocks_Osimps_I1_J_0) ).

thf(2103,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ E @ F @ tc_Value_Oval ) @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) )
      = ( c_Expr_Oexp_OBlock @ A @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_SmallStep_Oblocks @ ( c_Pair @ B @ ( c_Pair @ D @ ( c_Pair @ F @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(156,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(1104,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)],[156]) ).

thf(386,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_31) ).

thf(1697,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(205,axiom,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I4_J_0) ).

thf(1242,plain,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(501,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_OCast @ B @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_0) ).

thf(1975,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_OCast @ B @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(329,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I21_J_0) ).

thf(1564,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(599,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).

thf(2204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(5,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(678,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)],[5]) ).

thf(384,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Type_Oty ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_TypeRel_OMethod @ D @ E @ F @ A @ G @ ( c_Pair @ B @ H @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( hAPP @ ( c_State_Ohp @ J ) @ K )
       != ( c_Option_Ooption_OSome @ ( c_Pair @ E @ L @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ( c_SmallStep_Oredp @ D @ ( c_Expr_Oexp_OCall @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ K ) ) @ F @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ J @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ I ) @ A @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ K ) @ C @ tc_Value_Oval ) @ H @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ J ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedCall_0) ).

thf(1691,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Type_Oty ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_TypeRel_OMethod @ D @ E @ F @ A @ G @ ( c_Pair @ B @ H @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( hAPP @ ( c_State_Ohp @ J ) @ K )
       != ( c_Option_Ooption_OSome @ ( c_Pair @ E @ L @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ( c_SmallStep_Oredp @ D @ ( c_Expr_Oexp_OCall @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ K ) ) @ F @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ J @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ I ) @ A @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ K ) @ C @ tc_Value_Oval ) @ H @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ J ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(276,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ D @ E @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_6) ).

thf(1438,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ D @ E @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(562,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Objects_Otypeof__h @ A @ ( c_Value_Oval_OIntg @ B ) )
      = ( c_Option_Ooption_OSome @ c_Type_Oty_OInteger @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typeof__h_Osimps_I4_J_0) ).

thf(2118,plain,
    ! [B: $i,A: $i] :
      ( ( c_Objects_Otypeof__h @ A @ ( c_Value_Oval_OIntg @ B ) )
      = ( c_Option_Ooption_OSome @ c_Type_Oty_OInteger @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(236,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(1338,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)],[236]) ).

thf(531,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(2047,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)],[531]) ).

thf(175,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(1163,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)],[175]) ).

thf(172,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(1153,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)],[172]) ).

thf(33,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(761,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)],[33]) ).

thf(227,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(1311,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)],[227]) ).

thf(611,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_18) ).

thf(2232,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(641,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
       != ( c_Option_Ooption_OSome @ G @ D ) )
      | ( ( hAPP @ A @ F )
        = ( c_Option_Ooption_OSome @ G @ D ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).

thf(2296,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
       != ( c_Option_Ooption_OSome @ G @ D ) )
      | ( ( hAPP @ A @ F )
        = ( c_Option_Ooption_OSome @ G @ D ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(646,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).

thf(2307,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

thf(1067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(403,axiom,
    v_T_H____ = v_T____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1736,plain,
    v_T_H____ = v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(18,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(714,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)],[18]) ).

thf(458,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_0) ).

thf(1868,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(537,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_18) ).

thf(2061,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(360,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_7) ).

thf(1636,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(627,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != ( c_Value_Oval_OIntg @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I23_J_0) ).

thf(2264,plain,
    ! [B: $i,A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != ( c_Value_Oval_OIntg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(105,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(957,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)],[105]) ).

thf(103,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(952,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)],[103]) ).

thf(309,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_0) ).

thf(1519,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(633,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(2277,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)],[633]) ).

thf(209,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(1255,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)],[209]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OIntg @ A )
     != c_Value_Oval_OUnit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I9_J_0) ).

thf(862,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OIntg @ A )
     != c_Value_Oval_OUnit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem_0) ).

thf(1666,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

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(729,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(518,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).

thf(2015,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(254,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ ( c_Fun_Ofun__upd @ F @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__upd_0) ).

thf(1387,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ ( c_Fun_Ofun__upd @ F @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(87,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(910,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)],[87]) ).

thf(28,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(746,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)],[28]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).

thf(1091,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(58,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(825,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)],[58]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OIntg @ A )
       != ( c_Value_Oval_OIntg @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I2_J_0) ).

thf(1343,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OIntg @ A )
       != ( c_Value_Oval_OIntg @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(618,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCond_2) ).

thf(2249,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(39,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_OVoid @ F )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I22_J_0) ).

thf(778,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_OVoid @ F )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(1676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(568,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).

thf(2133,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(195,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(1217,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)],[195]) ).

thf(574,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAccNT_0) ).

thf(2147,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( B
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__2 @ C @ A @ B ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ t_a ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_2) ).

thf(1502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( B
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__2 @ C @ A @ B ) ) )
      | ( B = A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ t_a ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(409,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(1751,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(56,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ C )
      | ~ ( c_TypeRel_OMethod @ A @ B @ D @ E @ F @ G @ H @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__is__class_0) ).

thf(820,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ C )
      | ~ ( c_TypeRel_OMethod @ A @ B @ D @ E @ F @ G @ H @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

thf(1619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(248,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(1370,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)],[248]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).

thf(916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(487,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_17) ).

thf(1938,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(246,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I26_J_0) ).

thf(1365,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(181,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(1178,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)],[181]) ).

thf(382,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ I @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_27) ).

thf(1687,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ I @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(354,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

thf(1624,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(174,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(1159,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)],[174]) ).

thf(367,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).

thf(1656,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(661,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_17) ).

thf(2345,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(164,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(1128,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)],[164]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).

thf(1291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(131,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I16_J_0) ).

thf(1032,plain,
    c_Type_Oty_OInteger != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(446,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_35) ).

thf(1837,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(345,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_21) ).

thf(1602,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(445,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

thf(1836,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(424,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(1787,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(129,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).

thf(1027,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(604,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).

thf(2213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(186,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ J @ K @ L @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ L @ G ) ) )
      | ( F = c_Type_Oty_ONT )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_0) ).

thf(1195,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ J @ K @ L @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ L @ G ) ) )
      | ( F = c_Type_Oty_ONT )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(263,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wts__wts_H_0) ).

thf(1407,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(476,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ E ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedBlock_0) ).

thf(1910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(64,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I2_J_0) ).

thf(842,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(333,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(1573,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(111,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(974,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)],[111]) ).

thf(261,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(1402,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)],[261]) ).

thf(341,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ G @ I @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_29) ).

thf(1592,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ G @ I @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_0) ).

thf(1541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(413,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Type_Oty_OClass @ A )
       != ( c_Type_Oty_OClass @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).

thf(1762,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Type_Oty_OClass @ A )
       != ( c_Type_Oty_OClass @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(210,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I12_J_0) ).

thf(1259,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(666,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCond_0) ).

thf(2359,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(142,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(1064,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)],[142]) ).

thf(158,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(1111,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)],[158]) ).

thf(454,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_33) ).

thf(1856,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(271,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_14) ).

thf(1425,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I24_J_0) ).

thf(1096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(462,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OSeq @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTSeq_0) ).

thf(1878,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OSeq @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(629,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ G @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_15) ).

thf(2268,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ G @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(259,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(1397,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(616,axiom,
    c_TypeRel_OMethod @ v_P @ v_C____ @ v_M____ @ v_Ts____ @ v_T____ @ ( c_Pair @ v_pns____ @ v_body____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ v_D____ @ ( 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_method_0) ).

thf(2245,plain,
    c_TypeRel_OMethod @ v_P @ v_C____ @ v_M____ @ v_Ts____ @ v_T____ @ ( c_Pair @ v_pns____ @ v_body____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ v_D____ @ ( 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)],[616]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_1) ).

thf(1350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(486,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OSeq @ E @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ B @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OSeqRed_0) ).

thf(1936,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OSeq @ E @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ B @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(75,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(874,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)],[75]) ).

thf(578,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ E @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCond_1) ).

thf(2157,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ E @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(427,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ C ) @ F @ E @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ F @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__widens_0) ).

thf(1794,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ C ) @ F @ E @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ F @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(126,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(1017,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)],[126]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).

thf(1498,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(339,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_11) ).

thf(1587,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Onew @ A @ B )
       != ( c_Expr_Oexp_Onew @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I1_J_0) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Onew @ A @ B )
       != ( c_Expr_Oexp_Onew @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(395,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_2) ).

thf(1719,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(233,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(1329,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)],[233]) ).

thf(521,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCast @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCast_0) ).

thf(2023,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCast @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D )
      | ~ ( c_List_Olist__all @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_2) ).

thf(933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D )
      | ~ ( c_List_Olist__all @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(2,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ D @ J @ K @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ K @ G ) ) )
      | ( A = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_4) ).

thf(669,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ D @ J @ K @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ K @ G ) ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I16_J_0) ).

thf(901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(648,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_7) ).

thf(2312,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(387,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_1) ).

thf(1700,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(194,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(1214,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)],[194]) ).

thf(363,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).

thf(1644,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(349,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCond_0) ).

thf(1612,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(15,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Fun_Ofun__upd @ E @ B @ ( c_Option_Ooption_OSome @ F @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      | ~ ( c_Map_Omap__le @ A @ E @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__imp__upd__le_0) ).

thf(706,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Fun_Ofun__upd @ E @ B @ ( c_Option_Ooption_OSome @ F @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      | ~ ( c_Map_Omap__le @ A @ E @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(497,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(1964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(489,axiom,
    v_T_H____ = v_T____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_HisT_0) ).

thf(1942,plain,
    v_T_H____ = v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(368,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).

thf(1659,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(595,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ v_pns____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ v_D____ ) @ v_Ts____ @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ v_a____ ) @ v_vs____ @ tc_Value_Oval ) @ v_body____ @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ v_T_H_H____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(2196,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ v_pns____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ v_D____ ) @ v_Ts____ @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ v_a____ ) @ v_vs____ @ tc_Value_Oval ) @ v_body____ @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ v_T_H_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(614,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ C @ D @ B )
      | ~ ( c_WellType_OWT @ A @ C @ E @ B )
      | ~ ( c_WellType_OWT @ A @ C @ F @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCond @ F @ E @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCond_1) ).

thf(2240,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ C @ D @ B )
      | ~ ( c_WellType_OWT @ A @ C @ E @ B )
      | ~ ( c_WellType_OWT @ A @ C @ F @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCond @ F @ E @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(528,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_19) ).

thf(2038,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(1207,plain,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(547,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_0) ).

thf(2085,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(650,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OAddr @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit__asm_4) ).

thf(2317,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OAddr @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(119,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(997,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)],[119]) ).

thf(13,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(701,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)],[13]) ).

thf(171,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(1150,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)],[171]) ).

thf(223,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(1297,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)],[223]) ).

thf(201,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_0) ).

thf(1231,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_OSome @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(1131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_OSome @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(429,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCond_2) ).

thf(1799,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(1947,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(257,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(1393,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)],[257]) ).

thf(440,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_6) ).

thf(1825,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(636,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_25) ).

thf(2285,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(159,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(1114,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)],[159]) ).

thf(154,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(1099,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)],[154]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I34_J_0) ).

thf(985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(318,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ tc_Value_Oval ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ E @ G @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__Cons2_3) ).

thf(1539,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ tc_Value_Oval ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ E @ G @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(1456,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(252,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(1382,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)],[252]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(1002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(452,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

thf(1852,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(533,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCall @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ G @ H @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellType_OWTs @ A @ B @ E @ G )
      | ~ ( c_TypeRel_OMethod @ A @ I @ D @ H @ F @ ( c_Pair @ J @ K @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ L @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ B @ C @ ( c_Type_Oty_OClass @ I ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCall_0) ).

thf(2052,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCall @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ G @ H @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellType_OWTs @ A @ B @ E @ G )
      | ~ ( c_TypeRel_OMethod @ A @ I @ D @ H @ F @ ( c_Pair @ J @ K @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ L @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ B @ C @ ( c_Type_Oty_OClass @ I ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(344,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_0) ).

thf(1599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(356,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_OInteger @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_2) ).

thf(1627,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_OInteger @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(311,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ ( c_Value_Oval_OIntg @ F ) @ G )
      = ( hAPP @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I27_J_0) ).

thf(1525,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ ( c_Value_Oval_OIntg @ F ) @ G )
      = ( hAPP @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(508,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_22) ).

thf(1991,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(45,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(792,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)],[45]) ).

thf(91,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(921,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)],[91]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

thf(1846,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(132,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeRel_OMethod @ A @ B @ C @ D @ E @ F @ B @ G )
      | ~ ( c_TypeRel_OMethod @ A @ H @ C @ D @ E @ F @ B @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__idemp_0) ).

thf(1035,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeRel_OMethod @ A @ B @ C @ D @ E @ F @ B @ G )
      | ~ ( c_TypeRel_OMethod @ A @ H @ C @ D @ E @ F @ B @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(469,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

thf(1895,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(183,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(1185,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)],[183]) ).

thf(401,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

thf(1732,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(93,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(926,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)],[93]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(1086,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Onew @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I25_J_0) ).

thf(938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Onew @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(592,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H ) @ I ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ G @ H )
      | ~ ( c_TypeRel_Ohas__field @ A @ J @ E @ I @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAss_0) ).

thf(2189,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H ) @ I ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ G @ H )
      | ~ ( c_TypeRel_Ohas__field @ A @ J @ E @ I @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(351,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_11) ).

thf(1616,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).

thf(773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(658,axiom,
    c_WellType_OWT @ v_P @ ( c_Map_Omap__upds @ ( c_COMBK @ ( c_Option_Ooption_ONone @ tc_Type_Oty ) @ ( tc_Option_Ooption @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_List_Olist_OCons @ c_Type_Othis @ v_pns____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ v_D____ ) @ v_Ts____ @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty ) @ v_body____ @ v_T_H_H____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wtabody_0) ).

thf(2338,plain,
    c_WellType_OWT @ v_P @ ( c_Map_Omap__upds @ ( c_COMBK @ ( c_Option_Ooption_ONone @ tc_Type_Oty ) @ ( tc_Option_Ooption @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_List_Olist_OCons @ c_Type_Othis @ v_pns____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ v_D____ ) @ v_Ts____ @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty ) @ v_body____ @ v_T_H_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(166,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(1135,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)],[166]) ).

thf(586,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OFAcc @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAccRed_0) ).

thf(2176,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OFAcc @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(639,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCall @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCallObj_0) ).

thf(2292,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCall @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).

thf(1680,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(495,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(1959,plain,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OAddr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(215,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(1273,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)],[215]) ).

thf(407,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssThrow1_0) ).

thf(1747,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(483,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_22) ).

thf(1927,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(69,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(856,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)],[69]) ).

thf(9,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(689,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)],[9]) ).

thf(624,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(2260,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(612,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_9) ).

thf(2235,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(573,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

thf(2144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(108,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I28_J_0) ).

thf(965,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(29,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I33_J_0) ).

thf(750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ c_Value_Oval_ONull @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit_1) ).

thf(1727,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ c_Value_Oval_ONull @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(620,axiom,
    c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_Ts_H____ @ v_Ts____ @ tc_Type_Oty @ tc_Type_Oty,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subs_0) ).

thf(2253,plain,
    c_List_Olist__all2 @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_Ts_H____ @ v_Ts____ @ tc_Type_Oty @ tc_Type_Oty,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(632,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ ( c_Type_Oty_OClass @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_4) ).

thf(2275,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ ( c_Type_Oty_OClass @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(575,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_WellTypeRT_OWTrt @ D @ E @ A @ ( c_Expr_Oexp_OLAss @ B @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ G ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ D @ E @ A @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtLAss_0) ).

thf(2149,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_WellTypeRT_OWTrt @ D @ E @ A @ ( c_Expr_Oexp_OLAss @ B @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ G ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ D @ E @ A @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ c_Value_Oval_ONull ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ c_Type_Oty_ONT ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__Null_1) ).

thf(2028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ c_Value_Oval_ONull ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ c_Type_Oty_ONT ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(224,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(1301,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)],[224]) ).

thf(342,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H ) @ I ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ G @ H )
      | ~ ( c_TypeRel_Ohas__field @ A @ J @ E @ I @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I10_J_0) ).

thf(1595,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H ) @ I ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ G @ H )
      | ~ ( c_TypeRel_Ohas__field @ A @ J @ E @ I @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(358,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_Onew @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( 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_WTrt_H__WTrts_H_Ointros_I1_J_0) ).

thf(1631,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_Onew @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( 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)],[358]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(85,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(904,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)],[85]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ c_Type_Oty_ONT ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ D @ B ) @ c_Value_Oval_ONull ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__Null_0) ).

thf(1833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ c_Type_Oty_ONT ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ D @ B ) @ c_Value_Oval_ONull ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(465,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_5) ).

thf(1884,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__empty_0) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Onew @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I35_J_0) ).

thf(1125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Onew @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(27,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(743,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)],[27]) ).

thf(316,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssThrow2_0) ).

thf(1535,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAss @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).

thf(1226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(296,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(1488,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)],[296]) ).

thf(272,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_26) ).

thf(1428,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(607,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(2220,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)],[607]) ).

thf(390,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(1707,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)],[390]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(1271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(457,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_14) ).

thf(1865,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(234,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(1332,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)],[234]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(704,plain,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(101,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(947,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)],[101]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(651,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_0) ).

thf(2319,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(3,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_Onew @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I43_J_0) ).

thf(672,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_Onew @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(139,axiom,
    ! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).

thf(1058,plain,
    ! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(157,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(1107,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)],[157]) ).

thf(204,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(1239,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)],[204]) ).

thf(510,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(1997,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)],[510]) ).

thf(545,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Value_Oval_ONull )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ B @ C @ D ) @ A ) @ c_Type_Oty_ONT ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__NT_0) ).

thf(2079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Value_Oval_ONull )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ B @ C @ D ) @ A ) @ c_Type_Oty_ONT ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(192,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(1209,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)],[192]) ).

thf(60,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_OInteger @ F )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I24_J_0) ).

thf(831,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_OInteger @ F )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(218,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ H @ I @ J @ K @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ K @ G ) ) )
      | ( F = c_Type_Oty_ONT )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_16) ).

thf(1282,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ H @ I @ J @ K @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ K @ G ) ) )
      | ( F = c_Type_Oty_ONT )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(610,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_0) ).

thf(2229,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(605,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_30) ).

thf(2214,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Omap @ B @ C @ D @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).

thf(1011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Omap @ B @ C @ D @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(136,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(1048,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)],[136]) ).

thf(485,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_WellType_OWT @ D @ A @ ( c_Expr_Oexp_OLAss @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ( B = c_Type_Othis )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ F ) @ C ) )
      | ~ ( c_WellType_OWT @ D @ A @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTLAss_0) ).

thf(1933,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_WellType_OWT @ D @ A @ ( c_Expr_Oexp_OLAss @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ( B = c_Type_Othis )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ F ) @ C ) )
      | ~ ( c_WellType_OWT @ D @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(561,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ A @ B @ C @ ( c_Type_Oty_OClass @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTThrow_0) ).

thf(2116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ A @ B @ C @ ( c_Type_Oty_OClass @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(430,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ E @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCons_0) ).

thf(1801,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ E @ G )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(162,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(1122,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)],[162]) ).

thf(383,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OSeqThrow_0) ).

thf(1690,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(180,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I10_J_0) ).

thf(1175,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(34,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(764,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)],[34]) ).

thf(113,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(979,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(6,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(681,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)],[6]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(1853,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_OtakeWhile @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).

thf(784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ ( c_List_OtakeWhile @ A @ B @ C ) @ C )
      | ~ ( c_List_Odistinct @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(160,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ c_Value_Oval_OUnit @ F )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I24_J_0) ).

thf(1117,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ c_Value_Oval_OUnit @ F )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(617,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_Progress_OWTrt_H @ D @ A @ E @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I3_J_0) ).

thf(2246,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_Progress_OWTrt_H @ D @ A @ E @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(298,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ D @ I @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) )
      | ( A = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_12) ).

thf(1492,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ D @ I @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(642,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ G @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAssNT_0) ).

thf(2299,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ G @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(396,axiom,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1722,plain,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(169,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(1144,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)],[169]) ).

thf(417,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_23) ).

thf(1771,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).

thf(1376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_ONil @ B ) )
      | ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(596,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAccThrow_0) ).

thf(2197,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(499,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ E ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(1969,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(289,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_8) ).

thf(1471,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(32,axiom,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OIntg @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I8_J_0) ).

thf(758,plain,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OIntg @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(559,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ E ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(2111,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(628,axiom,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_Expr_Oexp_OCall @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ v_a____ ) ) @ v_M____ @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_vs____ @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T_H____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).

thf(2267,plain,
    c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_Expr_Oexp_OCall @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ v_a____ ) ) @ v_M____ @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_vs____ @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_T_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(400,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

thf(1731,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(456,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ B @ H @ I @ J @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ J @ G ) ) )
      | ( F = c_Type_Oty_ONT )
      | ( F = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_24) ).

thf(1862,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ B @ H @ I @ J @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ J @ G ) ) )
      | ( F = c_Type_Oty_ONT )
      | ( F = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).

thf(848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(222,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(1293,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)],[222]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_OBoolean ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I15_J_0) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_OBoolean ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(438,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_3) ).

thf(1820,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(80,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).

thf(890,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
      = ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E )
        = ( c_List_OtakeWhile @ A @ B @ E ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).

thf(1667,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) @ E )
        = ( c_List_OtakeWhile @ A @ B @ E ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(588,axiom,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I12_J_0) ).

thf(2180,plain,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(52,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_OVoid @ F )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I1_J_0) ).

thf(811,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_OVoid @ F )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(589,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT )
      | ( E = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ F @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_1) ).

thf(2182,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT )
      | ( E = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ F @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(522,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_27) ).

thf(2025,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(1080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(47,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(799,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)],[47]) ).

thf(22,axiom,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OIntg @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I14_J_0) ).

thf(726,plain,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OIntg @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(130,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(1029,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)],[130]) ).

thf(82,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(895,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)],[82]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_ONT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).

thf(1556,plain,
    ! [A: $i] :
      ( ( c_Type_Oty_OClass @ A )
     != c_Type_Oty_ONT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(285,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_30) ).

thf(1460,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(685,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(543,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ A @ C @ D @ E @ B ) ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_1) ).

thf(2075,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ A @ C @ D @ E @ B ) ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

thf(1474,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I36_J_0) ).

thf(868,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(40,axiom,
    class_Orderings_Olinorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

thf(780,plain,
    class_Orderings_Olinorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(2064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(637,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_6) ).

thf(2288,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(120,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ c_Value_Oval_ONull @ F )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Orecs_I2_J_0) ).

thf(1000,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ c_Value_Oval_ONull @ F )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(292,axiom,
    ( ( c_Nat_Osize__class_Osize @ v_Ts____ @ ( tc_List_Olist @ tc_Type_Oty ) )
    = ( c_Nat_Osize__class_Osize @ v_pns____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RedCall_I4_J_0) ).

thf(1477,plain,
    ( ( c_Nat_Osize__class_Osize @ v_Ts____ @ ( tc_List_Olist @ tc_Type_Oty ) )
    = ( c_Nat_Osize__class_Osize @ v_pns____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(554,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(2101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(644,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(2303,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(155,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(1102,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(601,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_9) ).

thf(2207,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(1694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_Othrow @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(1805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_Othrow @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(540,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OLAss @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OLAssRed_0) ).

thf(2069,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OLAss @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_OLAss @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_SmallStep_Oredp @ A @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(328,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

thf(1562,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(187,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(1198,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)],[187]) ).

thf(258,axiom,
    ! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(1396,plain,
    ! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(603,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OThrowThrow_0) ).

thf(2212,plain,
    ! [C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(584,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_0) ).

thf(2171,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ B ) )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(135,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(1044,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)],[135]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).

thf(695,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(206,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(1245,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)],[206]) ).

thf(571,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_Onew @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ C ) )
      | ~ ( c_Decl_Ois__class @ A @ C @ ( 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_WTNew_0) ).

thf(2139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_Onew @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ C ) )
      | ~ ( c_Decl_Ois__class @ A @ C @ ( 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)],[571]) ).

thf(78,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(883,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)],[78]) ).

thf(355,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ E ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ E ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OInitBlockThrow_0) ).

thf(1626,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ B @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ E ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ E ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(534,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(2054,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)],[534]) ).

thf(552,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ B @ C @ D @ A @ E ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ B @ C @ D @ A @ E ) @ tc_Type_Oty ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ B @ E ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ A @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_0) ).

thf(2096,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ B @ C @ D @ A @ E ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ B @ C @ D @ A @ E ) @ tc_Type_Oty ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ B @ E ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ A @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(176,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(1166,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)],[176]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(1203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odistinct @ A @ B )
      | ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(100,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(944,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)],[100]) ).

thf(62,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(836,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)],[62]) ).

thf(514,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_1) ).

thf(2005,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
      | ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(266,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(1413,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)],[266]) ).

thf(146,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(1076,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)],[146]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I40_J_0) ).

thf(675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(337,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ I ) @ H ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ ( c_Fun_Ofun__upd @ C @ F @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ E ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ G @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I22_J_0) ).

thf(1583,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ I ) @ H ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ ( c_Fun_Ofun__upd @ C @ F @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ E ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ G @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(225,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(1304,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)],[225]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).

thf(1873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(46,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(795,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)],[46]) ).

thf(630,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(2271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(474,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I18_J_0) ).

thf(1905,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(269,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_1) ).

thf(1420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(656,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_TypeRel_Ohas__field @ A @ H @ E @ G @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ H ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I8_J_0) ).

thf(2333,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAcc @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_TypeRel_Ohas__field @ A @ H @ E @ G @ F @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(622,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtThrow_0) ).

thf(2256,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(109,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(968,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)],[109]) ).

thf(182,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(1181,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)],[182]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).

thf(712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(308,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_31) ).

thf(1516,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(144,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_OInteger @ F )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I3_J_0) ).

thf(1070,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__rec @ A @ B @ C @ D @ E @ c_Type_Oty_OInteger @ F )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(173,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(1156,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)],[173]) ).

thf(79,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(887,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)],[79]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

thf(971,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(330,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ ( c_Value_Oval_OAddr @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I28_J_0) ).

thf(1566,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ ( c_Value_Oval_OAddr @ F ) @ G )
      = ( hAPP @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(346,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ ( c_List_Oappend @ A @ F @ B ) @ C @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).

thf(1605,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ ( c_List_Oappend @ A @ F @ B ) @ C @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ~ ( c_Objects_Ohext @ A @ D )
      | ( ( c_Objects_Otypeof__h @ D @ B )
        = ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__typeof__mono_0) ).

thf(1647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ~ ( c_Objects_Ohext @ A @ D )
      | ( ( c_Objects_Otypeof__h @ D @ B )
        = ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(26,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(739,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)],[26]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(1368,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OLAss @ c_Type_Othis @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I1_J_4) ).

thf(1780,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OLAss @ c_Type_Othis @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(410,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(1753,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)],[410]) ).

thf(314,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

thf(1531,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(323,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ F @ C @ D ) @ ( c_List_Oappend @ E @ A @ B ) @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ C @ A @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ F @ E @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).

thf(1547,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ F @ C @ D ) @ ( c_List_Oappend @ E @ A @ B ) @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ C @ A @ D @ B )
      | ~ ( c_List_Olist__all2 @ G @ F @ E @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_OUnit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I11_J_0) ).

thf(1748,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_OUnit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(488,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCondThrow_0) ).

thf(1941,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

thf(1252,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(391,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(1711,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)],[391]) ).

thf(581,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
      = ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).

thf(2165,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
      = ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(435,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OIntg @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ E @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit_3) ).

thf(1813,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OIntg @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ E @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(1188,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(19,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ J @ K @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_9) ).

thf(717,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ F @ J @ K @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(423,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ A @ D @ C @ E @ B ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ D @ C @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_2) ).

thf(1785,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ A @ D @ C @ E @ B ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ D @ C @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Olist_ONil @ D ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(472,axiom,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( c_Type_Oty_OClass @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).

thf(1901,plain,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( c_Type_Oty_OClass @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(652,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ H @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ H @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_30) ).

thf(2322,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ F @ G )
        = ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ H @ F @ G ) )
      | ( F
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ F @ E @ H @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(51,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I30_J_0) ).

thf(808,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(530,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_16) ).

thf(2044,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(335,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ F ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__widen_0) ).

thf(1579,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ F ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(235,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ c_Value_Oval_ONull @ F )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I25_J_0) ).

thf(1336,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__case @ A @ B @ C @ D @ E @ c_Value_Oval_ONull @ F )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).

thf(1220,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(503,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).

thf(1980,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(566,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).

thf(2128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_ONil @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

thf(1317,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(442,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(1830,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)],[442]) ).

thf(219,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(1285,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)],[219]) ).

thf(404,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_26) ).

thf(1738,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).

thf(2056,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(451,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Type_Oty ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_TypeRel_OMethod @ D @ E @ F @ A @ G @ ( c_Pair @ B @ H @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( hAPP @ ( c_State_Ohp @ J ) @ K )
       != ( c_Option_Ooption_OSome @ ( c_Pair @ E @ L @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ K ) ) @ F @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ J @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ I ) @ A @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ K ) @ C @ tc_Value_Oval ) @ H @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ J @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedCall_0) ).

thf(1849,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Type_Oty ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_TypeRel_OMethod @ D @ E @ F @ A @ G @ ( c_Pair @ B @ H @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ I @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ( ( hAPP @ ( c_State_Ohp @ J ) @ K )
       != ( c_Option_Ooption_OSome @ ( c_Pair @ E @ L @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ K ) ) @ F @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ J @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ I ) @ A @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ K ) @ C @ tc_Value_Oval ) @ H @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ J @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I4_J_0) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(388,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_24) ).

thf(1702,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(197,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I11_J_0) ).

thf(1221,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(494,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(1955,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)],[494]) ).

thf(338,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(1585,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)],[338]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

thf(1670,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(123,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ A @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ B @ L @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_2) ).

thf(1008,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ A @ H @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ B @ L @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(464,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(1881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I37_J_0) ).

thf(859,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Onew @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(117,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(991,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)],[117]) ).

thf(320,axiom,
    ! [A: $i] : ( c_Type_Ois__refT @ ( c_Type_Oty_OClass @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__refT__def_2) ).

thf(1543,plain,
    ! [A: $i] : ( c_Type_Ois__refT @ ( c_Type_Oty_OClass @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ c_Type_Oty_ONT ) @ ( c_Type_Oty_OClass @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_2) ).

thf(1766,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ c_Type_Oty_ONT ) @ ( c_Type_Oty_OClass @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(295,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_28) ).

thf(1485,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(500,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_WellTypeRT_OWTrt @ D @ A @ E @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtVal_0) ).

thf(1972,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Objects_Otypeof__h @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ tc_Type_Oty ) )
      | ( c_WellTypeRT_OWTrt @ D @ A @ E @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(137,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(1052,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)],[137]) ).

thf(394,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).

thf(1717,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

thf(2030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(65,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I4_J_0) ).

thf(845,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(517,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ ( c_Type_Oty_OClass @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_4) ).

thf(2013,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ ( c_Type_Oty_OClass @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(548,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

thf(2088,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(284,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ 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_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).

thf(1459,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ 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_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(498,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_13) ).

thf(1966,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(381,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(1685,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(325,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(1553,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_ONull ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(437,axiom,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OAddr @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I10_J_0) ).

thf(1817,plain,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OAddr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(647,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).

thf(2310,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(594,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

thf(2194,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(653,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_31) ).

thf(2325,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(541,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCallThrowObj_0) ).

thf(2071,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(402,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ I ) @ H ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ ( c_Fun_Ofun__upd @ C @ F @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ E ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ G @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtTry_0) ).

thf(1734,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ I ) @ H ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ ( c_Fun_Ofun__upd @ C @ F @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ E ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ G @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(280,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).

thf(1448,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(591,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ ( c_Fun_Ofun__upd @ B @ E @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ D ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ F @ G )
      | ~ ( c_WellType_OWT @ A @ B @ C @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTTry_0) ).

thf(2187,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ ( c_Fun_Ofun__upd @ B @ E @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ D ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ F @ G )
      | ~ ( c_WellType_OWT @ A @ B @ C @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(256,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(1390,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)],[256]) ).

thf(645,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).

thf(2305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(660,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(2342,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(609,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_35) ).

thf(2226,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(1453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(232,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(1326,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)],[232]) ).

thf(53,axiom,
    c_Type_Ois__refT @ c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__refT__def_1) ).

thf(813,plain,
    c_Type_Ois__refT @ c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(582,axiom,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_T_H_H____ ) @ v_T____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(2167,plain,
    hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ v_T_H_H____ ) @ v_T____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(585,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OAddr @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit_4) ).

thf(2174,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Value_Oval_Oval__case @ B @ C @ D @ E @ F @ ( c_Value_Oval_OAddr @ G ) @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).

thf(1341,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(361,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ H @ D @ I @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) )
      | ( A = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_20) ).

thf(1639,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ B @ H @ D @ I @ J @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ J @ G ) ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(619,axiom,
    ( ( c_Nat_Osize__class_Osize @ v_vs____ @ ( tc_List_Olist @ tc_Value_Oval ) )
    = ( c_Nat_Osize__class_Osize @ v_Ts____ @ ( tc_List_Olist @ tc_Type_Oty ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__vs_0) ).

thf(2251,plain,
    ( ( c_Nat_Osize__class_Osize @ v_vs____ @ ( tc_List_Olist @ tc_Value_Oval ) )
    = ( c_Nat_Osize__class_Osize @ v_Ts____ @ ( tc_List_Olist @ tc_Type_Oty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(569,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ G @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I11_J_0) ).

thf(2135,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ G @ H )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(439,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ I @ J @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_25) ).

thf(1822,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ F @ I @ J @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(43,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(786,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)],[43]) ).

thf(41,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ J @ E @ K @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ K @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_2) ).

thf(781,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ I @ J @ E @ K @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ K @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(216,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(1276,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)],[216]) ).

thf(340,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCast @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I2_J_0) ).

thf(1590,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OCast @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Type_Oty_OClass @ D ) )
      | ~ ( c_Decl_Ois__class @ A @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Type_Ois__refT @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(141,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrts @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrts__hext__mono_0) ).

thf(1062,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrts @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__1 @ B @ A @ C ) ) )
      | ( C = A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ B @ t_a ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_0) ).

thf(1508,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( c_Type_Oty_OClass @ ( v_sko__TypeRel__Xwiden__Xcases__1 @ B @ A @ C ) ) )
      | ( C = A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ B @ t_a ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(357,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_1) ).

thf(1629,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_Onew @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(513,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ F ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedTry_0) ).

thf(2004,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) @ F ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(576,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).

thf(2152,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(625,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ D ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ D ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OBlockThrow_0) ).

thf(2262,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OBlock @ B @ C @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ D ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_Othrow @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Value_Oval_OAddr @ D ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(529,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ G @ J @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_21) ).

thf(2041,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ G @ J @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCastThrow_0) ).

thf(1777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCast @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A ) @ v_T_H____ ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ v_pns____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ v_D____ ) @ v_Ts____ @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ v_a____ ) @ v_vs____ @ tc_Value_Oval ) @ v_body____ @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(667,plain,
    ! [A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A ) @ v_T_H____ ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ v_ha____ @ v_E____ @ ( c_SmallStep_Oblocks @ ( c_Pair @ ( c_List_Olist_OCons @ c_Type_Othis @ v_pns____ @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Type_Oty_OClass @ v_D____ ) @ v_Ts____ @ tc_Type_Oty ) @ ( c_Pair @ ( c_List_Olist_OCons @ ( c_Value_Oval_OAddr @ v_a____ ) @ v_vs____ @ tc_Value_Oval ) @ v_body____ @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(539,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_33) ).

thf(2066,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWTs @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__implies__WTrts_0) ).

thf(1212,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWTs @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(1513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1 @ B @ C @ A @ D ) ) )
      | ( A = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ D ) @ A ) @ ( c_Type_Oty_OClass @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_0) ).

thf(1661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Type_Oty_OClass @ ( c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1 @ B @ C @ A @ D ) ) )
      | ( A = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ D ) @ A ) @ ( c_Type_Oty_OClass @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_Onew @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I19_J_0) ).

thf(2120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_Onew @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(649,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ D ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ E @ F )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ G @ D @ C @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_1) ).

thf(2315,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( c_Option_Ooption_OSome @ ( c_Type_Oty_OClass @ D ) @ tc_Type_Oty ) @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Type_Oty ) ) @ E @ F )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ G @ D @ C @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(509,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(1994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(350,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_OVoid @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_0) ).

thf(1614,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ c_Type_Oty_OVoid @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(226,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ I @ J @ K @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ K @ G ) ) )
      | ( A = c_Type_Oty_ONT )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_8) ).

thf(1308,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ I @ J @ K @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ K @ G ) ) )
      | ( A = c_Type_Oty_ONT )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(597,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_20) ).

thf(2198,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(640,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ E @ G )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I15_J_0) ).

thf(2294,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrts_H @ A @ B @ C @ ( c_List_Olist_OCons @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ E @ G )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(2036,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(362,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ B )
      = ( c_Option_Ooption_OSome @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).

thf(1642,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ B )
      = ( c_Option_Ooption_OSome @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(418,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_29) ).

thf(1774,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(378,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellType_OWT @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__env__mono_0) ).

thf(1678,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellType_OWT @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(102,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wts_H__wts_0) ).

thf(950,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrts @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrts_H @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(411,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).

thf(1757,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(72,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( c_Option_Ooption_OSome @ G @ D ) @ E @ ( tc_Option_Ooption @ D ) ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).

thf(865,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( c_Option_Ooption_OSome @ G @ D ) @ E @ ( tc_Option_Ooption @ D ) ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(564,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_15) ).

thf(2123,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(623,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Map_Omap__le @ F @ C @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ F @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).

thf(2258,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Map_Omap__le @ F @ C @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(515,axiom,
    ( ( c_Nat_Osize__class_Osize @ v_pns____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) )
    = ( c_Nat_Osize__class_Osize @ v_Ts____ @ ( tc_List_Olist @ tc_Type_Oty ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__pns_0) ).

thf(2008,plain,
    ( ( c_Nat_Osize__class_Osize @ v_pns____ @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) )
    = ( c_Nat_Osize__class_Osize @ v_Ts____ @ ( tc_List_Olist @ tc_Type_Oty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(506,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_16) ).

thf(1986,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(312,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ E @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__trans_0) ).

thf(1527,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ E @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(376,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).

thf(1673,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
        = ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(207,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(1248,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)],[207]) ).

thf(532,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).

thf(2050,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(1314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(299,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

thf(1495,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( 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 ) @ ( 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_in @ ( 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 ) @ ( 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 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(425,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ G @ H @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_23) ).

thf(1789,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ E @ I @ G @ H @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(220,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(1288,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)],[220]) ).

thf(550,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

thf(2091,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

thf(828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(20,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(720,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)],[20]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(955,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(275,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ 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_SmallStep_Oredp @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OThrowRed_0) ).

thf(1436,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ 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_SmallStep_Oredp @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(455,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_24) ).

thf(1859,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(598,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_5) ).

thf(2201,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ( G
        = ( c_Type_Oty_OClass @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) )
      | ( G = c_Type_Oty_ONT )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(90,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(918,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)],[90]) ).

thf(507,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ C @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_0) ).

thf(1989,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ C @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(179,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ G @ K @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_5) ).

thf(1172,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ G @ K @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(265,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(1410,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)],[265]) ).

thf(35,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(767,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)],[35]) ).

thf(608,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ E @ A @ B ) @ ( c_List_Oappend @ F @ C @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ E @ F @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).

thf(2223,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ E @ A @ B ) @ ( c_List_Oappend @ F @ C @ D ) @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ A @ C @ B @ D )
      | ~ ( c_List_Olist__all2 @ G @ E @ F @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

thf(960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(2021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(348,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ ( c_Value_Oval_OIntg @ F ) @ G )
      = ( hAPP @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Orecs_I4_J_0) ).

thf(1610,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Value_Oval_Oval__rec @ A @ B @ C @ D @ E @ ( c_Value_Oval_OIntg @ F ) @ G )
      = ( hAPP @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(203,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I3_J_0) ).

thf(1236,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(213,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(1268,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)],[213]) ).

thf(324,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

thf(1550,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(243,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_OBoolean @ F )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I23_J_0) ).

thf(1357,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Type_Oty_Oty__case @ A @ B @ C @ D @ E @ c_Type_Oty_OBoolean @ F )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).

thf(908,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( c_Value_Othe__Addr @ ( c_Value_Oval_OAddr @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__Addr_Osimps_0) ).

thf(1500,plain,
    ! [A: $i] :
      ( ( c_Value_Othe__Addr @ ( c_Value_Oval_OAddr @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(57,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ H @ A @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ L @ B @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_3) ).

thf(822,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ F @ G @ H @ A @ I )
      | ~ ( c_TypeRel_OMethod @ C @ D @ E @ J @ K @ L @ B @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(74,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(871,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)],[74]) ).

thf(152,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_Onew @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I29_J_0) ).

thf(1093,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_Onew @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(484,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__def_0) ).

thf(1930,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(664,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_28) ).

thf(2353,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(63,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(839,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)],[63]) ).

thf(579,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(2159,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)],[579]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(1352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_List_Olinorder__class_Osorted @ B @ A )
      | ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(67,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(850,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)],[67]) ).

thf(392,axiom,
    c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ v_E____ @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_vs____ @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ v_Ts_H____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wtes_0) ).

thf(1713,plain,
    c_WellTypeRT_OWTrts @ v_P @ v_ha____ @ v_E____ @ ( c_List_Omap @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ v_vs____ @ tc_Value_Oval @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ v_Ts_H____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(343,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_36) ).

thf(1597,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(463,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).

thf(1880,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 @ ( hAPP @ ( c_Expr_Oexp_OVal @ ( tc_List_Olist @ tc_String_Ochar ) ) @ 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 ) @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(273,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCast @ B @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_2) ).

thf(1431,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCast @ B @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
       != ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(1505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ B )
       != ( hAPP @ ( c_Expr_Oexp_OVal @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(260,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ K @ L @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_1) ).

thf(1399,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) )
       != ( hAPP @ C @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ E @ F @ G @ H @ A @ B @ D )
        = ( c_Type_Oty_Oty__case @ I @ J @ K @ L @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(353,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_10) ).

thf(1621,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ( G = c_Type_Oty_ONT )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(49,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(803,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)],[49]) ).

thf(230,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I5_J_0) ).

thf(1320,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(496,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ E @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ F @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_1) ).

thf(1962,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ E @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ F @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(97,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(935,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)],[97]) ).

thf(286,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCond @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCondRed_0) ).

thf(1463,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OCond @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( c_Expr_Oexp_OCond @ F @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_SmallStep_Oredp @ A @ B @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(519,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( c_Option_Ooption_OSome @ F @ D ) @ G @ ( tc_Option_Ooption @ D ) ) @ B )
        = ( c_Option_Ooption_OSome @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).

thf(2018,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( c_Option_Ooption_OSome @ F @ D ) @ G @ ( tc_Option_Ooption @ D ) ) @ B )
        = ( c_Option_Ooption_OSome @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(267,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__elim__cases_0) ).

thf(1416,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(593,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I18_J_0) ).

thf(2191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Onew @ A @ B )
     != ( hAPP @ ( c_Expr_Oexp_OVal @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(557,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ D @ E @ I @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ I @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_14) ).

thf(2106,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ A @ G )
        = ( c_Type_Oty_Oty__case @ H @ C @ D @ E @ I @ A @ G ) )
      | ( A
        = ( c_Type_Oty_OClass @ ( c_Type_Osko__Type__Xty__Xcase__cong__1__1 @ A @ F @ I @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(288,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_20) ).

thf(1468,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(16,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(708,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)],[16]) ).

thf(366,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__TypeSafe__Mirabelle__Xwt__blocks__1 @ D @ B @ E @ A ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrt @ D @ E @ F @ ( c_SmallStep_Oblocks @ ( c_Pair @ C @ ( c_Pair @ B @ ( c_Pair @ A @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__blocks_2) ).

thf(1653,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ tc_Value_Oval ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) )
       != ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ tc_Type_Oty ) ) )
      | ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__TypeSafe__Mirabelle__Xwt__blocks__1 @ D @ B @ E @ A ) @ B @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrt @ D @ E @ F @ ( c_SmallStep_Oblocks @ ( c_Pair @ C @ ( c_Pair @ B @ ( c_Pair @ A @ G @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_List_Olist @ tc_Type_Oty ) @ ( tc_prod @ ( tc_List_Olist @ tc_Value_Oval ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ) ) @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(490,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_12) ).

thf(1944,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__asm__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(613,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ F @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__hext_0) ).

thf(2238,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ F @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(297,axiom,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCall_0) ).

thf(1490,plain,
    ! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ H @ I @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_TypeRel_OMethod @ A @ J @ E @ I @ G @ ( c_Pair @ K @ L @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) @ M @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_Type_Oty_OClass @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(133,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(1037,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)],[133]) ).

thf(38,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(775,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)],[38]) ).

thf(416,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCallNT_0) ).

thf(1769,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCall @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G )
      | ~ ( c_WellTypeRT_OWTrts @ A @ B @ C @ F @ H )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(479,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_36) ).

thf(1917,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_Type_Oty_Oty__case @ B @ C @ D @ E @ F @ G @ t_a ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ F @ ( v_sko__Type__Xty__Xsplit__1 @ A @ F @ G ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(663,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OTryCatch @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OTryRed_0) ).

thf(2351,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_SmallStep_Oredp @ A @ ( c_Expr_Oexp_OTryCatch @ B @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( c_Expr_Oexp_OTryCatch @ G @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H )
      | ~ ( c_SmallStep_Oredp @ A @ B @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(150,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(1088,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)],[150]) ).

thf(125,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I6_J_0) ).

thf(1014,plain,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(459,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ A @ ( c_List_Oappend @ C @ F @ D ) @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).

thf(1870,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Map_Omap__upds @ E @ A @ ( c_List_Oappend @ C @ F @ D ) @ B @ D )
        = ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(2361,plain,
    $false,
    inference(e,[status(thm)],[2094,1024,1168,1633,2263,1559,1729,1899,1840,941,2331,1950,2163,892,2109,2131,2031,2072,1767,1083,962,1982,2077,977,1522,994,1422,1544,1205,1533,1041,1924,1005,2210,1443,1808,2099,2282,2114,1142,1671,1608,1999,2141,1233,814,1919,913,1354,930,1497,1705,2168,698,898,1835,2348,1914,1782,1576,1441,2010,1650,1359,1386,2082,1529,1803,1887,1724,1475,1904,1265,1228,1482,2328,1792,1985,2339,1907,2217,1323,802,1279,2185,1191,2126,1059,2356,724,1055,1409,1760,1660,1511,2274,1545,853,1147,1890,1479,1347,770,1568,1362,1847,1922,817,1892,1379,1741,881,2301,1815,1875,1778,2178,924,1465,1714,789,2090,1373,1911,1682,2034,806,756,1664,2105,1811,1450,1828,1978,2291,1020,2254,1581,2335,981,2281,1119,2137,2002,1433,1201,2154,2205,1843,2058,1169,687,1896,877,692,1796,1072,2242,988,2103,1405,1104,1697,1242,1975,1564,2204,678,1691,1438,2118,1338,2047,1163,1153,761,1311,2232,2296,2307,1067,1736,714,1868,2061,1636,2264,957,952,1519,2277,1255,862,1666,729,2015,1387,910,746,1091,825,1343,2249,778,1676,2133,1217,2147,1502,1751,820,1619,1370,916,1938,1365,1178,1687,1624,1159,1656,2345,1128,1291,1032,1837,1602,1836,1787,1027,2213,1195,1407,1910,842,1573,974,1402,1592,1541,1762,1259,2359,1064,1111,1856,1425,1096,1878,2268,1397,2245,1350,1936,874,2157,1794,1017,1498,1587,1138,1719,1329,2023,933,753,669,901,2312,1700,1214,1644,1612,706,1419,1964,1942,1659,2196,2240,2038,1446,1207,2085,2317,1744,997,701,1150,1297,1231,1131,1799,1947,1393,1825,2285,1114,1099,985,1539,1456,1382,1002,1852,2052,1599,1627,1525,1991,792,921,1846,1035,1895,1185,1732,926,1086,938,2189,1616,773,2338,1135,2176,2292,1680,1959,1273,1747,1927,856,689,2260,2235,2144,965,750,1727,2253,2275,2149,2028,1301,1595,1631,733,904,1833,1884,1389,1125,743,1535,1226,1488,1428,2220,1707,1271,1865,1332,704,947,1224,2319,672,1058,1107,1239,1997,2079,1209,831,1282,2229,2214,1011,1048,1933,2116,1801,1122,1690,1175,764,979,681,1853,784,1117,2246,1492,2299,1722,1144,1771,737,1571,1376,2197,1969,1471,758,2111,2267,1731,1862,848,1293,1952,1820,890,1667,2180,811,2182,2025,1080,799,726,1029,895,1556,1460,685,2075,1474,868,780,2064,2288,1000,1477,2101,2303,1102,2207,1694,1805,2069,1562,1198,1396,2212,2171,1044,695,1245,2139,883,1626,2054,2096,1166,1203,944,836,2005,1413,1076,675,1583,1304,1873,795,2271,1905,1420,2333,2256,968,1181,712,1516,1070,1156,887,971,1566,1605,1647,739,1368,1780,1753,1531,1547,1748,1941,1252,1711,2165,1813,1188,717,1785,1262,1901,2322,808,2044,1579,1336,1220,1980,2128,1317,1830,1285,1738,2056,1849,1536,1702,1221,1955,1585,1670,1008,1881,859,991,1543,1766,1485,1972,1052,1717,2030,845,2013,2088,1459,1966,1685,1553,1817,2310,2194,2325,2071,1734,1448,2187,1390,2305,2342,2226,1453,1326,813,2167,2174,1341,1639,2251,2135,1822,786,781,1276,1590,1062,1508,1629,2004,2152,2262,2041,1777,667,929,2066,1212,1513,1661,2120,2315,1994,1614,1308,2198,2294,2036,1642,1774,1678,833,950,1757,865,2123,2258,2008,1986,1527,1673,1248,2050,1314,1495,1789,1288,2091,828,720,955,1436,1859,2201,918,1989,1172,1410,767,2223,960,2021,1610,1236,1268,1550,1357,908,1500,822,871,1093,1930,2353,839,2159,1352,850,1713,1597,1880,1431,1505,1399,1621,803,1320,1962,935,1463,2018,1416,2191,2106,1468,708,1653,1944,2238,1490,1037,775,1769,1917,2351,1088,1014,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV939-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n017.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Fri May 19 01:44:46 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.97/1.16  % [INFO] 	 Parsing done (246ms). 
% 1.97/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.54/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.54/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.54/1.38  % [INFO] 	 Scanning for conjecture ... 
% 3.12/1.53  % [INFO] 	 Found a conjecture and 665 axioms. Running axiom selection ... 
% 3.78/1.70  % [INFO] 	 Axiom selection finished. Selected 665 axioms (removed 0 axioms). 
% 4.61/1.92  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.61/1.94  % [INFO] 	 Type checking passed. 
% 4.61/1.94  % [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 ... 
% 13.55/4.06  % External prover 'e' found a proof!
% 13.55/4.06  % [INFO] 	 Killing All external provers ... 
% 13.55/4.06  % Time passed: 3537ms (effective reasoning time: 2889ms)
% 13.55/4.06  % 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)>
% 13.55/4.07  % Axioms used in derivation (665): cls_Nil__is__map__conv_1, cls_exp_Osimps_I56_J_0, cls_sees__method__fun_1, cls_red__reds_OInitBlockThrow_0, cls_WTSeq_0, cls_val_Osplit__asm_4, cls_ty_Osplit__asm_23, cls_exp_Osimps_I92_J_0, cls_widens__Cons_2, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I184_J_0, cls_red__reds_ORedInitBlock_0, cls_ty_Osplit__asm_29, cls_option_Oinject_0, cls_map__le__upd_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_ty_Osplit__asm_12, cls_red__reds_OLAssThrow_0, cls_WTTry_0, cls_ty_Osplit_9, cls_WTrtThrow_0, cls_conf__def_2, cls_ty_Osplit__asm_30, cls_val_Osimps_I5_J_0, cls_Cons__eq__append__conv_5, cls_WTrtBlock_0, cls_redp__redsp_OCastThrow_0, cls_exp_Osimps_I213_J_0, cls_widen_Ocases_1, cls_list__all_Osimps_I2_J_1, cls_ty_Osplit_4, cls_red__reds_OFAssRed2_0, cls_ty_Osplit_24, cls_list__all2__Cons_2, cls_redp__redsp_OThrowRed_0, cls_redp__redsp_ORedCastNull_0, cls_exp_Osimps_I218_J_0, cls_remove1_Osimps_I2_J_0, cls_val_Osimps_I10_J_0, cls_list__all__append_1, cls_red__reds_OFAssRed1_0, cls_redp__redsp_OFAssRed1_0, cls_exp_Osimps_I193_J_0, cls_append__self__conv_0, cls_T_HisT_0, cls_exp_Osimps_I137_J_0, cls_ty_Ocase__cong_14, cls_ty_Ocase__cong_4, cls_exp_Osimps_I7_J_2, cls_WTrtCallNT_0, cls_ty_Ocase__cong_5, cls_blocks_Osimps_I2_J_0, cls_list__all2__eq_1, cls_ty_Osimps_I22_J_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_val_Orecs_I4_J_0, cls_map__le__trans_0, cls_fun__upd__apply_1, cls_map__upd__Some__unfold_4, cls_ty_Osplit_5, cls_ty_Osimps_I17_J_0, cls_ty_Osimps_I25_J_0, cls_redp__redsp_OThrowThrow_0, cls_list_Oinject_0, cls_exp_Osimps_I219_J_0, cls_WT__elim__cases_I1_J_4, cls_CHAINED_0, cls_exp_Osimps_I42_J_0, cls_Cons__eq__map__conv_3, cls_WTrtCond_0, cls_exp_Osimps_I15_J_1, cls_redp__redsp_OSeqRed_0, cls_WTrt__elim__cases_I10_J_0, cls_WT__elim__cases_I10_J_1, cls_ty_Ocase__cong_25, cls_exp_Osimps_I204_J_0, cls_ty_Osplit_0, cls_ty_Osplit__asm_34, cls_map__upd__Some__unfold_3, cls_ty_Osplit_11, cls_ty_Ocase__cong_28, cls_COMBK__def_0, cls_WT__elim__cases_I8_J_0, cls_val_Osimps_I4_J_0, cls_exp_Osimps_I11_J_0, cls_ty_Ocase__cong_20, cls_ty_Osplit_27, cls_not__Cons__self2_0, cls_exp_Osimps_I28_J_0, cls_WTrt__elim__cases_I5_J_1, cls_exp_Osimps_I25_J_0, cls_ty_Osimps_I5_J_0, cls_exp_Osimps_I36_J_0, cls_option_Osimps_I2_J_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_exp_Osimps_I19_J_0, cls_ty_Osimps_I8_J_0, cls_WTrt_H__WTrts_H_Ointros_I13_J_0, cls_not__refTE_0, cls_widen__Class_2, cls_ty_Ocase__cong_8, cls_ty_Osplit_32, cls_ty_Osplit__asm_28, cls_redp__redsp_OCallObj_0, cls_WTs__implies__WTrts_0, cls_val_Osimps_I14_J_0, cls_ty_Ocase__cong_18, cls_exp_Osimps_I211_J_0, cls_WTLAss_0, cls_WTCond_2, cls_wts__wts_H_0, cls_ty_Osimps_I13_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I154_J_0, cls_COMBI__def__raw_0, cls_exp_Osimps_I185_J_0, cls_eq__Nil__appendI_0, cls_self__append__conv_0, cls_exp_Osimps_I141_J_0, cls_ty_Osplit__asm_5, cls_redp__redsp_ORedCall_0, cls_ty_Osplit_21, cls_list_Osimps_I5_J_0, cls_exp_Osimps_I199_J_0, cls_WTrt__elim__cases_I6_J_0, cls_append__eq__Cons__conv_4, cls_WTrt_H__elim__cases_0, cls_WTrt__elim__cases_I10_J_1, cls_val_Osimps_I8_J_0, cls_ty_Osplit_16, cls_red__reds_OFAssThrow2_0, cls_exp_Osimps_I188_J_0, cls_ty_Osimps_I20_J_0, cls_same__append__eq_0, cls_val_Osplit__asm_3, cls_val_Orecs_I2_J_0, cls_append__Cons_0, cls_exp_Osimps_I212_J_0, cls_typeof__conf_0, cls_list__all_Osimps_I2_J_0, cls_map__le__empty_0, cls_Nil__is__map__conv_0, cls_redp__redsp_OCondThrow_0, cls_redp__redsp_ORedInitBlock_0, cls_T_H_HsubT_0, cls_redp__redsp_OCallThrowObj_0, cls_ty_Osplit_36, cls_exp_Osimps_I2_J_1, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, cls_ty_Ocase__cong_31, cls_exp_Osimps_I8_J_3, cls_length__map_0, cls_wt__blocks_2, cls_sees__method__fun_2, cls_ty_Osplit_14, cls_ty_Osplit_10, cls_append__eq__append__conv2_4, cls_exp_Osimps_I11_J_1, cls_widens__trans_0, cls_exp_Osimps_I40_J_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_2, cls_sorted_Osimps_I3_J_1, cls_WTrt_H__WTrts_H_Ointros_I9_J_0, cls_sorted__takeWhile_0, cls_WTrt__elim__cases_I6_J_3, cls_ty_Osplit__asm_17, cls_red__reds_OLAssRed_0, cls_exp_Osimps_I194_J_0, cls_ty_Osimps_I24_J_0, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_ty_Osplit__asm_9, cls_WTThrow_0, cls_exp_Osimps_I171_J_0, cls_ty_Osplit_25, cls_red__reds_OCallThrowObj_0, cls_list__all2__append2_5, cls_append1__eq__conv_1, cls_exp_Osimps_I157_J_0, cls_val_Osimps_I23_J_0, cls_val_Osimps_I25_J_0, cls_ty_Ocase__cong_13, cls_exp_Osimps_I67_J_0, cls_widen__refl_0, cls_distinct_Osimps_I2_J_1, cls_map__upd__Some__unfold_0, cls_exp_Osimps_I160_J_0, cls_list__all2__Cons_1, cls_distinct_Osimps_I1_J_0, cls_ty_Osplit__asm_26, cls_WTrt__elim__cases_I5_J_2, cls_exp_Osimps_I17_J_0, cls_confs__Cons2_3, cls_WT__elim__cases_I4_J_0, cls_val_Osimps_I27_J_0, cls_redp__redsp_OInitBlockThrow_0, cls_hext__trans_0, cls_fun__upd__other_0, cls_exp_Osimps_I84_J_0, cls_RedCall_I3_J_0, cls_takeWhile_Osimps_I1_J_0, cls_WTrt_H__WTrts_H_Ointros_I16_J_0, cls_redp__redsp_OFAccThrow_0, cls_ty_Osplit__asm_15, cls_hext__refl_0, cls_redp__redsp_OFAssRed2_0, cls_exp_Osimps_I142_J_0, cls_exp_Osimps_I24_J_0, cls_exp_Osimps_I74_J_0, cls_red__reds_OThrowThrow_0, cls_ty_Ocase__cong_29, cls_val_Osplit_0, cls_exp_Osimps_I29_J_0, cls_redp__redsp_OFAssThrow1_0, cls_distinct__remove1_0, cls_exp_Osimps_I205_J_0, cls_list_Osimps_I4_J_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_ty_Osimps_I11_J_0, cls_red__reds_OCallObj_0, cls_val_Osimps_I15_J_0, cls_ty_Osplit_12, cls_widen_Ocases_0, cls_exp_Osimps_I143_J_0, cls_ty_Osplit_6, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_conf__NT_1, cls_redp__redsp_OTryRed_0, cls_ty_Osimps_I3_J_0, cls_append__self__conv2_0, cls_WTrtFAssNT_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_typeof__h_Osimps_I2_J_0, cls_Nil__is__append__conv_0, cls_not__None__eq_1, cls_list__all__append_2, cls_append__Nil2_0, cls_widens__refl_0, cls_ty_Osimps_I9_J_0, cls_ty_Ocase__cong_26, cls_conf__widen_0, cls_exp_Osimps_I43_J_0, cls_ty_Osplit__asm_19, cls_ty_Ocase__cong_3, cls_self__append__conv2_0, cls_distinct__map_0, cls_conf__Null_0, cls_CHAINED_0_01, cls_WT__elim__cases_I5_J_2, cls_distinct__append_0, cls_map__eq__Cons__conv_3, cls_WTrtFAccNT_0, cls_self__append__conv2_1, cls_map__upds__Cons_0, cls_sees__method__fun_0, cls_WTrt__hext__mono_0, cls_WTrtFAss_0, cls_takeWhile__tail_0, cls_map__le__refl_0, cls_subs_0, cls_WTrt_H__WTrts_H_Ointros_I11_J_0, cls_redp__redsp_OBlockThrow_0, cls_typeof__h_Osimps_I4_J_0, cls_list_Osplit_0, cls_ty_Osplit__asm_18, cls_exp_Osimps_I61_J_0, cls_map__is__Nil__conv_0, cls_map__le__upds_0, cls_exp_Osimps_I180_J_0, cls_append__eq__append__conv2_5, cls_ty_Osplit_1, cls_WT__elim__cases_I6_J_0, cls_ty_Osplit__asm_33, cls_red__preserves__sconf_0, cls_map__upd__nonempty_0, cls_exp_Osimps_I77_J_0, cls_WTrt_H__WTrts_H_Ointros_I15_J_0, cls_redp__redsp_ORedTry_0, cls_ty_Osimps_I12_J_0, cls_red__reds_OTryRed_0, cls_append__is__Nil__conv_2, cls_exp_Osimps_I69_J_0, cls_ty_Osplit_13, cls_append__Nil_0, cls_widen_Ocases_3, cls_WTrt__env__mono_0, cls_exp_Osimps_I15_J_0, cls_wts_H__wts_0, cls_exp_Osimps_I183_J_0, cls_exp_Osimps_I26_J_0, cls_append__eq__Cons__conv_5, cls_red__reds_ORedBlock_0, cls_fun__upd__triv_0, cls_exp_Osimps_I12_J_2, cls_exp_Osimps_I76_J_0, cls_WTrtTry_0, cls_exp_Osimps_I8_J_2, cls_list__all2__Cons_0, cls_exp_Osimps_I177_J_0, cls_ty_Osimps_I18_J_0, cls_map__upds__Nil2_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_ty_Osimps_I15_J_0, cls_exp_Osimps_I207_J_0, cls_ty_Ocase__cong_7, cls_val_Osimps_I9_J_0, cls_exp_Osimps_I83_J_0, cls_ty_Osimps_I19_J_0, cls_exp_Osimps_I2_J_0, cls_ty_Osplit__asm_6, cls_WTrtNew_0, cls_conf__Null_1, cls_ty_Ocase__cong_17, cls_ty_Osplit_22, cls_exp_Osimps_I62_J_0, cls_ty_Osplit_33, cls_exp_Osimps_I27_J_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_RedCall_I4_J_0, cls_exp_Osimps_I159_J_0, cls_WTrt_H__WTrts_H_Ointros_I2_J_0, cls_ty_Osplit__asm_22, cls_self__append__conv_1, cls_is__refT__def_1, cls_ty_Osplit__asm_11, cls_map__eq__imp__length__eq_0, cls_ty_Osplit_35, cls_val_Osimps_I16_J_0, cls_ty_Ocase__cong_30, cls_exp_Osimps_I60_J_0, cls_list__all2__appendI_0, cls_fun__upds__append2__drop_0, cls_ty_Osimps_I7_J_0, cls_exp_Osimps_I158_J_0, cls_redp__redsp_OSeqThrow_0, cls_exp_Osimps_I162_J_0, cls_list__all2__Nil_1, cls_widens__Cons_0, cls_not__Cons__self_0, cls_ty_Orecs_I1_J_0, cls_ty_Osplit_19, cls_ty_Osplit_2, cls_map__upd__Some__unfold_1, cls_mem__def_0, cls_val_Osplit_1, cls_exp_Osimps_I7_J_1, cls_red__reds_OBlockThrow_0, cls_neq__Nil__conv_1, cls_redp__redsp_OLAssThrow_0, cls_exp_Osimps_I30_J_0, cls_list__all2__def_0, cls_exp_Osimps_I75_J_0, cls_exp_Osimps_I15_J_3, cls_ty_Osimps_I16_J_0, cls_exp_Osimps_I169_J_0, cls_map__upd__triv_0, cls_exp_Osimps_I166_J_0, cls_append__same__eq_0, cls_red__reds_OFAssThrow1_0, cls_ty_Ocase__cong_9, cls_ty_Osimps_I26_J_0, cls_exp_Osimps_I55_J_0, cls_fun__upds__append__drop_0, cls_Nil__is__append__conv_1, cls_WTrtSeq_0, cls_wtabody_0, cls_exp_Osimps_I189_J_0, cls_sorted__Cons_0, cls_exp_Osimps_I224_J_0, cls_WTrtCall_0, cls_fun__upd__twist_0, cls_typeof__h_Osimps_I1_J_0, cls_WT__elim__cases_I1_J_0, cls_ty_Osplit__asm_25, cls_ty_Osplit__asm_10, cls_exp_Osimps_I145_J_0, cls_exp_Osimps_I59_J_0, cls_Pair__eq_0, cls_ty_Osplit_29, cls_append__assoc_0, cls_red__reds_OSeqRed_0, cls_exp_Osimps_I80_J_0, cls_distinct__takeWhile_0, cls_exp_Osimps_I16_J_0, clsarity_Int__Oint__Orderings_Olinorder, cls_ty_Osplit_30, cls_ty_Ocase__cong_12, cls_ty_Osplit_7, cls_WT__elim__cases_I5_J_1, cls_exp_Osimps_I1_J_0, cls_map__upds__Nil1_0, cls_remove1_Osimps_I1_J_0, cls_the__Addr_Osimps_0, cls_not__Some__eq_1, cls_exp_Osimps_I35_J_0, cls_ty_Osplit__asm_36, cls_WTrt_H__WTrts_H_Ointros_I19_J_0, cls_exp_Osimps_I182_J_0, cls_fun__upd__apply_0, cls_WT__implies__WTrt_0, cls_wt_0, cls_ty_Oinject_0, cls_WTrt__elim__cases_I2_J_0, cls_redp__redsp_OCondRed_0, cls_exp_Osimps_I68_J_0, cls_map__le__antisym_0, cls_list__all2__Nil2_0, cls_val_Osimps_I28_J_0, cls_ty_Osplit_18, cls_exp_Osimps_I203_J_0, cls_exp_Osimps_I41_J_0, cls_exp_Osimps_I57_J_0, cls_ty_Ocase__cong_10, cls_red__reds_OCastThrow_0, cls_distinct__append_1, cls_exp_Osimps_I216_J_0, cls_map__append_0, cls_WTrt_H__WTrts_H_Ointros_I18_J_0, cls_ty_Osplit__asm_14, cls_WTCons_0, cls_ty_Osplit__asm_32, cls_WTCond_0, cls_Class__widen_0, cls_exp_Osimps_I93_J_0, cls_ty_Ocase__cong_2, cls_WTrt_H__WTrts_H_Ointros_I8_J_0, cls_ty_Orecs_I2_J_0, cls_exp_Osimps_I53_J_0, cls_sorted_Osimps_I1_J_0, cls_ty_Orecs_I3_J_0, cls_list__all2__Nil_0, cls_exp_Osimps_I50_J_0, cls_sorted__remove1_0, cls_exp_Osimps_I152_J_0, cls_red__reds_OThrowRed_0, cls_ty_Ocase__cong_22, cls_list_Osplit__asm_1, cls_val_Osimps_I17_J_0, cls_WTrtFAcc_0, cls_red__reds_OFAccRed_0, cls_WTrt_H__WTrts_H_Ointros_I3_J_0, cls_sorted__append_0, cls_conf__hext_0, cls_map__is__Nil__conv_1, cls_map__le__imp__upd__le_0, cls_widen__Class_0, cls_CHAINED_0_02, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, cls_exp_Osimps_I54_J_0, cls_takeWhile_Osimps_I2_J_1, cls_val_Osimps_I11_J_0, cls_exp_Osimps_I86_J_0, cls_wt__blocks_0, cls_exp_Osimps_I37_J_0, cls_list_Osimps_I3_J_0, cls_exp_Osimps_I8_J_1, cls_WTNew_0, cls_list__all2__Cons1_3, cls_wt_H__wt_0, cls_exp_Osimps_I66_J_0, cls_exp_Osimps_I34_J_0, cls_exp_Osimps_I6_J_0, cls_map_Osimps_I2_J_0, cls_exp_Osimps_I58_J_0, cls_ty_Orecs_I4_J_0, cls_ty_Osplit__asm_7, cls_ty_Osplit_8, cls_ty_Osplit_23, cls_exp_Osimps_I90_J_0, cls_ty_Osimps_I21_J_0, cls_ty_Osimps_I23_J_0, cls_val_Orecs_I1_J_0, cls_list__all2__append1_5, cls_val_Osimps_I2_J_0, cls_is__refT__def_2, cls_ty_Osimps_I6_J_0, cls_exp_Osimps_I155_J_0, cls_append__is__Nil__conv_1, cls_ty_Ocase__cong_16, cls_list__all2__append_0, cls_red__reds_OCondThrow_0, cls_val_Osplit_4, cls_exp_Osimps_I12_J_1, cls_ty_Osplit__asm_21, cls_ty_Osplit_34, cls_fun__upd__idem__iff_0, cls_fun__upd__idem_0, cls_redp__redsp_OFAccRed_0, cls_widens__Cons_1, cls_widen__trans_0, cls_ty_Osplit__asm_8, cls_ty_Osplit__asm_13, cls_redp__redsp_OFAssThrow2_0, cls_exp_Osimps_I82_J_0, cls_WT__elim__cases_I5_J_0, cls_WTrts__hext__mono_0, cls_exp_Osimps_I14_J_0, cls_list__all2__append_2, cls_exp_Osimps_I9_J_2, cls_Cons__eq__appendI_0, cls_exp_Osimps_I161_J_0, cls_WTrtVal_0, cls_WTrtCons_0, cls_confs__hext_0, cls_exp_Osimps_I167_J_0, cls_confs__widens_0, cls_WTrt_H__WTrts_H_Ointros_I12_J_0, cls_ty_Osplit__asm_24, cls_Cons__eq__append__conv_4, cls_exp_Osimps_I7_J_0, cls_fun__upd__same_0, cls_exp_Osimps_I151_J_0, cls_append__is__Nil__conv_0, cls_exp_Osimps_I217_J_0, cls_redp__redsp_ORedBlock_0, cls_ty_Orecs_I5_J_0, cls_exp_Osimps_I153_J_0, cls_ty_Ocase__cong_24, cls_exp_Osimps_I45_J_0, cls_exp_Osimps_I8_J_0, cls_red__reds_ORedCastNull_0, cls_WTrt_H__WTrts_H_Ointros_I21_J_0, cls_sees__method__fun_3, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_append__eq__appendI_0, cls_list__all_Osimps_I2_J_2, cls_wtes_0, cls_list_Oinject_1, cls_blocks_Osimps_I1_J_0, cls_ty_Osplit__asm_35, cls_map__upd__Some__unfold_2, cls_exp_Osimps_I44_J_0, cls_ty_Ocase__cong_0, cls_exp_Osimps_I18_J_0, cls_exp_Osimps_I192_J_0, cls_val_Osimps_I24_J_0, cls_ty_Ocase__cong_27, cls_remove1_Osimps_I2_J_1, cls_exp_Osimps_I32_J_0, cls_WTrt_H__WTrts_H_Ointros_I1_J_0, cls_exp_Osimps_I51_J_0, cls_WTrt__elim__cases_I1_J_0, cls_option_Osimps_I3_J_0, cls_red__hext__incr_0, cls_ty_Osplit_17, cls_exp_Osimps_I6_J_1, cls_list__all_Osimps_I1_J_0, cls_WTCall_0, cls_sees__method__idemp_0, cls_ty_Ocase__cong_11, cls_red__reds_OSeqThrow_0, cls_exp_Osimps_I52_J_0, cls_list_Osplit_1, cls_exp_Osimps_I31_J_0, cls_length__vs_0, cls_WTrt__elim__cases_I8_J_0, cls_WTrtCond_1, cls_exp_Osimps_I187_J_0, cls_list__all2__eq_0, cls_RedCall_I5_J_0, cls_WT__elim__cases_I10_J_0, cls_ty_Osplit_28, cls_hp_0, cls_red__reds_OFAccThrow_0, cls_exp_Osimps_I10_J_0, cls_ty_Osimps_I2_J_0, cls_Nil__is__append__conv_2, cls_red__reds_OCastRed_0, cls_ty_Ocase__cong_15, cls_ty_Osplit__asm_20, cls_exp_Osimps_I15_J_2, cls_val_Orecs_I5_J_0, cls_ty_Ocase__cong_6, cls_red__reds_ORedCall_0, cls_wt__env__mono_0, cls_sorted_Osimps_I2_J_0, cls_WTrt__elim__cases_I5_J_0, cls_method_0, cls_takeWhile_Osimps_I2_J_0, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I168_J_0, cls_ty_Osplit_26, cls_sorted__append_1, cls_exp_Osimps_I181_J_0, cls_ty_Osimps_I14_J_0, cls_ty_Osimps_I10_J_0, cls_elem_0, cls_ty_Osplit__asm_4, cls_wt__wt_H_0, cls_exp_Osimps_I196_J_0, cls_WT__elim__cases_I2_J_0, cls_WTrtCond_2, cls_exp_Osimps_I63_J_0, cls_WTrt_H__WTrts_H_Ointros_I22_J_0, cls_ty_Osimps_I4_J_0, cls_red__reds_OCondRed_0, cls_sees__method__is__class_0, cls_ty_Ocase__cong_1, cls_redp__redsp_OLAssRed_0, cls_exp_Osimps_I140_J_0, cls_exp_Osimps_I87_J_0, cls_WTrtLAss_0, cls_ty_Osplit__asm_27, cls_ty_Osplit_31, cls_conf__NT_0, cls_ty_Ocase__cong_19, cls_ty_Osplit_15, cls_fun__upd__upd_0, cls_COMBI__def_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_1, cls_exp_Osimps_I78_J_0, cls_widens__Cons_3, cls_Pair__eq_1, cls_exp_Osimps_I33_J_0, cls_exp_Osimps_I173_J_0, cls_list_Osimps_I2_J_0, cls_WTrtCast_0, cls_upd__None__map__le_0, cls_insert_0, cls_hext__typeof__mono_0, cls_exp_Osimps_I198_J_0, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_exp_Osimps_I202_J_0, cls_val_Osplit_3, cls_exp_Osimps_I12_J_0, cls_redp__redsp_OCastRed_0, cls_exp_Osimps_I163_J_0, cls_red__reds_ORedSeq_0, cls_val_Osimps_I22_J_0, cls_exp_Osimps_I147_J_0, cls_WTrt_H__WTrts_H_Ointros_I10_J_0, cls_exp_Osimps_I3_J_0, cls_ty_Osplit_3, cls_ty_Osplit__asm_31, cls_redp__redsp_ORedSeq_0, cls_WTrt__elim__cases_I8_J_1, cls_ty_Osplit_20, cls_list__all2__append_1, cls_widen_Ocases_2, cls_list__all__append_0, cls_ty_Osplit__asm_16, cls_red__reds_ORedTry_0, cls_ty_Ocase__cong_21, cls_exp_Osimps_I197_J_0, cls_WT__elim__cases_I6_J_2, cls_WTCond_1, cls_fun__upd__idem__iff_1, cls_ty_Ocase__cong_23, cls_length__pns_0
% 13.55/4.07  % No. of inferences in proof: 1333
% 13.55/4.07  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3537 ms resp. 2889 ms w/o parsing
% 14.60/4.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.60/4.36  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------