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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV939-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:01:04 AM UTC 2026

% Result   : Unsatisfiable 20.32s 6.04s
% Output   : Refutation 22.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  666
% Syntax   : Number of formulae    : 1333 ( 615 unt;   0 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  :    0 (   0   >;   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_decl,type,
    hBOOL: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Type_Osko__Type__Xty__Xcase__cong__1__1_decl,type,
    c_Type_Osko__Type__Xty__Xcase__cong__1__1: $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_sko__Type__Xty__Xsplit__asm__1_decl,type,
    v_sko__Type__Xty__Xsplit__asm__1: $i > $i > $i > $i ).

thf(v_sko__Type__Xty__Xsplit__1_decl,type,
    v_sko__Type__Xty__Xsplit__1: $i > $i > $i > $i ).

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

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

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

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

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

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

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

thf(v_sko__TypeRel__Xwiden__Xcases__2_decl,type,
    v_sko__TypeRel__Xwiden__Xcases__2: $i > $i > $i > $i ).

thf(v_sko__TypeRel__Xwiden__Xcases__1_decl,type,
    v_sko__TypeRel__Xwiden__Xcases__1: $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

thf(v_sko__TypeSafe__Mirabelle__Xwt__blocks__1_decl,type,
    v_sko__TypeSafe__Mirabelle__Xwt__blocks__1: $i > $i > $i > $i > $i ).

thf(c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1_decl,type,
    c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1: $i > $i > $i > $i > $i ).

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

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

thf(c_TypeRel_Osko__TypeRel__XClass__widen__1__1_decl,type,
    c_TypeRel_Osko__TypeRel__XClass__widen__1__1: $i > $i ).

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

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

thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2_decl,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_decl,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_decl,type,
    v_sko__TypeRel__Xwiden__Xcases__3: $i > $i ).

thf(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1_decl,type,
    c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1: $i > $i > $i > $i > $i > $i ).

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

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

thf(78,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).

thf(892,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

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

thf(1665,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

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_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_8) ).

thf(1337,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_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

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

thf(2094,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

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

thf(1190,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

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

thf(1454,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( I @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(312,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__trans_0) ).

thf(1559,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

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

thf(1729,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(1840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

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

thf(1850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

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

thf(941,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

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

thf(777,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

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

thf(1554,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

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

thf(2250,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(170,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(1168,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(623,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).

thf(2295,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

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

thf(760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(644,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(2341,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(2072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(402,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( E @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( F @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtTry_0) ).

thf(1767,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( E @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( F @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(495,axiom,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( A @ c_Value_Oval_OAddr ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I16_J_0) ).

thf(1995,plain,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( A @ c_Value_Oval_OAddr ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(609,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_35) ).

thf(2263,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

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

thf(1083,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

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

thf(1982,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(394,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).

thf(1750,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(1211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

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

thf(1158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
       != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

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

thf(1596,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

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

thf(1882,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_ONT @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

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] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCall_0) ).

thf(1522,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] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(248,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).

thf(1401,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

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

thf(2014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_List_OListMem ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OListMem ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(72,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != ( D @ tc_Option_Ooption @ ( E @ ( D @ ( G @ c_Option_Ooption_OSome ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).

thf(873,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != ( D @ tc_Option_Ooption @ ( E @ ( D @ ( G @ c_Option_Ooption_OSome ) @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(206,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

thf(1269,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(660,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(2380,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

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

thf(1971,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( E @ c_Expr_Oexp_OSeq ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

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

thf(1692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(217,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).

thf(1305,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

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

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(68,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).

thf(861,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(653,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_31) ).

thf(2363,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(438,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_3) ).

thf(1855,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(181,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).

thf(1200,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(529,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_21) ).

thf(2077,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(594,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

thf(2231,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(137,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).

thf(1068,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(256,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).

thf(1422,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

thf(1939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(616,axiom,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_D____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_body____ @ ( v_pns____ @ c_Pair ) ) ) @ ( v_T____ @ ( v_Ts____ @ ( v_M____ @ ( v_C____ @ ( v_P @ c_TypeRel_OMethod ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_method_0) ).

thf(2282,plain,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_D____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_body____ @ ( v_pns____ @ c_Pair ) ) ) @ ( v_T____ @ ( v_Ts____ @ ( v_M____ @ ( v_C____ @ ( v_P @ c_TypeRel_OMethod ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

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

thf(1591,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(141,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrts__hext__mono_0) ).

thf(1078,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

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_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_20) ).

thf(1671,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_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

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

thf(1608,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

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

thf(2035,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

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

thf(2141,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

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

thf(1872,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(192,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).

thf(1233,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

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

thf(814,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

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(1260,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

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

thf(1919,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

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

thf(1640,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

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

thf(1497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( E @ ( A @ c_Option_Ooption_OSome ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( E @ ( B @ c_Option_Ooption_OSome ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(579,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(2195,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(376,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).

thf(1705,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
        = ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(136,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(1063,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(1954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

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

thf(1507,plain,
    ! [A: $i] :
      ( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( A @ ( tc_Value_Oval @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_Type_Oty @ c_List_Olist_ONil @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ c_List_Olist_ONil @ c_Pair ) ) ) @ c_SmallStep_Oblocks )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(187,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).

thf(1222,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(652,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F
        = ( G @ ( H @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( H @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_30) ).

thf(2360,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F
        = ( G @ ( H @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( H @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(392,axiom,
    v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( v_vs____ @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wtes_0) ).

thf(1746,plain,
    v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( v_vs____ @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrts ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(647,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).

thf(2348,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

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

thf(2046,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

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

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( c_Value_Oval_ONull @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(16,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

thf(709,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(841,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

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

thf(1613,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( F @ ( D @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
      | ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_WellType_OWTs ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

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

thf(1475,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( I @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( I @ ( H @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

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

thf(1703,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( B @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

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

thf(1482,plain,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(452,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

thf(1887,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(38,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).

thf(782,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

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

thf(1441,plain,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(107,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

thf(973,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

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

thf(885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

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

thf(2173,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(235,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_ONull @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I25_J_0) ).

thf(1366,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_ONull @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

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

thf(2067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( t_a @ ( C @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B
        = ( A @ ( B @ ( C @ v_sko__TypeRel__Xwiden__Xcases__1 ) ) @ c_Type_Oty_OClass ) )
      | ( A
        = ( A @ v_sko__TypeRel__Xwiden__Xcases__3 @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

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

thf(1529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).

thf(1055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

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

thf(1985,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OBoolean @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

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

thf(1760,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Value_Oval_ONull @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

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] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_9) ).

thf(719,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

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

thf(2269,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(445,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

thf(1871,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(46,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

thf(802,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

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(1191,plain,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

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

thf(2126,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( B @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ c_Expr_Oexp_OBlock ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

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

thf(949,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

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

thf(2339,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

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

thf(785,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

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

thf(1860,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

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] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I12_J_0) ).

thf(2217,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] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( M @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( L @ ( K @ c_Pair ) ) ) @ ( G @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

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

thf(1511,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(13,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

thf(702,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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

thf(2185,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( A @ ( E @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ ( E @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

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

thf(1577,plain,
    ( ( v_a____ @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ c_State_Ohp @ hAPP ) )
    = ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_fs____ @ ( v_C____ @ c_Pair ) ) ) @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(1545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

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(853,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(164,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).

thf(1147,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(517,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_4) ).

thf(2049,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

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

thf(2373,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OInteger ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

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

thf(1875,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OVoid ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

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

thf(1922,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( E @ ( D @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( B @ ( E @ ( A @ ( D @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

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

thf(902,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] :
      ( ~ ( I @ ( L @ ( K @ ( J @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( I @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

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

thf(2169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

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

thf(1514,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(222,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

thf(1319,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

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

thf(870,plain,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OIntg )
     != c_Value_Oval_OUnit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

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

thf(1931,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I4_J_0) ).

thf(1568,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

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

thf(2301,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Value_Oval_OAddr )
     != ( B @ c_Value_Oval_OIntg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( c_Type_Othis @ c_Expr_Oexp_OLAss ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I1_J_4) ).

thf(1815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( c_Type_Othis @ c_Expr_Oexp_OLAss ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(590,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

thf(2222,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

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

thf(924,plain,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OIntg )
     != c_Value_Oval_ONull ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(216,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

thf(1302,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(540,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OLAssRed_0) ).

thf(2105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(534,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(2090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

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

thf(1373,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Value_Oval_OIntg )
       != ( B @ c_Value_Oval_OIntg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

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

thf(1418,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).

thf(937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(966,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(53,axiom,
    c_Type_Oty_ONT @ c_Type_Ois__refT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__refT__def_1) ).

thf(821,plain,
    c_Type_Oty_ONT @ c_Type_Ois__refT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).

thf(905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

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

thf(1946,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

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

thf(1465,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

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

thf(1714,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

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

thf(2027,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

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

thf(1040,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

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

thf(1109,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

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

thf(1682,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(160,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_OUnit @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I24_J_0) ).

thf(1136,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_OUnit @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

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

thf(2291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

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] :
      ( ~ ( I @ ( L @ ( B @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_2) ).

thf(1020,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] :
      ( ~ ( I @ ( L @ ( B @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

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

thf(2254,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

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

thf(1843,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( I @ ( H @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( G @ c_Option_Ooption_OSome ) @ ( F @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ ( D @ c_Progress_OWTrt_H ) ) ) ) )
      | ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( F @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) @ ( E @ ( A @ ( D @ c_Progress_OWTrt_H ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

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

thf(2190,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

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

thf(1796,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Oty_OClass )
       != ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(554,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).

thf(2137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(498,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_13) ).

thf(2002,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

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

thf(1600,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

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

thf(1104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

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

thf(2154,plain,
    ! [B: $i,A: $i] :
      ( ( B @ c_Value_Oval_OIntg @ ( A @ c_Objects_Otypeof__h ) )
      = ( tc_Type_Oty @ ( c_Type_Oty_OInteger @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

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

thf(2205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( C @ ( B @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtNew_0) ).

thf(1696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(340,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I2_J_0) ).

thf(1622,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(35,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).

thf(774,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(656,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I8_J_0) ).

thf(2371,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

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

thf(2242,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Value_Oval_OAddr @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__rec ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

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

thf(988,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

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

thf(2286,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( E @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

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

thf(1863,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

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

thf(1651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

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

thf(1074,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

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

thf(2011,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(582,axiom,
    v_T____ @ ( v_T_H_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(2204,plain,
    v_T____ @ ( v_T_H_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(5,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    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] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

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

thf(1691,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(43,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

thf(793,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(566,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
        = ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).

thf(2164,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
        = ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

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

thf(2118,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( A @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( F @ ( E @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( H @ ( G @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( C @ ( F @ c_Map_Omap__upds ) ) ) ) @ ( E @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
       != ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
      | ( ( tc_Value_Oval @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

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

thf(810,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( A @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(219,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

thf(1311,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(531,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(2083,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

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

thf(1163,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( F @ c_Map_Omap__upds ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

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

thf(1470,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(463,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).

thf(1915,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

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

thf(1708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).

thf(714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

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

thf(1868,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( c_Value_Oval_ONull @ ( B @ ( D @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(522,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_27) ).

thf(2061,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

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

thf(2000,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(603,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OThrowThrow_0) ).

thf(2249,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

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

thf(1255,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(559,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( F @ ( E @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(2147,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( F @ ( E @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

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

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).

thf(1238,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

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

thf(1900,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

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

thf(1723,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] :
      ( ( J @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( H @ ( tc_Value_Oval @ ( C @ ( K @ c_Value_Oval_OAddr @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( A @ ( I @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( J @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( F @ ( K @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OCall ) ) ) @ ( D @ c_SmallStep_Oredp ) ) ) ) )
      | ( ( K @ ( J @ c_State_Ohp @ hAPP ) )
       != ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ ( L @ ( E @ c_Pair ) ) ) @ c_Option_Ooption_OSome ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( H @ ( B @ c_Pair ) ) ) @ ( G @ ( A @ ( F @ ( E @ ( D @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( ( tc_Value_Oval @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
       != ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
      | ( ( tc_Type_Oty @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(55,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).

thf(825,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(1343,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(130,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).

thf(1042,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

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

thf(952,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
     != ( E @ ( D @ tc_Option_Ooption @ ( D @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(232,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).

thf(1355,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

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

thf(2277,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( F @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( E @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

thf(1174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

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

thf(1676,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(425,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_23) ).

thf(1824,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

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
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( E @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_2) ).

thf(788,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( E @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

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

thf(1619,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

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

thf(2150,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(552,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( A @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( B @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( tc_Type_Oty @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_0) ).

thf(2132,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( A @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( B @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( tc_Type_Oty @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( E @ ( A @ ( D @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(22,axiom,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( A @ c_Value_Oval_OIntg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I14_J_0) ).

thf(729,plain,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( A @ c_Value_Oval_OIntg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(63,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

thf(847,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(127,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

thf(1032,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(640,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I15_J_0) ).

thf(2332,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(1888,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

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

thf(1457,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

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

thf(1624,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( I @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

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

thf(1836,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( G @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(354,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

thf(1656,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

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

thf(2213,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( F @ c_Expr_Oexp_OFAcc ) ) ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

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

thf(1291,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

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

thf(1910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

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

thf(1573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(120,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_ONull @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__rec ) ) ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Orecs_I2_J_0) ).

thf(1012,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_ONull @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__rec ) ) ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(150,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

thf(1106,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

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

thf(1968,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ ( D @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = c_Type_Othis )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OLAss ) ) @ ( A @ ( D @ c_WellType_OWT ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(74,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).

thf(879,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

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

thf(2200,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OBoolean @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

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] :
      ( ~ ( I @ ( B @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__method__fun_3) ).

thf(830,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] :
      ( ~ ( I @ ( B @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

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

thf(757,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

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

thf(2345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(585,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Value_Oval_OAddr @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit_4) ).

thf(2211,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Value_Oval_OAddr @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).

thf(1407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

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

thf(1634,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(593,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( C @ ( B @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I18_J_0) ).

thf(2228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( C @ ( B @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(472,axiom,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).

thf(1936,plain,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

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

thf(2115,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( A @ ( D @ ( C @ ( B @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = c_Value_Oval_ONull ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

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

thf(2377,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(416,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCallNT_0) ).

thf(1804,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(257,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

thf(1425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

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

thf(1878,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( H @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(396,axiom,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1755,plain,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(626,axiom,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RedCall_I5_J_0) ).

thf(2300,plain,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

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

thf(1762,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( A @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( G @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( E @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( F @ ( E @ ( B @ ( D @ c_State_Ohp @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( D @ ( B @ ( A @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ( C @ ( B @ ( A @ c_TypeSafe__Mirabelle_Osconf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(2100,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

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

thf(1534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( t_a @ ( C @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = A )
      | ( B
        = ( B @ ( A @ ( C @ v_sko__TypeRel__Xwiden__Xcases__2 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

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

thf(1794,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( E @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(122,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).

thf(1017,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(152,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I29_J_0) ).

thf(1111,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(1227,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( t_a @ ( B @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = A )
      | ( A
        = ( C @ ( A @ ( B @ v_sko__TypeRel__Xwiden__Xcases__1 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen_Ocases_0) ).

thf(1540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( t_a @ ( B @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = A )
      | ( A
        = ( C @ ( A @ ( B @ v_sko__TypeRel__Xwiden__Xcases__1 ) ) @ c_Type_Oty_OClass ) )
      | ( A = c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

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(1006,plain,
    c_Value_Oval_ONull != c_Value_Oval_OUnit,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

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

thf(1138,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

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

thf(1719,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

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

thf(1567,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(224,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I205_J_0) ).

thf(1329,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(234,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

thf(1361,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

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

thf(2323,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(390,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(1739,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

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_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    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_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(2312,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(530,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_16) ).

thf(2080,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(411,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).

thf(1791,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

thf(1214,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

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

thf(1644,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( E @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

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

thf(1419,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

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

thf(1942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( t_a @ ( B @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = C )
      | ( A
        = ( A @ ( C @ ( B @ v_sko__TypeRel__Xwiden__Xcases__2 ) ) @ c_Type_Oty_OClass ) )
      | ( A
        = ( A @ v_sko__TypeRel__Xwiden__Xcases__3 @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

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

thf(1659,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OInteger @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(686,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(140,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).

thf(1075,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

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

thf(2108,plain,
    ! [A: $i] :
      ( c_Type_Oty_OInteger
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

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

thf(2038,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OBoolean @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(166,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).

thf(1155,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(391,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(1744,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

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

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

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

thf(1530,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

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

thf(1668,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

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

thf(2355,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Value_Oval_OAddr @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(133,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(1050,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

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

thf(911,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(437,axiom,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( A @ c_Value_Oval_OAddr ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I10_J_0) ).

thf(1852,plain,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( A @ c_Value_Oval_OAddr ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

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

thf(1429,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(490,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_12) ).

thf(1979,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

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

thf(2272,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

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

thf(1393,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

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

thf(1627,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(223,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

thf(1324,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

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

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(204,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).

thf(1263,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

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

thf(997,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).

thf(1588,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(111,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).

thf(985,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

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

thf(1150,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Option_Ooption_OSome ) )
       != ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

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

thf(1478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

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

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(628,axiom,
    v_T_H____ @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( v_vs____ @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( v_M____ @ ( v_a____ @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OCall ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).

thf(2304,plain,
    v_T_H____ @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( v_vs____ @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( v_M____ @ ( v_a____ @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OCall ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

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(1266,plain,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

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

thf(1831,plain,
    ! [A: $i] :
      ( c_Type_Oty_OBoolean
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

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

thf(1231,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(144,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I3_J_0) ).

thf(1086,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(195,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).

thf(1241,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(584,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_0) ).

thf(2208,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

thf(921,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(314,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

thf(1563,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

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

thf(1071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(358,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I1_J_0) ).

thf(1663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

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(1026,plain,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(175,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).

thf(1185,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

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

thf(1732,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(261,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

thf(1434,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(439,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_25) ).

thf(1857,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

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

thf(1712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

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

thf(1846,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(2057,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(32,axiom,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( A @ c_Value_Oval_OIntg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I8_J_0) ).

thf(765,plain,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( A @ c_Value_Oval_OIntg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

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

thf(1648,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(400,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

thf(1764,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(664,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_28) ).

thf(2391,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

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

thf(1219,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] :
      ( ( F = c_Type_Oty_OVoid )
      | ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( L @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( L @ ( K @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

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

thf(1747,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Type_Oty_OClass @ ( C @ ( B @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( A @ c_TypeRel_Osko__TypeRel__XClass__widen__1__1 @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).

thf(856,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

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

thf(2376,plain,
    v_T_H_H____ @ ( v_body____ @ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_Type_Oty @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__upds ) ) ) ) @ ( v_P @ c_WellType_OWT ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

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

thf(1631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(608,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).

thf(2260,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

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

thf(2121,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(597,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_20) ).

thf(2235,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

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

thf(1698,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_OListMem ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

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

thf(1959,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( F @ ( A @ hAPP ) )
        = ( D @ ( G @ c_Option_Ooption_OSome ) ) )
      | ( ( F @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( D @ ( G @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(613,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_confs__hext_0) ).

thf(2275,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(510,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(2033,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(308,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_31) ).

thf(1548,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

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

thf(1927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(52,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I1_J_0) ).

thf(819,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(1916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
       != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

thf(1125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
       != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(576,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).

thf(2188,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

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

thf(1752,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(503,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).

thf(2016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(243,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I23_J_0) ).

thf(1388,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(101,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).

thf(958,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(484,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
        = ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__def_0) ).

thf(1965,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
        = ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(1520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

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

thf(1488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

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

thf(732,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

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] :
      ( ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( J @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( H @ ( tc_Value_Oval @ ( C @ ( K @ c_Value_Oval_OAddr @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( A @ ( I @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( J @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( F @ ( K @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( K @ ( J @ c_State_Ohp @ hAPP ) )
       != ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ ( L @ ( E @ c_Pair ) ) ) @ c_Option_Ooption_OSome ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( H @ ( B @ c_Pair ) ) ) @ ( G @ ( A @ ( F @ ( E @ ( D @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( ( tc_Value_Oval @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
       != ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
      | ( ( tc_Type_Oty @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_ORedCall_0) ).

thf(1884,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] :
      ( ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( J @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( H @ ( tc_Value_Oval @ ( C @ ( K @ c_Value_Oval_OAddr @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( A @ ( I @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( J @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ c_List_Omap ) ) ) @ ( F @ ( K @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OCall ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( ( K @ ( J @ c_State_Ohp @ hAPP ) )
       != ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ ( L @ ( E @ c_Pair ) ) ) @ c_Option_Ooption_OSome ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( H @ ( B @ c_Pair ) ) ) @ ( G @ ( A @ ( F @ ( E @ ( D @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( ( tc_Value_Oval @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
       != ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
      | ( ( tc_Type_Oty @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(337,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( E @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( F @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I22_J_0) ).

thf(1615,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( E @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( F @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( I @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

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

thf(1784,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(258,axiom,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(1428,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(289,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_8) ).

thf(1503,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(637,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_6) ).

thf(2326,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(622,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtThrow_0) ).

thf(2293,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(40,axiom,
    tc_Int_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

thf(787,plain,
    tc_Int_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(442,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(1865,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(135,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

thf(1058,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(225,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

thf(1332,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(401,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

thf(1765,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

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

thf(2319,plain,
    v_T____ @ ( v_T_H_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(3,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    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] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

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

thf(2193,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(410,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Value_Oval_OAddr )
       != ( B @ c_Value_Oval_OAddr ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).

thf(1786,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Value_Oval_OAddr )
       != ( B @ c_Value_Oval_OAddr ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(630,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(2308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).

thf(1371,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(456,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( J @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( J @ ( I @ ( H @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_24) ).

thf(1897,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( J @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( J @ ( I @ ( H @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).

thf(919,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = ( B @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(109,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).

thf(979,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

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] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_5) ).

thf(1194,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

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

thf(2311,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( C @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( c_Value_Oval_ONull @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( c_Value_Oval_ONull @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( A @ c_Expr_Oexp_OCast ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(80,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).

thf(900,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(6,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    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] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(2383,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(455,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_24) ).

thf(1894,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(154,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).

thf(1117,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(417,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_23) ).

thf(1806,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

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_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_12) ).

thf(1524,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_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

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

thf(1048,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( H @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( G @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_2) ).

thf(1801,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(156,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).

thf(1122,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

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(1349,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

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

thf(2097,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(607,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(2257,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(113,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(990,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(285,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_30) ).

thf(1492,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1603,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(625,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_Expr_Oexp_OBlock ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OBlockThrow_0) ).

thf(2299,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_Expr_Oexp_OBlock ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

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

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

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

thf(1144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(404,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_26) ).

thf(1771,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

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

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

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

thf(1571,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( G @ ( E @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Value_Oval @ ( tc_Type_Oty @ ( G @ ( F @ c_List_Olist_OCons ) ) @ ( tc_Value_Oval @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

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

thf(1439,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(49,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

thf(811,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(51,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I30_J_0) ).

thf(816,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(543,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( B @ ( E @ ( D @ ( C @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_1) ).

thf(2111,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( B @ ( E @ ( D @ ( C @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(45,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).

thf(799,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

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

thf(1838,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = ( G @ ( D @ ( F @ ( C @ ( G @ tc_Option_Ooption @ ( D @ ( G @ ( E @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__upds ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(126,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

thf(1029,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

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

thf(1460,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(423,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( C @ ( D @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( E @ ( C @ ( D @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__Cons_2) ).

thf(1820,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( tc_Type_Oty @ ( C @ ( D @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( E @ ( C @ ( D @ ( A @ c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 ) ) ) ) @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

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

thf(1688,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

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

thf(890,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

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

thf(2180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(507,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_0) ).

thf(2025,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(142,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

thf(1080,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(67,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).

thf(858,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

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

thf(1557,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Value_Oval_OIntg @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = ( F @ ( D @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(633,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(2314,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(645,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).

thf(2343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(173,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

thf(1177,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

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

thf(1381,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
      | ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

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

thf(2329,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(91,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).

thf(932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(479,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_36) ).

thf(1952,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(171,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

thf(1171,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

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

thf(1396,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

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

thf(2350,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(569,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I11_J_0) ).

thf(2171,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(33,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

thf(768,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(266,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).

thf(1445,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(532,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).

thf(2086,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

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

thf(780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

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

thf(2139,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( tc_Value_Oval @ ( F @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks )
      = ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( F @ c_Pair ) ) ) @ ( D @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( A @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(619,axiom,
    ( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__vs_0) ).

thf(2288,plain,
    ( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(506,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_16) ).

thf(2022,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( C @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I19_J_0) ).

thf(2156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( C @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

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

thf(1973,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(328,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

thf(1594,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
        = ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).

thf(1699,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
        = ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

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

thf(2051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( E @ ( D @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

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(1245,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

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

thf(2064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( c_Type_Oty_ONT @ ( C @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( c_Value_Oval_ONull @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

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

thf(2369,plain,
    ( ( tc_Value_Oval @ tc_List_Olist @ ( v_vs____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(601,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_9) ).

thf(2244,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

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

thf(1000,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(1726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

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

thf(1250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I40_J_0) ).

thf(675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(418,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_29) ).

thf(1809,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(541,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCallThrowObj_0) ).

thf(2107,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

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

thf(944,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(459,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).

thf(1905,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

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

thf(927,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(292,axiom,
    ( ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RedCall_I4_J_0) ).

thf(1509,plain,
    ( ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(27,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).

thf(749,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(227,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).

thf(1340,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(105,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

thf(968,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(499,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( F @ ( E @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(2005,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( F @ ( E @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(252,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

thf(1413,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(519,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ tc_Option_Ooption @ ( G @ ( D @ ( F @ c_Option_Ooption_OSome ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome ) ) )
      | ( B = E )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).

thf(2054,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ tc_Option_Ooption @ ( G @ ( D @ ( F @ c_Option_Ooption_OSome ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome ) ) )
      | ( B = E )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

thf(722,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(182,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).

thf(1203,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(183,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

thf(1208,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

thf(1277,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(548,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

thf(2124,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(596,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAccThrow_0) ).

thf(2234,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAcc ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(494,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(1990,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(581,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).

thf(2202,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
      = ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

thf(836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

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

thf(1551,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(117,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).

thf(1003,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

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

thf(2397,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

thf(971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

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

thf(1605,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

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

thf(1252,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Ois__refT )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

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

thf(1780,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

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

thf(2386,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(1098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(9,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

thf(690,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(330,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Value_Oval_OAddr @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I28_J_0) ).

thf(1598,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Value_Oval_OAddr @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__case ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

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

thf(705,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(335,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__widen_0) ).

thf(1611,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

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

thf(1225,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

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

thf(707,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( C @ ( F @ c_Option_Ooption_OSome ) @ ( B @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(236,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).

thf(1368,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(571,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Decl_Ois__class ) ) )
      | ( C @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Onew ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTNew_0) ).

thf(2175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Decl_Ois__class ) ) )
      | ( C @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Onew ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).

thf(2092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).

thf(791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(176,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(1188,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(642,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAssNT_0) ).

thf(2337,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(589,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_1) ).

thf(2219,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

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

thf(1317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(355,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( B @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ c_Expr_Oexp_OBlock ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OInitBlockThrow_0) ).

thf(1658,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( B @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ c_Expr_Oexp_OBlock ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ c_Objects_Otypeof__h ) )
        = ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) )
      | ~ ( D @ ( A @ c_Objects_Ohext ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__typeof__mono_0) ).

thf(1679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ c_Objects_Otypeof__h ) )
        = ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) )
      | ~ ( D @ ( A @ c_Objects_Ohext ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(515,axiom,
    ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__pns_0) ).

thf(2044,plain,
    ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( v_pns____ @ c_Nat_Osize__class_Osize ) )
    = ( tc_Type_Oty @ tc_List_Olist @ ( v_Ts____ @ c_Nat_Osize__class_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

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(1285,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OBoolean ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I15_J_0) ).

thf(1987,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OBoolean ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(591,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( G @ ( F @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( D @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( E @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTTry_0) ).

thf(2224,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( G @ ( F @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( D @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( E @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

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

thf(1813,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( D @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( tc_Type_Oty @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( tc_Type_Oty @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(269,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_1) ).

thf(1452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(346,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).

thf(1637,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
        = ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(158,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

thf(1130,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(323,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).

thf(1579,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

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

thf(1934,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Value_Oval_OIntg @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(26,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

thf(744,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

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

thf(1543,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OUnit @ ( A @ c_Objects_Otypeof__h ) )
      = ( tc_Type_Oty @ ( c_Type_Oty_OVoid @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(202,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).

thf(1257,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

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

thf(2113,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(162,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).

thf(1141,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( C @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

thf(1702,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( C @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(69,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I50_J_0) ).

thf(864,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

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

thf(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
      = ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OAddr )
     != c_Value_Oval_ONull ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I17_J_0) ).

thf(1585,plain,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OAddr )
     != c_Value_Oval_ONull ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(1617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(249,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

thf(1404,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(233,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

thf(1358,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

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

thf(2247,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_ONull @ ( A @ c_Objects_Otypeof__h ) )
      = ( tc_Type_Oty @ ( c_Type_Oty_ONT @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

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

thf(1802,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

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

thf(1023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( D @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

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

thf(2279,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

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

thf(2357,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

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

thf(2145,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( E @ c_Option_Ooption_OSome ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( D @ ( C @ c_Expr_Oexp_OVal @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

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

thf(2320,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

thf(1506,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( E @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(381,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(1717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(509,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(2030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

thf(1881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(207,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

thf(1272,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

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

thf(2266,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(73,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I36_J_0) ).

thf(876,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(474,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I18_J_0) ).

thf(1940,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

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

thf(1421,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

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

thf(2088,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] :
      ( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( L @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( K @ ( J @ c_Pair ) ) ) @ ( F @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( G @ ( E @ ( B @ ( A @ c_WellType_OWTs ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( H @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(174,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

thf(1180,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(366,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( A @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( F @ ( E @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( A @ ( E @ ( B @ ( D @ v_sko__TypeSafe__Mirabelle__Xwt__blocks__1 ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
       != ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
      | ( ( tc_Value_Oval @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__blocks_2) ).

thf(1685,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( G @ ( A @ c_Pair ) ) ) @ ( B @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( F @ ( E @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( B @ ( A @ ( E @ ( B @ ( D @ v_sko__TypeSafe__Mirabelle__Xwt__blocks__1 ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) )
       != ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) )
      | ( ( tc_Value_Oval @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( tc_Type_Oty @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

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

thf(1949,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( E @ ( A @ ( D @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    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] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_13) ).

thf(1817,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OAddr )
     != c_Value_Oval_OUnit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osimps_I11_J_0) ).

thf(1781,plain,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OAddr )
     != c_Value_Oval_OUnit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(267,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_Progress_OWTrt_H ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__elim__cases_0) ).

thf(1448,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) @ ( D @ ( C @ ( B @ c_Progress_OWTrt_H ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(496,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_1) ).

thf(1998,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

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

thf(1834,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

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

thf(1913,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

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

thf(976,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

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

thf(688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
      | ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

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

thf(2215,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( H @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 ) ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(295,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_28) ).

thf(1517,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

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

thf(1390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

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

thf(2305,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(320,axiom,
    ! [A: $i] : ( A @ c_Type_Oty_OClass @ c_Type_Ois__refT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__refT__def_2) ).

thf(1575,plain,
    ! [A: $i] : ( A @ c_Type_Oty_OClass @ c_Type_Ois__refT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(62,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).

thf(844,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

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

thf(2226,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(388,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_24) ).

thf(1734,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(34,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

thf(771,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(350,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OVoid @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_0) ).

thf(1646,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OVoid @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(12,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

thf(699,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(362,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = ( D @ ( C @ c_Option_Ooption_OSome ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).

thf(1674,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = ( D @ ( C @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(343,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_36) ).

thf(1629,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(551,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

thf(2130,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( D @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

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

thf(2152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

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

thf(2394,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(102,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wts_H__wts_0) ).

thf(961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

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

thf(1385,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(103,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

thf(963,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

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

thf(2167,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( D @ ( E @ ( H @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( F @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( E @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(617,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( E @ ( A @ ( D @ c_Progress_OWTrt_H ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I3_J_0) ).

thf(2283,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( E @ ( A @ ( D @ c_Progress_OWTrt_H ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(663,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OTryRed_0) ).

thf(2389,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

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

thf(2290,plain,
    tc_Type_Oty @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_Ts_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

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

thf(2251,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

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

thf(1903,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

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

thf(2135,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(97,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).

thf(946,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(148,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).

thf(1101,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).

thf(1244,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

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

thf(1822,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(284,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).

thf(1491,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Value_Oval_OAddr @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_Othrow ) @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(85,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).

thf(914,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(514,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_1) ).

thf(2041,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

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

thf(1777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

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

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

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

thf(2066,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(565,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

thf(2162,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

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

thf(2183,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

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

thf(763,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Value_Oval_OUnit @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__rec ) ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(357,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_1) ).

thf(1661,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(265,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).

thf(1442,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

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(1045,plain,
    c_Type_Oty_OInteger != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(18,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

thf(716,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_body____ @ ( tc_Value_Oval @ ( v_vs____ @ ( v_a____ @ c_Value_Oval_OAddr @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( v_T_H____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(667,plain,
    ! [A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_body____ @ ( tc_Value_Oval @ ( v_vs____ @ ( v_a____ @ c_Value_Oval_OAddr @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( v_T_H____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(213,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

thf(1294,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(90,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

thf(929,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

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

thf(2330,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( F @ c_Expr_Oexp_OCall ) ) ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCall ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(159,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).

thf(1133,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

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

thf(1774,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(209,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

thf(1280,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

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

thf(1957,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).

thf(833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(500,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( E @ ( A @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtVal_0) ).

thf(2008,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( E @ ( A @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(299,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

thf(1527,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( E @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

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

thf(1248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(280,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).

thf(1480,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
      | ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).

thf(1908,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(557,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_14) ).

thf(2142,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(348,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Value_Oval_OIntg @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__rec ) ) ) ) ) ) )
      = ( F @ ( D @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Orecs_I4_J_0) ).

thf(1642,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Value_Oval_OIntg @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Value_Oval_Oval__rec ) ) ) ) ) ) )
      = ( F @ ( D @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(539,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_33) ).

thf(2102,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(28,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).

thf(752,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

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

thf(1229,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

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

thf(2233,plain,
    v_T_H_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ tc_prod ) @ ( tc_Type_Oty @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_List_Olist @ ( v_body____ @ ( tc_Value_Oval @ ( v_vs____ @ ( v_a____ @ c_Value_Oval_OAddr @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_Type_Oty @ ( v_Ts____ @ ( v_D____ @ c_Type_Oty_OClass @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_pns____ @ ( c_Type_Othis @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_SmallStep_Oblocks @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I37_J_0) ).

thf(867,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

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

thf(1757,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(220,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).

thf(1314,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(286,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCondRed_0) ).

thf(1495,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

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

thf(2334,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( A @ hAPP ) )
        = ( D @ ( G @ c_Option_Ooption_OSome ) ) )
      | ( ( F @ ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( D @ ( G @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(47,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).

thf(807,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

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

thf(1561,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Value_Oval_OUnit @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

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

thf(2366,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

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

thf(1891,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

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

thf(828,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( C @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(277,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( B @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( A @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

thf(1473,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( G @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( F @ ( B @ c_Pair ) ) ) @ ( E @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( D @ ( A @ c_Pair ) ) ) @ ( C @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(169,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).

thf(1165,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(100,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

thf(955,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

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

thf(796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
      | ( A
        = ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ c_Type_Oty_OClass @ ( A @ ( D @ ( C @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( D @ ( A @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1 ) ) ) @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_0) ).

thf(1693,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ c_Type_Oty_OClass @ ( A @ ( D @ ( C @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( D @ ( A @ ( C @ ( B @ c_TypeRel_Osko__TypeRel__Xwiden__Class__1__1 ) ) ) @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

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

thf(2070,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(79,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).

thf(897,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

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

thf(1410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

thf(1288,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
       != ( D @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(378,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__env__mono_0) ).

thf(1710,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

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(1197,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(513,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedTry_0) ).

thf(2040,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome ) )
     != ( B @ c_Option_Ooption_ONone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).

thf(696,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome ) )
     != ( B @ c_Option_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

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

thf(2021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome ) )
     != ( B @ c_Option_Ooption_ONone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

thf(1346,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome ) )
     != ( B @ c_Option_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

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

thf(1827,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( H @ ( D @ ( G @ ( F @ ( A @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 ) ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(302,axiom,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OAddr @ c_Value_Othe__Addr )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__Addr_Osimps_0) ).

thf(1532,plain,
    ! [A: $i] :
      ( ( A @ c_Value_Oval_OAddr @ c_Value_Othe__Addr )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
       != ( C @ ( A @ c_Expr_Oexp_OVal @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(1537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
       != ( C @ ( A @ c_Expr_Oexp_OVal @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(239,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

thf(1378,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(324,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

thf(1582,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(488,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCondThrow_0) ).

thf(1976,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(288,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_20) ).

thf(1500,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(54,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).

thf(822,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

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

thf(1925,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

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

thf(215,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).

thf(1299,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(1399,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(155,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(1120,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(146,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(1093,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(469,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

thf(1930,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( F @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( A @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(649,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( C @ ( D @ ( G @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( F @ ( E @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( D @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_1) ).

thf(2353,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( C @ ( D @ ( G @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( F @ ( E @ ( tc_Type_Oty @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_Type_Oty @ ( D @ c_Type_Oty_OClass @ c_Option_Ooption_OSome ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

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

thf(839,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWTs ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__implies__WTrts_0) ).

thf(1236,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWTs ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrts ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

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

thf(2241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( D @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ c_Expr_Oexp_OSeq ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(550,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
        = A )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

thf(2127,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
        = A )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(564,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_15) ).

thf(2159,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

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

thf(1352,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] :
      ( ~ ( I @ ( L @ ( K @ ( B @ ( J @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_OMethod ) ) ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

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

thf(1829,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Value_Oval @ ( F @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( F @ ( C @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Value_Oval @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

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

thf(1977,plain,
    v_T_H____ = v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(83,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).

thf(908,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(114,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

thf(992,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

thf(982,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

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] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( L @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_1) ).

thf(1431,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] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( L @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

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

thf(1962,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(389,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

thf(1737,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
      | ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ tc_prod ) @ ( H @ c_SmallStep_Ored @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ tc_prod ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ tc_prod ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

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

thf(2074,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

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

thf(2018,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Value_Oval_OIntg )
     != ( B @ c_Value_Oval_OAddr ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

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

thf(1769,plain,
    v_T_H____ = v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(145,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

thf(1088,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCastThrow_0) ).

thf(1812,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ c_Expr_Oexp_OCast ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(275,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OThrowRed_0) ).

thf(1468,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(353,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_10) ).

thf(1653,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(940,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Objects_Ohext ) )
      | ~ ( B @ ( C @ c_Objects_Ohext ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Objects_Ohext ) )
      | ~ ( B @ ( C @ c_Objects_Ohext ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

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

thf(1945,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ c_Expr_Oexp_OVal @ hAPP ) @ ( C @ ( B @ c_Expr_Oexp_OBlock ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(119,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

thf(1009,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(273,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( B @ c_Expr_Oexp_OCast ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_2) ).

thf(1463,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( B @ c_Expr_Oexp_OCast ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

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

thf(1565,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( F @ ( C @ ( B @ ( A @ c_Progress_OWTrts_H ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(435,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Value_Oval_OIntg @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_val_Osplit_3) ).

thf(1848,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( E @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Value_Oval_OIntg @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Value_Oval_Oval__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

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

thf(2059,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(598,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_5) ).

thf(2238,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

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(1037,plain,
    c_Type_Oty_ONT != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

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

thf(2297,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(75,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

thf(882,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

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

thf(2177,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal @ hAPP ) )
     != ( A @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

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

thf(1014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

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

thf(1870,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Type_Oty_ONT @ ( c_Value_Oval_ONull @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(2428,plain,
    $false,
    inference(e,[status(thm)],[892,1665,1337,2094,1190,1454,1559,1729,1840,1850,941,777,1554,2250,1168,2295,760,2341,2072,1767,1995,2263,1083,1982,1750,1211,1158,1596,1882,1522,1401,2014,873,1269,2380,1971,1692,1305,1437,861,2363,1855,1200,2077,2231,1068,1422,1939,2282,1591,1078,1671,1608,2035,2141,1872,1233,814,1260,1919,1640,1497,2195,1705,1063,1954,1507,1222,2360,1746,2348,2046,1576,709,841,1613,1475,1703,1482,1887,782,1441,973,885,2173,1366,2067,1529,1055,1985,1760,719,2269,1871,802,1191,2126,949,2339,785,1860,2217,1511,702,2185,1577,1545,853,1147,2049,2373,1875,1922,902,2169,1514,1319,870,1931,1568,2301,1815,2222,924,1302,2105,2090,1373,1418,937,966,821,905,1946,1465,1714,2027,1040,1109,1682,1136,2291,1383,1020,2254,1843,2190,1796,2137,2002,1600,1104,2154,2205,1696,1622,774,2371,2242,988,2286,1863,1651,1074,2011,2204,678,1691,793,2164,2118,810,1311,2083,1163,1470,1915,1708,714,1868,2061,2000,2249,1255,2147,693,1238,1900,1723,825,1343,1042,952,1355,2277,1174,1676,1824,788,1619,2150,2132,729,847,1032,2332,1888,1457,1624,1836,1656,2213,1291,1910,1573,1012,1106,1968,879,2200,830,757,2345,2211,1407,1634,2228,1936,2115,2377,1804,1425,1878,1755,742,2300,1762,2100,1534,1794,1017,1111,1227,1540,1006,1138,1719,1567,1329,1361,2323,1739,669,2312,2080,1791,1214,1644,1419,1942,1659,686,1075,2108,2038,1155,1744,1297,1530,1668,2355,1050,911,1852,1429,1979,2272,1393,1627,1324,1114,1263,997,1588,985,1150,1478,1451,2304,1266,1831,1231,1086,1241,2208,921,1563,1071,1663,1026,1185,1732,1434,1857,1712,1846,2057,765,1648,1764,2391,1219,1747,856,2376,1631,2260,2121,2235,1698,1959,2275,2033,1548,1927,819,1916,1125,2188,1752,2016,1388,958,1965,1520,1488,732,1884,1615,1784,1428,1503,2326,2293,787,1865,1058,1332,1765,2319,672,2193,1786,2308,1371,1897,919,979,1194,2311,900,681,2383,1894,1117,1806,1524,1048,1801,1122,1349,2097,2257,990,1492,1603,2299,1722,1144,1771,737,1571,1439,811,816,2111,799,1838,1029,1460,1820,1688,890,2180,2025,1080,858,1557,2314,2343,1177,1381,2329,932,1952,1171,1396,2350,2171,768,1445,2086,780,2139,2288,2022,2156,1973,1594,1699,2051,1245,2064,2369,2244,1000,1726,1250,675,1809,2107,944,1905,927,1509,749,1340,968,2005,1413,2054,722,1203,1208,1277,2124,2234,1990,2202,836,1551,1003,2397,971,1605,1252,1780,2386,1098,690,1598,705,1611,1225,707,1368,2175,2092,791,1188,2337,2219,1317,1658,1679,2044,1285,1987,2224,1813,1452,1637,1130,1579,1934,744,1543,1257,2113,1141,1702,864,727,1585,1617,1404,1358,2247,1802,1023,2279,2357,2145,1485,2320,1506,1717,2030,1881,1272,2266,876,1940,1421,2088,1180,1685,1949,1817,1781,1448,1998,1834,1913,976,688,2215,1517,1390,2305,1575,844,2226,1734,771,1646,699,1674,1629,2130,2152,2394,961,1385,963,2167,2283,2389,2290,2251,1903,2135,946,1101,1244,1822,1491,914,2041,1777,1308,2066,2162,2183,763,1661,1442,1045,716,667,1294,929,2330,1133,1774,1280,1957,833,2008,1527,1248,1480,1908,2142,1642,2102,752,1229,2233,867,1757,1314,1495,2334,807,1561,2366,1891,828,1473,1165,955,796,1693,2070,897,1410,1288,1710,1197,2040,696,2021,1346,1827,1532,1537,1378,1582,1976,1500,822,1925,850,1299,1399,1120,1093,1930,2353,839,1236,2241,2127,2159,1352,1829,1977,908,992,982,1431,1962,1737,2074,2018,1769,1088,1812,1468,1653,940,935,1945,1009,1463,1565,1848,2059,2238,1037,2297,882,2177,1014,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : SWV939-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/0.46  % Computer : n011.cluster.edu
% 0.18/0.46  % Model    : x86_64 x86_64
% 0.18/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46  % Memory   : 8046.5625MB
% 0.18/0.46  % OS       : Linux 6.8.0-71-generic
% 0.18/0.46  % CPULimit : 300
% 0.18/0.46  % WCLimit  : 300
% 0.18/0.46  % DateTime : Sat Sep 26 15:11:59 UTC 2026
% 0.18/0.46  % CPUTime  : 
% 0.18/0.46  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.03/1.04  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.17/1.46  % [INFO] 	 Parsing done (416ms). 
% 2.17/1.48  % [INFO] 	 Running in sequential loop mode. 
% 3.33/1.84  % [INFO] 	 eprover registered as external prover. 
% 3.33/1.85  % [INFO] 	 Scanning for conjecture ... 
% 4.03/2.13  % [INFO] 	 Found a conjecture (or negated_conjecture) and 665 axioms. Running axiom selection ... 
% 5.03/2.39  % [INFO] 	 Axiom selection finished. Selected 665 axioms (removed 0 axioms). 
% 6.46/2.73  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 6.46/2.76  % [INFO] 	 Type checking passed. 
% 6.46/2.76  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 20.32/6.03  % External prover 'e' found a proof!
% 20.32/6.03  % [INFO] 	 Killing All external provers ... 
% 20.32/6.03  % Time passed: 5430ms (effective reasoning time: 4545ms)
% 20.32/6.04  % 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
% 20.32/6.04  % No. of inferences in proof: 1333
% 20.32/6.04  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5430 ms resp. 4545 ms w/o parsing
% 22.35/6.56  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.35/6.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------