TSTP Solution File: SWV988-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV988-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:19:40 EDT 2023

% Result   : Unsatisfiable 44.91s 9.79s
% Output   : Refutation 46.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  520
% Syntax   : Number of formulae    :  956 ( 433 unt;  85 typ;   0 def)
%            Number of atoms       : 1576 ( 599 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 51347 ( 998   ~; 705   |;   0   &;49644   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  224 ( 224   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   87 (  85 usr;  24 con; 0-8 aty)
%            Number of variables   : 4874 (   0   ^;4874   !;   0   ?;4874   :)

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

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

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

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

thf(v_s_H_type,type,
    v_s_H: $i ).

thf(v_E_type,type,
    v_E: $i ).

thf(v_e_H_type,type,
    v_e_H: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Conform_Osko__Conform__Xconfs__Cons2__1__1_type,type,
    c_Conform_Osko__Conform__Xconfs__Cons2__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Conform_Osko__Conform__Xconfs__Cons2__1__2_type,type,
    c_Conform_Osko__Conform__Xconfs__Cons2__1__2: $i > $i > $i > $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Expr_Obop_OAdd_type,type,
    c_Expr_Obop_OAdd: $i ).

thf(c_Expr_Obop_OEq_type,type,
    c_Expr_Obop_OEq: $i ).

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

thf(c_Conform_Olconf_type,type,
    c_Conform_Olconf: $i > $i > $i > $i > $i > $o ).

thf(c_Aux_Ofun__of_type,type,
    c_Aux_Ofun__of: $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(v_b_______type,type,
    v_b______: $i ).

thf(v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1_type,type,
    v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1: $i > $i > $i > $i > $i > $i ).

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

thf(c_JWellForm_Owf__J__mdecl_type,type,
    c_JWellForm_Owf__J__mdecl: $i ).

thf(c_Conform_Osko__Conform__Xconf__def__1__1_type,type,
    c_Conform_Osko__Conform__Xconf__def__1__1: $i > $i > $i > $i > $i > $i ).

thf(v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1_type,type,
    v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1: $i > $i > $i > $i > $i > $i ).

thf(c_WellType_Osko__WellType__XWT__elim__cases__2__2_type,type,
    c_WellType_Osko__WellType__XWT__elim__cases__2__2: $i > $i > $i > $i > $i > $i ).

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

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2_type,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2: $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1_type,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1: $i > $i > $i > $i > $i > $i > $i ).

thf(v_sko__CHAINED__1_type,type,
    v_sko__CHAINED__1: $i > $i > $i > $i > $i > $i ).

thf(v_ba_______type,type,
    v_ba______: $i ).

thf(v_aa_______type,type,
    v_aa______: $i ).

thf(c_WellType_Osko__WellType__XWT__elim__cases__2__1_type,type,
    c_WellType_Osko__WellType__XWT__elim__cases__2__1: $i > $i > $i > $i > $i > $i ).

thf(c_fst_type,type,
    c_fst: $i > $i > $i ).

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

thf(v_a_______type,type,
    v_a______: $i ).

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

thf(v_sko__local__Xstep__Xhyps__3__1_type,type,
    v_sko__local__Xstep__Xhyps__3__1: $i > $i > $i > $i > $i > $i ).

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

thf(v_sko__local__Xstep__3__1_type,type,
    v_sko__local__Xstep__3__1: $i > $i > $i > $i > $i > $i ).

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

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

thf(c_Conform_Osko__Conform__Xconfs__conv__map__1__1_type,type,
    c_Conform_Osko__Conform__Xconfs__conv__map__1__1: $i > $i > $i > $i > $i > $i ).

thf(69,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_OUnit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I11_J_0) ).

thf(645,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_OUnit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(326,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_0) ).

thf(1337,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(193,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).

thf(1024,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(342,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed2_0) ).

thf(1369,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(109,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

thf(760,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(218,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

thf(1105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(64,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(628,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(165,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I200_J_0) ).

thf(941,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(114,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

thf(777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(76,axiom,
    c_Expr_Obop_OAdd != c_Expr_Obop_OEq,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bop_Osimps_I2_J_0) ).

thf(666,plain,
    c_Expr_Obop_OAdd != c_Expr_Obop_OEq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(434,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCond_0) ).

thf(1549,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(220,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).

thf(1110,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsNull_0) ).

thf(1158,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).

thf(1005,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(99,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).

thf(730,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(379,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedSeq_0) ).

thf(1443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(183,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

thf(994,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( C = H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(369,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_0) ).

thf(1422,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(208,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

thf(1073,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(291,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).

thf(1269,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(401,axiom,
    c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_b______ ) @ v_E @ v_a______ @ v_T____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1486,plain,
    c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_b______ ) @ v_E @ v_a______ @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(406,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Map_Omap__le @ F @ C @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ F @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).

thf(1497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Map_Omap__le @ F @ C @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(311,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ A @ D @ C @ E @ B ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ D @ C @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_2) ).

thf(1310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ A @ D @ C @ E @ B ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ D @ C @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(38,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

thf(550,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(22,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).

thf(500,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).

thf(797,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(294,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssRedsThrow_0) ).

thf(1275,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(88,axiom,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OAddr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I10_J_0) ).

thf(698,plain,
    ! [A: $i] :
      ( c_Value_Oval_OUnit
     != ( c_Value_Oval_OAddr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(157,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

thf(913,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(205,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(1063,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(162,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).

thf(930,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(126,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(814,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(320,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccThrow_0) ).

thf(1327,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(215,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

thf(1095,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

thf(1001,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(353,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

thf(1391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(378,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OTryRed_0) ).

thf(1441,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(134,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).

thf(841,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedCastNull_0) ).

thf(1359,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ c_Value_Oval_ONull @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(351,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( B = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ B @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_16) ).

thf(1386,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( B = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ B @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A ) @ v_T____ ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(436,plain,
    ! [A: $i] :
      ( ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ A ) @ v_T____ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(418,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ B ) @ ( c_List_Olist_OCons @ F @ G @ C ) @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ E @ G @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ F @ B @ C ) @ A @ ( tc_prod @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__list__all2__Cons_2) ).

thf(1518,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ B ) @ ( c_List_Olist_OCons @ F @ G @ C ) @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ E @ G @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ F @ B @ C ) @ A @ ( tc_prod @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

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

thf(651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(176,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I92_J_0) ).

thf(973,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(148,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).

thf(885,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).

thf(565,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(341,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ E @ F @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_2) ).

thf(1366,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ E @ F @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(271,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ A @ B @ D @ E @ F @ C ) ) @ E ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_1) ).

thf(1228,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ A @ B @ D @ E @ F @ C ) ) @ E ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(284,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OAdd @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OInteger )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ c_Type_Oty_OInteger )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I6_J_0) ).

thf(1254,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OAdd @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OInteger )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ c_Type_Oty_OInteger )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(97,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).

thf(724,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(300,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowRed_0) ).

thf(1287,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(373,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_0) ).

thf(1430,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(95,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

thf(719,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(23,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).

thf(504,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(289,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OWhile @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I3_J_0) ).

thf(1264,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OWhile @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(296,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondRedsThrow_0) ).

thf(1279,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(9,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

thf(460,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(317,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) @ ( c_Wellfounded_Olex__prod @ G @ H @ C @ D ) @ ( tc_prod @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ G @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_2) ).

thf(1323,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) @ ( c_Wellfounded_Olex__prod @ G @ H @ C @ D ) @ ( tc_prod @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ G @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(61,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).

thf(619,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(133,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).

thf(838,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(158,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I10_J_0) ).

thf(917,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(106,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).

thf(751,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).

thf(934,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(253,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1 @ C @ A @ E @ D @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ G @ E )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ C @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ ( c_Pair @ B @ I @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction2_0) ).

thf(1191,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1 @ C @ A @ E @ D @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ G @ E )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ C @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ ( c_Pair @ B @ I @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(432,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ E @ F @ G @ G ) @ H @ ( tc_prod @ G @ G ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ A @ G @ C ) @ ( c_Pair @ F @ B @ G @ C ) @ ( tc_prod @ G @ C ) @ ( tc_prod @ G @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ D @ G @ C ) @ ( tc_prod @ ( tc_prod @ G @ C ) @ ( tc_prod @ G @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_1) ).

thf(1545,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ E @ F @ G @ G ) @ H @ ( tc_prod @ G @ G ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ A @ G @ C ) @ ( c_Pair @ F @ B @ G @ C ) @ ( tc_prod @ G @ C ) @ ( tc_prod @ G @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ D @ G @ C ) @ ( tc_prod @ ( tc_prod @ G @ C ) @ ( tc_prod @ G @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(41,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).

thf(559,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(398,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OAdd @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OInteger )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ c_Type_Oty_OInteger )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtBinOpAdd_0) ).

thf(1479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OAdd @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OInteger )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ c_Type_Oty_OInteger )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(331,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtWhile_0) ).

thf(1347,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(357,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed2_0) ).

thf(1398,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(273,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ A @ C @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ A @ C @ D @ E @ F ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ A @ C @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ A @ C @ D @ E @ F ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ B @ ( c_Expr_Oexp_OCond @ G @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_3) ).

thf(1232,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ A @ C @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ A @ C @ D @ E @ F ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ A @ C @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ A @ C @ D @ E @ F ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ B @ ( c_Expr_Oexp_OCond @ G @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    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] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCond_2) ).

thf(1319,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ F @ C )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ G @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(870,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(5,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).

thf(448,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(405,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_0) ).

thf(1494,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(160,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).

thf(924,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OSeq @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(307,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ E @ C @ A @ F @ G @ D @ H @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_0) ).

thf(1302,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ E @ C @ A @ F @ G @ D @ H @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OTryCatch @ D @ E @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(118,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(789,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(198,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I149_J_0) ).

thf(1040,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(367,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ A @ C @ D @ E @ B ) ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_1) ).

thf(1418,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ A @ C @ D @ E @ B ) ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(325,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( A = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ A @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_15) ).

thf(1334,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( A = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ A @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

thf(1136,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(937,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(46,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).

thf(574,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(128,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

thf(821,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(16,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I105_J_0) ).

thf(480,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(249,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondThrow_0) ).

thf(1183,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(298,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsThrowObj_0) ).

thf(1283,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(355,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1 @ B @ A @ C @ D @ E ) ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ B @ G @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ ( c_Pair @ E @ I @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction2_1) ).

thf(1394,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction2__1 @ B @ A @ C @ D @ E ) ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ B @ G @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ ( c_Pair @ F @ H @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ ( c_Pair @ E @ I @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(422,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ C @ A @ E @ D @ F @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ G @ D @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_1) ).

thf(1526,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ C @ A @ E @ D @ F @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ G @ D @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(334,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I18_J_0) ).

thf(1351,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(184,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).

thf(998,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(374,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OWhile @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTWhile_0) ).

thf(1433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OWhile @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(360,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds2_0) ).

thf(1405,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(258,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_1) ).

thf(1201,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(278,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ D )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ D ) @ B @ E @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ G @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__preserves__sconf_0) ).

thf(1242,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ D )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ D ) @ B @ E @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ G @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
       != ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).

thf(507,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
       != ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(382,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ E @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtCond_1) ).

thf(1447,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ E @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(170,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).

thf(956,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).

thf(1119,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(774,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(330,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OSeq @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTSeq_0) ).

thf(1345,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OSeq @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(181,axiom,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I4_J_0) ).

thf(988,plain,
    c_Value_Oval_OUnit != c_Value_Oval_ONull,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Expr_Obop_OAdd ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Expr_Obop_OEq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bop_Oinduct_0) ).

thf(1206,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Expr_Obop_OAdd ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Expr_Obop_OEq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(920,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OVal @ A @ B )
       != ( c_Expr_Oexp_OVal @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(80,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

thf(678,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(119,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(793,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(309,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ D @ F @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_3) ).

thf(1306,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ D @ F @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(257,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssRed_0) ).

thf(1199,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(235,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ C @ F ) @ ( c_Pair @ B @ G @ C @ F ) @ ( tc_prod @ C @ F ) @ ( tc_prod @ C @ F ) ) @ ( c_Wellfounded_Olex__prod @ D @ H @ C @ F ) @ ( tc_prod @ ( tc_prod @ C @ F ) @ ( tc_prod @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_0) ).

thf(1153,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ C @ F ) @ ( c_Pair @ B @ G @ C @ F ) @ ( tc_prod @ C @ F ) @ ( tc_prod @ C @ F ) ) @ ( c_Wellfounded_Olex__prod @ D @ H @ C @ F ) @ ( tc_prod @ ( tc_prod @ C @ F ) @ ( tc_prod @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(124,axiom,
    ! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).

thf(810,plain,
    ! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(393,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallObj_0) ).

thf(1470,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(33,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).

thf(534,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(376,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ E @ C @ D ) @ ( c_List_Olist_OCons @ A @ F @ C ) @ ( c_List_Olist_OCons @ B @ G @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__list__all2__Cons_0) ).

thf(1438,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ E @ C @ D ) @ ( c_List_Olist_OCons @ A @ F @ C ) @ ( c_List_Olist_OCons @ B @ G @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OAddr @ A )
       != ( c_Value_Oval_OAddr @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I3_J_0) ).

thf(661,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Value_Oval_OAddr @ A )
       != ( c_Value_Oval_OAddr @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(200,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I205_J_0) ).

thf(1047,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(203,axiom,
    c_Expr_Obop_OEq != c_Expr_Obop_OAdd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bop_Osimps_I1_J_0) ).

thf(1057,plain,
    c_Expr_Obop_OEq != c_Expr_Obop_OAdd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(156,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

thf(910,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(329,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowRedsThrow_0) ).

thf(1343,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(192,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

thf(1021,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(224,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).

thf(1123,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(245,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_Conform_Osko__Conform__Xconf__def__1__1 @ A @ C @ D @ E @ B ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ D @ B ) @ E ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__def_1) ).

thf(1174,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_Conform_Osko__Conform__Xconf__def__1__1 @ A @ C @ D @ E @ B ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ D @ B ) @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(409,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCond_2) ).

thf(1502,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(402,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I1_J_0) ).

thf(1487,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(86,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).

thf(693,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__CHAINED__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) ) @ A ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

thf(1238,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__CHAINED__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) ) @ A ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(268,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedTry_0) ).

thf(1223,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(151,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).

thf(894,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(265,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ F ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__widen_0) ).

thf(1217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ C ) @ F ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

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

thf(598,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(63,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).

thf(625,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(146,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

thf(879,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(247,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( B = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_OBinOp @ F @ A @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_3) ).

thf(1178,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( B = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_OBinOp @ F @ A @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(297,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssRed1_0) ).

thf(1281,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(189,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).

thf(1012,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(304,axiom,
    c_in @ ( c_Pair @ ( c_Pair @ v_a______ @ v_b______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).

thf(1296,plain,
    c_in @ ( c_Pair @ ( c_Pair @ v_a______ @ v_b______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ B @ A @ C @ D ) @ C @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).

thf(665,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ B @ A @ C @ D ) @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(49,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).

thf(583,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(29,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).

thf(522,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

thf(493,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I4_J_0) ).

thf(1210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).

thf(1079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(194,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).

thf(1027,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(255,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LAssReds_0) ).

thf(1195,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(361,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBlockThrow_0) ).

thf(1407,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ C ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(302,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1 @ B @ A @ C @ D @ E ) ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ F ) @ B @ G @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_1) ).

thf(1291,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1 @ B @ A @ C @ D @ E ) ) @ C ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ F ) @ B @ G @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(92,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).

thf(710,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCond @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(231,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

thf(1143,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(287,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ A @ D @ C @ E ) )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ F @ C @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_1) ).

thf(1259,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ A @ D @ C @ E ) )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ F @ C @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(167,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).

thf(948,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(321,axiom,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_b______,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1328,plain,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_b______,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(370,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

thf(1425,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OSeq @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(429,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Conform_Olconf @ A @ E @ F @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ E @ D @ G @ H )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ ( c_Pair @ E @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ I @ ( c_Pair @ B @ C @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__preserves__lconf_0) ).

thf(1540,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_Conform_Olconf @ A @ E @ F @ D @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ E @ D @ G @ H )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ ( c_Pair @ E @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ I @ ( c_Pair @ B @ C @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

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

thf(610,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(116,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).

thf(783,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(139,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).

thf(857,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(338,axiom,
    c_in @ ( c_Pair @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_e_H @ v_s_H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_I2_J_0) ).

thf(1360,plain,
    c_in @ ( c_Pair @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_e_H @ v_s_H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(333,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow1_0) ).

thf(1350,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(28,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I178_J_0) ).

thf(519,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OWhile @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(103,axiom,
    c_Value_Oval_ONull != c_Value_Oval_OUnit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I5_J_0) ).

thf(742,plain,
    c_Value_Oval_ONull != c_Value_Oval_OUnit,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(213,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I5_J_0) ).

thf(1089,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(274,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAccRed_0) ).

thf(1234,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(13,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ A @ B @ D @ E @ F @ C ) @ F @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_2) ).

thf(471,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ A @ B @ D @ E @ F @ C ) @ F @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ ( c_List_Olist_OCons @ E @ F @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(322,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqReds_0) ).

thf(1329,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(238,axiom,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_b______,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_I4_J_0) ).

thf(1160,plain,
    c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_b______,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(211,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).

thf(1082,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(339,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ C @ A @ D @ E @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ C @ A @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ C @ A @ D @ E @ F ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ F @ B @ ( c_Expr_Oexp_OCond @ G @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_5) ).

thf(1361,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ C @ A @ D @ E @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ C @ A @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ C @ A @ D @ E @ F ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ F @ B @ ( c_Expr_Oexp_OCond @ G @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

thf(669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCast @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).

thf(686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(68,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I215_J_0) ).

thf(642,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(365,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ B ) @ ( c_List_Olist_OCons @ F @ G @ C ) @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ E @ G @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ F @ B @ C ) @ A @ ( tc_prod @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__list__all2__Cons2_3) ).

thf(1414,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ B ) @ ( c_List_Olist_OCons @ F @ G @ C ) @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ E @ G @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ F @ B @ C ) @ A @ ( tc_prod @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(19,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).

thf(489,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(175,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I11_J_0) ).

thf(970,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(37,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).

thf(547,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(388,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastRed_0) ).

thf(1461,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(34,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

thf(537,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(62,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

thf(622,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).

thf(701,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(305,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).

thf(1297,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellTypeRT_OWTrt @ B @ C @ D @ ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(384,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWT @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).

thf(1451,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_WellType_OWT @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

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

thf(654,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(372,axiom,
    c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_b______ ) @ v_E @ v_a______ @ v_T____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_I5_J_0) ).

thf(1429,plain,
    c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_b______ ) @ v_E @ v_a______ @ v_T____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(280,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryRedsVal_0) ).

thf(1246,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OLAssThrow_0) ).

thf(1393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(216,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).

thf(1099,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(180,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).

thf(985,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(397,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedInitBlock_0) ).

thf(1478,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(282,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OTryCatch @ D @ B @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_2) ).

thf(1249,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OTryCatch @ D @ B @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(424,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccRedsThrow_0) ).

thf(1530,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(386,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ F @ G @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_2) ).

thf(1456,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ F @ G @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__Xstep__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) ) @ A ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_I3_J_0) ).

thf(1382,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__Xstep__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) ) @ A ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(204,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I165_J_0) ).

thf(1060,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(201,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).

thf(1050,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

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

thf(657,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(243,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastRedsThrow_0) ).

thf(1170,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(391,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpRed1_0) ).

thf(1466,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(251,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CallRedsObj_0) ).

thf(1187,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCall @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(417,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ C @ A @ D @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ C @ A @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ C @ A @ D @ E ) ) )
      | ~ ( c_WellType_OWT @ C @ B @ ( c_Expr_Oexp_OCond @ F @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_5) ).

thf(1515,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ C @ A @ D @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ C @ A @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ C @ A @ D @ E ) ) )
      | ~ ( c_WellType_OWT @ C @ B @ ( c_Expr_Oexp_OCond @ F @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(242,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_17) ).

thf(1167,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(50,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I2_J_0) ).

thf(586,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(149,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).

thf(888,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(414,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ F @ C ) @ D ) @ E ) )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conf__hext_0) ).

thf(1510,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ F @ C ) @ D ) @ E ) )
      | ~ ( c_Objects_Ohext @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(283,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ E @ D @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_18) ).

thf(1251,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger )
      | ( D = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ E @ D @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(293,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I3_J_1) ).

thf(1273,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(104,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

thf(745,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAcc @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(345,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).

thf(1374,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(100,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(733,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OVal @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

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

thf(601,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(26,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

thf(513,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(232,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).

thf(1146,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCond @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(266,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ B ) @ ( c_List_Olist_OCons @ F @ G @ C ) @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ E @ G @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ F @ B @ C ) @ A @ ( tc_prod @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__list__all2__Cons1_3) ).

thf(1219,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ B ) @ ( c_List_Olist_OCons @ F @ G @ C ) @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ E @ G @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ F @ B @ C ) @ A @ ( tc_prod @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

thf(824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(352,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_0) ).

thf(1389,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(426,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_Conform_Osko__Conform__Xconfs__conv__map__1__1 @ A @ C @ D @ E @ B ) @ C @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ D @ B ) @ E @ C @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__conv__map_1) ).

thf(1535,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ ( c_Conform_Osko__Conform__Xconfs__conv__map__1__1 @ A @ C @ D @ E @ B ) @ C @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ D @ B ) @ E @ C @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(359,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp2Reds_0) ).

thf(1403,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(419,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ C @ A @ E @ F @ D @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ G @ F @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_2) ).

thf(1520,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ C @ A @ E @ F @ D @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OCond @ G @ F @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).

thf(562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_Othrow @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(154,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

thf(904,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Othrow @ A @ B )
       != ( c_Expr_Oexp_Othrow @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

thf(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_Othrow @ A @ B )
       != ( c_Expr_Oexp_Othrow @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(47,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

thf(577,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(285,axiom,
    c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf_0) ).

thf(1256,plain,
    c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(270,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ A @ D @ E @ C ) )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ F @ E @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_2) ).

thf(1226,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ A @ D @ E @ C ) )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ F @ E @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(229,axiom,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1139,plain,
    ! [A: $i] : ( c_Objects_Ohext @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(4,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

thf(445,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ ( v_sko__local__Xstep__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_I3_J_1) ).

thf(1312,plain,
    ! [A: $i] :
      ( ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ ( v_sko__local__Xstep__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(93,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

thf(713,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(324,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WhileRedsThrow_0) ).

thf(1332,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(122,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).

thf(804,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OLAss @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(390,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds1_0) ).

thf(1464,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(269,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__lcl__add_0) ).

thf(1224,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(336,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ F @ E @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_14) ).

thf(1356,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ F @ E @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(35,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).

thf(540,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(78,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

thf(672,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(292,axiom,
    ( c_State_Ohp
    = ( c_fst @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hp__def_0) ).

thf(1271,plain,
    ( c_State_Ohp
    = ( c_fst @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(343,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedBlock_0) ).

thf(1371,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(11,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).

thf(466,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(214,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

thf(1092,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(153,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).

thf(900,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
       != ( c_Expr_Oexp_OWhile @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(131,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(831,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(101,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).

thf(736,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCastThrow_0) ).

thf(1349,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(404,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ c_Expr_Obop_OEq @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ E ) @ F ) )
      | ~ ( c_WellType_OWT @ A @ B @ D @ F )
      | ~ ( c_WellType_OWT @ A @ B @ C @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTBinOpEq_0) ).

thf(1492,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ c_Expr_Obop_OEq @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ E ) @ F ) )
      | ~ ( c_WellType_OWT @ A @ B @ D @ F )
      | ~ ( c_WellType_OWT @ A @ B @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

thf(1542,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(6,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

thf(451,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( B = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(199,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

thf(1043,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I221_J_0) ).

thf(616,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(346,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_TryReds_0) ).

thf(1376,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OTryCatch @ F @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(141,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).

thf(863,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(110,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

thf(764,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(178,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I3_J_0) ).

thf(979,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(56,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(604,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OCall @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(81,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).

thf(681,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBlock @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(362,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).

thf(1408,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ D @ E )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_Othrow @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(125,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).

thf(811,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(327,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAccReds_0) ).

thf(1339,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAcc @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(17,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

thf(483,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(136,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).

thf(848,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ ( c_Expr_Oexp_OSeq @ B @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_ORedWhile_0) ).

thf(1325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ ( c_Expr_Oexp_OSeq @ B @ ( c_Expr_Oexp_OWhile @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_OVal @ c_Value_Oval_OUnit @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(233,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__elim__cases_0) ).

thf(1149,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ B @ C @ D @ ( c_Expr_Oexp_OLAss @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(173,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).

thf(964,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(356,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

thf(1396,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(395,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Pair @ A @ E @ C @ D ) @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) @ ( c_Recdef_Osame__fst @ F @ G @ C @ D ) @ ( tc_prod @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_in @ ( c_Pair @ B @ E @ D @ D ) @ ( hAPP @ G @ A ) @ ( tc_prod @ D @ D ) )
      | ~ ( hBOOL @ ( hAPP @ F @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__fstI_0) ).

thf(1474,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Pair @ A @ E @ C @ D ) @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) @ ( c_Recdef_Osame__fst @ F @ G @ C @ D ) @ ( tc_prod @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_in @ ( c_Pair @ B @ E @ D @ D ) @ ( hAPP @ G @ A ) @ ( tc_prod @ D @ D ) )
      | ~ ( hBOOL @ ( hAPP @ F @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(171,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      | ~ ( c_Map_Omap__le @ B @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).

thf(959,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      | ~ ( c_Map_Omap__le @ B @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

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

thf(636,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(115,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).

thf(780,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(7,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ B @ C @ A @ D @ E @ F ) @ tc_Value_Oval ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ B @ C @ F ) @ A @ ( c_List_Olist_OCons @ D @ E @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_0) ).

thf(455,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Conform_Osko__Conform__Xconfs__Cons2__1__2 @ B @ C @ A @ D @ E @ F ) @ tc_Value_Oval ) )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ B @ C @ F ) @ A @ ( c_List_Olist_OCons @ D @ E @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(190,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

thf(1015,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(246,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCondRed_0) ).

thf(1176,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(221,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).

thf(1113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(375,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ B @ C @ D @ A @ E ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ B @ C @ D @ A @ E ) @ tc_Type_Oty ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ B @ E ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ A @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__Cons_0) ).

thf(1435,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_List_Olist_OCons @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1 @ B @ C @ D @ A @ E ) @ ( c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2 @ B @ C @ D @ A @ E ) @ tc_Type_Oty ) )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ B @ E ) @ ( c_List_Olist_OCons @ C @ D @ tc_Type_Oty ) @ A @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(340,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ E @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ F @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_1) ).

thf(1364,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ E @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ F @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ C @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ C @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(2,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).

thf(438,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(263,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ tc_Value_Oval ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ E @ G @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__Cons2_3) ).

thf(1213,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ tc_Value_Oval ) @ ( c_List_Olist_OCons @ F @ G @ tc_Type_Oty ) @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ E @ G @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Conform_Oconf @ A @ B @ C ) @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(130,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

thf(827,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( D = I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(206,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).

thf(1066,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(381,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).

thf(1445,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(423,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ D )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ D ) @ B @ E @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ G @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__preserves__sconf_0) ).

thf(1528,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ C )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ B @ D )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ D ) @ B @ E @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ E @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ G @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(137,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).

thf(851,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(217,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).

thf(1102,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(96,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_Conform_Olconf @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lconf__hext_0) ).

thf(722,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Conform_Olconf @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_Conform_Olconf @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I89_J_0) ).

thf(1034,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(79,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I64_J_0) ).

thf(675,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ ( v_sko__local__Xstep__Xhyps__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_Ohyps_I3_J_1) ).

thf(1304,plain,
    ! [A: $i] :
      ( ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ ( v_sko__local__Xstep__Xhyps__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(368,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).

thf(1420,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(161,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).

thf(927,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(295,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OEq @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I5_J_0) ).

thf(1277,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OEq @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(70,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I111_J_0) ).

thf(648,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBinOp @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(413,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow1_0) ).

thf(1509,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(27,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

thf(516,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(394,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow1_0) ).

thf(1472,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(191,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).

thf(1018,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_Othrow @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(39,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).

thf(553,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCast @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(435,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOp1Reds_0) ).

thf(1551,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(14,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

thf(473,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
       != ( c_Expr_Oexp_OLAss @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(209,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).

thf(1076,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OCond @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(261,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow2_0) ).

thf(1208,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ I @ ( tc_List_Olist @ tc_String_Ochar ) ) @ H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

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

thf(589,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

thf(531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OVal @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(166,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

thf(944,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCast @ A @ B @ C )
       != ( c_Expr_Oexp_OCast @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

thf(458,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
      = ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(248,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__trans_0) ).

thf(1181,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(433,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

thf(1547,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
      | ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(30,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).

thf(525,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_Othrow @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(580,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OVal @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(85,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I191_J_0) ).

thf(690,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OCall @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(236,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCast @ B @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_2) ).

thf(1156,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCast @ B @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(169,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ D @ E @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ F @ D @ B ) @ ( c_List_Olist_OCons @ G @ E @ C ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__list__all2__Cons_1) ).

thf(954,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ D @ E @ B @ C )
      | ~ ( c_List_Olist__all2 @ ( c_Aux_Ofun__of @ A @ B @ C ) @ ( c_List_Olist_OCons @ F @ D @ B ) @ ( c_List_Olist_OCons @ G @ E @ C ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(102,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).

thf(739,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

thf(1267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(207,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).

thf(1070,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OLAss @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(144,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).

thf(872,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(358,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ C @ A @ D @ E @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ C @ A @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ C @ A @ D @ E @ F ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ F @ B @ ( c_Expr_Oexp_OCond @ G @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_4) ).

thf(1400,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ C @ A @ D @ E @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__1 @ B @ C @ A @ D @ E @ F ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__2__2 @ B @ C @ A @ D @ E @ F ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ C @ F @ B @ ( c_Expr_Oexp_OCond @ G @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(91,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

thf(707,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ A @ D @ B )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

thf(1230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ A @ D @ B )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(400,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ C @ D @ B )
      | ~ ( c_WellType_OWT @ A @ C @ E @ B )
      | ~ ( c_WellType_OWT @ A @ C @ F @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCond @ F @ E @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCond_1) ).

thf(1484,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ B ) )
      | ~ ( c_WellType_OWT @ A @ C @ D @ B )
      | ~ ( c_WellType_OWT @ A @ C @ E @ B )
      | ~ ( c_WellType_OWT @ A @ C @ F @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ C @ ( c_Expr_Oexp_OCond @ F @ E @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(306,axiom,
    ! [A: $i] :
      ( ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ ( v_sko__CHAINED__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).

thf(1300,plain,
    ! [A: $i] :
      ( ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_s_H ) @ v_E @ v_e_H @ ( v_sko__CHAINED__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(3,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).

thf(441,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

thf(463,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(314,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OWhile @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I3_J_1) ).

thf(1317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OWhile @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(212,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(1085,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(299,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CastReds_0) ).

thf(1285,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCast @ A @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ B @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

thf(907,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OSeq @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(202,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

thf(1053,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OFAss @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(407,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OBinOpThrow2_0) ).

thf(1499,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(428,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CondReds_0) ).

thf(1538,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCond @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OCond @ E @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(168,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

thf(951,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OTryCatch @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ c_Expr_Obop_OAdd @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OInteger )
      | ~ ( c_WellType_OWT @ A @ B @ D @ c_Type_Oty_OInteger )
      | ~ ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTBinOpAdd_0) ).

thf(1543,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ c_Expr_Obop_OAdd @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OInteger )
      | ~ ( c_WellType_OWT @ A @ B @ D @ c_Type_Oty_OInteger )
      | ~ ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(286,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I20_J_0) ).

thf(1257,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Progress_OWTrt_H @ A @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OVoid )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ E @ F )
      | ~ ( c_Progress_OWTrt_H @ A @ B @ C @ D @ c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(59,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).

thf(613,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAss @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(267,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SeqRedsThrow_0) ).

thf(1221,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(335,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_13) ).

thf(1353,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ E @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(411,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_fst @ B @ C ) @ ( c_Pair @ D @ E @ B @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ F @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_0) ).

thf(1506,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( c_fst @ B @ C ) @ ( c_Pair @ D @ E @ B @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ F @ E ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(371,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_2) ).

thf(1427,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ F @ C )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ G @ B )
      | ~ ( c_Progress_OWTrt_H @ A @ D @ E @ H @ c_Type_Oty_OBoolean )
      | ( c_Progress_OWTrt_H @ A @ D @ E @ ( c_Expr_Oexp_OCond @ H @ G @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(230,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).

thf(1140,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

thf(1008,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).

thf(571,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OBinOp @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(21,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).

thf(497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_fst @ A @ B ) @ ( c_Pair @ C @ D @ A @ B ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__conv_0) ).

thf(1504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_fst @ A @ B ) @ ( c_Pair @ C @ D @ A @ B ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(98,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

thf(727,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OTryCatch @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(344,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_0) ).

thf(1372,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ C @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(53,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I4_J_0) ).

thf(595,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(277,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BinOpRedsThrow1_0) ).

thf(1240,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBinOp @ A @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(182,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

thf(991,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OFAcc @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(135,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).

thf(845,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OLAss @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(387,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Pair @ A @ E @ C @ D ) @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) @ ( c_Wellfounded_Olex__prod @ F @ G @ C @ D ) @ ( tc_prod @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_in @ ( c_Pair @ B @ E @ D @ D ) @ G @ ( tc_prod @ D @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lex__prod_3) ).

thf(1459,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Pair @ A @ E @ C @ D ) @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) @ ( c_Wellfounded_Olex__prod @ F @ G @ C @ D ) @ ( tc_prod @ ( tc_prod @ C @ D ) @ ( tc_prod @ C @ D ) ) )
      | ~ ( c_in @ ( c_Pair @ B @ E @ D @ D ) @ G @ ( tc_prod @ D @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(40,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).

thf(556,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCall @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(316,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_3) ).

thf(1321,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Decl_Ois__class @ A @ B @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ C @ D @ ( c_Expr_Oexp_OCast @ B @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(177,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).

thf(976,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBlock @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ A @ D @ B )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).

thf(1412,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ A @ D @ B )
      | ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(150,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).

thf(891,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCall @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
        = ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).

thf(1126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
        = ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(252,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ E @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__trans_0) ).

thf(1189,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ E @ D @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ E @ tc_Type_Oty @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(188,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ F @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__hext_0) ).

thf(1010,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ F @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(112,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).

thf(771,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OWhile @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(219,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).

thf(1108,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
      | ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(301,axiom,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1289,plain,
    ( ( c_COMBI @ v_P @ t_a )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(385,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_1) ).

thf(1453,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ c_Type_Oty_OInteger )
      | ( E = c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqThrow_0) ).

thf(1326,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ D ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).

thf(961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCast @ A @ B @ C )
     != ( c_Expr_Oexp_OSeq @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(396,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

thf(1476,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ C @ tc_Type_Oty @ tc_Type_Oty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__refl_0) ).

thf(1508,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ B ) @ C @ C @ tc_Type_Oty @ tc_Type_Oty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(399,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ C @ A @ D @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ C @ A @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ C @ A @ D @ E ) ) )
      | ~ ( c_WellType_OWT @ C @ B @ ( c_Expr_Oexp_OCond @ F @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_4) ).

thf(1481,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ C @ A @ D @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ C @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ C @ A @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ C @ A @ D @ E ) ) )
      | ~ ( c_WellType_OWT @ C @ B @ ( c_Expr_Oexp_OCond @ F @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

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

thf(632,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(279,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellType_OWT @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt__env__mono_0) ).

thf(1244,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Type_Oty )
      | ~ ( c_WellType_OWT @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(421,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I3_J_0) ).

thf(1523,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OWhile @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(117,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).

thf(786,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(328,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssReds2_0) ).

thf(1341,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ F @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(105,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).

thf(748,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OWhile @ A @ B @ C )
     != ( c_Expr_Oexp_OBlock @ D @ E @ F @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(195,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

thf(1030,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OCond @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

thf(568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(25,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).

thf(510,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(377,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1440,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(310,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ C ) @ F @ E @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ F @ tc_Value_Oval @ tc_Type_Oty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_confs__widens_0) ).

thf(1308,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ E @ tc_Value_Oval @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_TypeRel_Owiden @ A @ C ) @ F @ E @ tc_Type_Oty @ tc_Type_Oty )
      | ~ ( c_List_Olist__all2 @ ( c_Conform_Oconf @ A @ B @ C ) @ D @ F @ tc_Value_Oval @ tc_Type_Oty ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(254,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OEq @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrtBinOpEq_0) ).

thf(1193,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ c_Expr_Obop_OEq @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ E @ F )
      | ~ ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(416,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(1513,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ B @ C @ D @ E )
      | ~ ( c_Objects_Ohext @ F @ B )
      | ~ ( c_WellTypeRT_OWTrt @ A @ F @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_Objects_Ohext @ C @ B )
      | ~ ( c_Objects_Ohext @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(380,axiom,
    c_in @ ( c_Pair @ ( c_Pair @ v_a______ @ v_b______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_I1_J_0) ).

thf(1444,plain,
    c_in @ ( c_Pair @ ( c_Pair @ v_a______ @ v_b______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(94,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

thf(716,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OCast @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(239,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ A @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ B @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__hext__incr_0) ).

thf(1161,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Objects_Ohext @ A @ B )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ C @ ( c_Pair @ A @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ B @ F @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ G ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(121,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

thf(800,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(222,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

thf(1116,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(227,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).

thf(1133,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAss @ C @ D @ E @ F @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(415,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OFAssThrow2_0) ).

thf(1512,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ ( c_Expr_Oexp_OVal @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(174,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).

thf(967,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_Othrow @ A @ B )
     != ( c_Expr_Oexp_OFAcc @ C @ D @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(132,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).

thf(835,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OCond @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(127,axiom,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OAddr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I16_J_0) ).

thf(818,plain,
    ! [A: $i] :
      ( c_Value_Oval_ONull
     != ( c_Value_Oval_OAddr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(348,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ThrowReds_0) ).

thf(1380,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ C @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(138,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

thf(854,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OCast @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OThrowThrow_0) ).

thf(1248,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ C ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(142,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).

thf(867,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OLAss @ F @ G @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(313,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( B = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ A @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_3) ).

thf(1314,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( B = c_Type_Oty_OBoolean )
      | ~ ( c_WellType_OWT @ C @ D @ ( c_Expr_Oexp_OBinOp @ E @ A @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(123,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).

thf(807,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBinOp @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(256,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

thf(1197,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
      | ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ E @ A @ C @ D ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).

thf(696,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ E @ A @ C @ D ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(241,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).

thf(1165,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
      | ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(244,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ B ) @ C @ D @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1 @ C @ A @ E @ D @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ F ) @ C @ G @ E )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ C @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

thf(1172,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ B ) @ C @ D @ ( v_sko__TypeSafe__Mirabelle__Xsubject__reduction__1 @ C @ A @ E @ D @ B ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ ( hAPP @ c_State_Ohp @ F ) @ C @ G @ E )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ A @ C @ F )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ G @ F @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ B @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ A ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_WellForm_Owf__prog @ c_JWellForm_Owf__J__mdecl @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(152,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).

thf(897,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OBinOp @ E @ F @ G @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( hAPP @ ( c_fst @ B @ C ) @ ( c_Pair @ A @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eqD_0) ).

thf(1410,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( A
      = ( hAPP @ ( c_fst @ B @ C ) @ ( c_Pair @ A @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(111,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

thf(767,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
       != ( c_Expr_Oexp_OFAcc @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(275,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTCond_0) ).

thf(1236,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ B ) @ C ) )
      | ~ ( c_WellType_OWT @ A @ D @ E @ C )
      | ~ ( c_WellType_OWT @ A @ D @ F @ B )
      | ~ ( c_WellType_OWT @ A @ D @ G @ c_Type_Oty_OBoolean )
      | ( c_WellType_OWT @ A @ D @ ( c_Expr_Oexp_OCond @ G @ F @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(226,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

thf(1129,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
       != ( c_Expr_Oexp_OSeq @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(288,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( B = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_OBinOp @ F @ B @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I9_J_12) ).

thf(1261,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( B = c_Expr_Obop_OEq )
      | ~ ( c_WellTypeRT_OWTrt @ C @ D @ E @ ( c_Expr_Oexp_OBinOp @ F @ B @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ B ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(347,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Red__lcl__add_0) ).

thf(1378,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ ( c_Map_Omap__add @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ ( c_Map_Omap__add @ C @ G @ ( tc_List_Olist @ tc_String_Ochar ) @ tc_Value_Oval ) @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ ( c_Pair @ B @ D @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ E @ ( c_Pair @ F @ G @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_ONull ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_val_Osimps_I17_J_0) ).

thf(528,plain,
    ! [A: $i] :
      ( ( c_Value_Oval_OAddr @ A )
     != c_Value_Oval_ONull ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(408,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ A @ C @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ A @ C @ D @ E ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ A @ C @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ A @ C @ D @ E ) ) )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ F @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_3) ).

thf(1500,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ A @ C @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ A @ C @ D @ E ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__1 @ B @ A @ C @ D @ E ) ) @ ( c_WellType_Osko__WellType__XWT__elim__cases__2__2 @ B @ A @ C @ D @ E ) ) )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OCond @ F @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(179,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).

thf(982,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OBlock @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(57,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).

thf(607,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBlock @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OTryCatch @ E @ F @ G @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(425,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( A = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ A @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I9_J_19) ).

thf(1532,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Expr_Obop_OAdd )
      | ( A = c_Expr_Obop_OEq )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OBinOp @ D @ A @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).

thf(860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OVal @ A @ B )
     != ( c_Expr_Oexp_OWhile @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(350,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ C @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_0) ).

thf(1384,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ C @ D )
      | ~ ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OTryCatch @ C @ E @ F @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(427,axiom,
    c_in @ ( c_Pair @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_e_H @ v_s_H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).

thf(1537,plain,
    c_in @ ( c_Pair @ ( c_Pair @ v_aa______ @ v_ba______ @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ v_e_H @ v_s_H @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ v_P ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(323,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OCallThrowObj_0) ).

thf(1331,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OCall @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ B @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ A @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ E ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(18,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I208_J_0) ).

thf(486,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OSeq @ A @ B @ C )
     != ( c_Expr_Oexp_OWhile @ D @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(469,plain,
    ! [B: $i,A: $i] :
      ( ( c_COMBI @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(250,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OLAss @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__elim__cases_I1_J_0) ).

thf(1184,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ~ ( c_WellType_OWT @ B @ C @ ( c_Expr_Oexp_OLAss @ D @ E @ ( tc_List_Olist @ tc_String_Ochar ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(389,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OInitBlockThrow_0) ).

thf(1463,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OBlock @ A @ B @ ( c_Expr_Oexp_OSeq @ ( c_Expr_Oexp_OLAss @ A @ ( c_Expr_Oexp_OVal @ C @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ ( c_Expr_Oexp_OVal @ ( c_Value_Oval_OAddr @ D ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(36,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

thf(543,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Expr_Oexp_OTryCatch @ A @ B @ C @ D @ E )
       != ( c_Expr_Oexp_OTryCatch @ F @ G @ H @ I @ E ) )
      | ( A = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(366,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__Xstep__Xhyps__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) ) @ A ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_step_Ohyps_I3_J_0) ).

thf(1416,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ v_P @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( v_sko__local__Xstep__Xhyps__3__1 @ v_E @ v_P @ A @ v_e_H @ v_s_H ) ) @ A ) )
      | ~ ( c_WellTypeRT_OWTrt @ v_P @ ( hAPP @ c_State_Ohp @ v_ba______ ) @ v_E @ v_aa______ @ A )
      | ~ ( c_TypeSafe__Mirabelle_Osconf @ v_P @ v_E @ v_ba______ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(67,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).

thf(639,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ E )
     != ( c_Expr_Oexp_OCall @ F @ G @ H @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(147,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).

thf(882,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OLAss @ A @ B @ C )
     != ( c_Expr_Oexp_OFAss @ D @ E @ F @ G @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(403,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ D @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FAssRedsThrow2_0) ).

thf(1490,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OFAss @ A @ B @ C @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ D @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_Othrow @ F @ ( tc_List_Olist @ tc_String_Ochar ) ) @ G @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OVal @ J @ ( tc_List_Olist @ tc_String_Ochar ) ) @ I @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_SmallStep_Ored @ H ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

thf(1037,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OFAcc @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OVal @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(259,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_red__reds_OSeqRed_0) ).

thf(1204,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ A @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ ( c_Expr_Oexp_OSeq @ D @ B @ ( tc_List_Olist @ tc_String_Ochar ) ) @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) )
      | ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ C @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( c_Pair @ D @ E @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( c_SmallStep_Ored @ F ) @ ( tc_prod @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) @ ( tc_prod @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_prod @ ( tc_fun @ tc_nat @ ( tc_Option_Ooption @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_fun @ ( tc_prod @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) @ ( tc_fun @ ( tc_List_Olist @ tc_String_Ochar ) @ ( tc_Option_Ooption @ tc_Value_Oval ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(383,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ c_Expr_Obop_OEq @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ E ) @ F ) )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTBinOpEq_1) ).

thf(1449,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_WellType_OWT @ A @ B @ ( c_Expr_Oexp_OBinOp @ C @ c_Expr_Obop_OEq @ D @ ( tc_List_Olist @ tc_String_Ochar ) ) @ c_Type_Oty_OBoolean )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ E ) @ F ) )
      | ~ ( c_WellType_OWT @ A @ B @ D @ E )
      | ~ ( c_WellType_OWT @ A @ B @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(52,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).

thf(592,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Expr_Oexp_OBinOp @ A @ B @ C @ D )
     != ( c_Expr_Oexp_OSeq @ E @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(392,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ B @ C @ A @ D @ E @ F @ G @ H ) ) @ D ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ H @ C @ ( c_Expr_Oexp_OTryCatch @ F @ B @ E @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_2) ).

thf(1468,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_TypeRel_Owiden @ A @ ( tc_prod @ ( tc_List_Olist @ ( tc_List_Olist @ tc_String_Ochar ) ) @ ( tc_Expr_Oexp @ ( tc_List_Olist @ tc_String_Ochar ) ) ) ) @ ( c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 @ B @ C @ A @ D @ E @ F @ G @ H ) ) @ D ) )
      | ~ ( c_WellTypeRT_OWTrt @ A @ H @ C @ ( c_Expr_Oexp_OTryCatch @ F @ B @ E @ G @ ( tc_List_Olist @ tc_String_Ochar ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(9718,plain,
    $false,
    inference(e,[status(thm)],[645,1337,1024,1369,760,1105,628,941,777,666,1549,1110,1158,1005,730,1522,1443,994,1422,1073,1269,1486,1497,1310,550,500,797,1275,698,913,1063,930,814,1327,1095,1001,1391,1441,841,1359,1386,436,1518,651,973,885,565,1366,1228,1254,724,1287,1430,719,504,1264,1279,460,1323,619,838,917,751,934,1191,1545,559,1479,1347,1398,1232,1319,870,448,1494,924,1302,789,1040,1418,1334,1136,937,574,821,480,1183,1283,1215,1394,1526,1351,998,1433,1405,1201,1242,507,1447,956,1119,774,1345,988,1206,920,678,793,1306,1199,1153,810,1470,534,1438,661,1047,1057,1163,910,1343,1021,1123,1174,1502,1487,693,1238,1223,894,1217,598,625,879,1178,757,1281,1012,1296,665,583,522,493,1210,1079,1027,1195,1407,1291,710,1143,1259,948,1328,1425,1540,610,783,857,1360,1350,519,742,1089,1234,471,1329,1160,1082,1361,669,686,642,1414,489,970,547,1461,537,622,701,1297,1451,654,1429,1246,1393,1099,985,1478,1249,1530,1456,1382,1060,1050,657,1170,1466,1187,1515,1167,586,888,1510,1251,1273,745,689,1374,733,601,513,1146,1219,824,1389,1535,1403,1520,562,904,875,577,1256,1226,1139,445,1312,713,1332,804,704,1464,1224,1356,540,672,1271,1371,466,1092,900,831,736,1349,1492,1542,451,1043,616,1376,863,764,979,604,681,1408,477,811,1339,483,848,1325,1293,1149,964,1396,1474,959,636,780,455,1015,1176,1113,1435,1364,438,1213,827,1066,1445,1528,851,1102,722,1034,675,1304,1420,927,1277,648,1509,516,1472,1018,754,553,1551,473,1076,1208,589,531,944,458,1181,1547,525,580,690,1156,954,739,1267,1070,872,1400,707,1230,1484,1300,441,463,1317,1085,1285,907,1053,1499,1538,951,1543,1257,613,1221,1353,1506,1427,1140,1008,571,497,1504,727,1372,595,1240,991,845,1459,556,1321,976,1412,891,1126,1189,1010,771,1108,1289,1453,1326,961,1476,1508,1481,632,1244,1523,786,1341,748,1030,568,510,1440,1308,1193,1513,684,1444,716,1161,800,1116,1133,1512,967,835,818,1380,854,1248,867,1314,807,1197,696,1165,1172,897,1410,767,1236,1129,1261,1152,1378,528,1500,982,607,1532,860,1384,1537,1331,486,469,1184,1463,543,1416,639,882,1490,1037,1204,1449,592,1468]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV988-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri May 19 02:52:13 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.91/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.77/1.09  % [INFO] 	 Parsing done (253ms). 
% 1.77/1.10  % [INFO] 	 Running in sequential loop mode. 
% 2.41/1.30  % [INFO] 	 eprover registered as external prover. 
% 2.41/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 2.41/1.31  % [INFO] 	 Scanning for conjecture ... 
% 3.16/1.48  % [INFO] 	 Found a conjecture and 434 axioms. Running axiom selection ... 
% 3.72/1.66  % [INFO] 	 Axiom selection finished. Selected 434 axioms (removed 0 axioms). 
% 4.73/1.93  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.73/1.95  % [INFO] 	 Type checking passed. 
% 4.73/1.95  % [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 ... 
% 44.91/9.78  % External prover 'e' found a proof!
% 44.91/9.78  % [INFO] 	 Killing All external provers ... 
% 44.91/9.78  % Time passed: 9260ms (effective reasoning time: 8674ms)
% 44.91/9.78  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 44.91/9.79  % Axioms used in derivation (434): cls_red__reds_ORedInitBlock_0, cls_exp_Osimps_I156_J_0, cls_red__reds_OInitBlockThrow_0, cls_WTSeq_0, cls_red__reds_OLAssThrow_0, cls_widens__Cons_2, cls_WTrt_H__WTrts_H_Ointros_I5_J_0, cls_red__lcl__add_0, cls_exp_Osimps_I56_J_0, cls_WTrt__elim__cases_I2_J_2, cls_val_Osimps_I3_J_0, cls_exp_Osimps_I9_J_1, cls_rtrancl__idemp_0, cls_exp_Osimps_I92_J_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_subject__reduction2_0, cls_exp_Osimps_I184_J_0, cls_red__reds_OFAssRed2_0, cls_val_Osimps_I5_J_0, cls_list__all2__Cons_2, cls_CallRedsThrowObj_0, cls_hp__def_0, cls_WT__elim__cases_I9_J_17, cls_exp_Osimps_I218_J_0, cls_exp_Osimps_I213_J_0, cls_val_Osimps_I10_J_0, cls_WTrt__elim__cases_I9_J_0, cls_list__all2__eq_1, cls_red__reds_OFAssRed1_0, cls_rel__list__all2__Cons_2, cls_map__add__assoc_0, cls_subject__reduction_0, cls_map__le__trans_0, cls_exp_Osimps_I193_J_0, cls_CastReds_0, cls_exp_Osimps_I10_J_1, cls_exp_Osimps_I225_J_0, cls_exp_Osimps_I138_J_0, cls_exp_Osimps_I81_J_0, cls_exp_Osimps_I137_J_0, cls_BinOpRedsThrow2_0, cls_exp_Osimps_I165_J_0, cls_exp_Osimps_I7_J_2, cls_list_Oinject_0, cls_CallRedsObj_0, cls_BinOpRedsThrow1_0, cls_exp_Osimps_I219_J_0, cls_exp_Osimps_I149_J_0, cls_lconf__hext_0, cls_exp_Osimps_I190_J_0, cls_WT__elim__cases_I9_J_2, cls_WTrtCond_0, cls_exp_Osimps_I15_J_1, cls_exp_Osimps_I204_J_0, cls_WTrt__elim__cases_I2_J_5, cls_CHAINED_0, cls_bop_Oinduct_0, cls_WT__elim__cases_I8_J_0, cls_exp_Osimps_I221_J_0, cls_val_Osimps_I4_J_0, cls_exp_Osimps_I11_J_0, cls_not__Cons__self2_0, cls_exp_Osimps_I115_J_0, cls_ty_Osimps_I5_J_0, cls_rtrancl__trans_0, cls_BinOp2Reds_0, cls_exp_Osimps_I211_J_0, cls_CHAINED_0_04, cls_map__le__iff__map__add__commute_0, cls_mem__def_1, cls_exp_Osimps_I13_J_0, cls_exp_Osimps_I199_J_0, cls_COMBI__def__raw_0, cls_exp_Osimps_I185_J_0, cls_SeqReds2_0, cls_exp_Osimps_I141_J_0, cls_step_I4_J_0, cls_exp_Osimps_I109_J_0, cls_WTCond_2, cls_FAssReds2_0, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I170_J_0, cls_step_I3_J_1, cls_exp_Osimps_I154_J_0, cls_LAssReds_0, cls_WTrt_H__elim__cases_0, cls_exp_Osimps_I208_J_0, cls_red__reds_OFAssThrow2_0, cls_exp_Osimps_I188_J_0, cls_exp_Osimps_I212_J_0, cls_WTrt__elim__cases_I9_J_15, cls_confs__conv__map_1, cls_exp_Osimps_I178_J_0, cls_exp_Osimps_I2_J_1, cls_exp_Osimps_I8_J_3, cls_WT__elim__cases_I2_J_1, cls_in__lex__prod_1, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, cls_exp_Osimps_I194_J_0, cls_exp_Osimps_I223_J_0, cls_exp_Osimps_I11_J_1, cls_widens__trans_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_2, cls_WT__elim__cases_I2_J_4, cls_WTrt__elim__cases_I6_J_3, cls_exp_Osimps_I171_J_0, cls_red__reds_OCallThrowObj_0, cls_red__reds_OLAssRed_0, cls_exp_Osimps_I157_J_0, cls_exp_Osimps_I113_J_0, cls_WTrt__elim__cases_I9_J_3, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_exp_Osimps_I4_J_1, cls_WTrtBinOpEq_0, cls_WTrt__elim__cases_I5_J_2, cls_rel__list__all2__Cons_0, cls_exp_Osimps_I67_J_0, cls_converse__rtrancl__into__rtrancl_0, cls_exp_Osimps_I4_J_0, cls_confs__Cons2_3, cls_WT__elim__cases_I4_J_0, cls_hext__trans_0, cls_exp_Osimps_I160_J_0, cls_exp_Osimps_I84_J_0, cls_list__all2__Cons_1, cls_widen__refl_0, cls_CondReds_0, cls_step_Ohyps_I3_J_1, cls_WT__elim__cases_I2_J_3, cls_WT__elim__cases_I9_J_3, cls_hext__refl_0, cls_exp_Osimps_I142_J_0, cls_exp_Osimps_I74_J_0, cls_exp_Osimps_I110_J_0, cls_fst__eqD_0, cls_WTrt__elim__cases_I2_J_1, cls_exp_Osimps_I205_J_0, cls_red__reds_OThrowThrow_0, cls_WT__elim__cases_I3_J_0, cls_exp_Osimps_I209_J_0, cls_WT__elim__cases_I9_J_19, cls_WhileRedsThrow_0, cls_step_I3_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_exp_Osimps_I176_J_0, cls_exp_Osimps_I143_J_0, cls_refl__on__def_1, cls_exp_Osimps_I146_J_0, cls_widens__refl_0, cls_exp_Osimps_I148_J_0, cls_ty_Osimps_I3_J_0, cls_conf__widen_0, cls_red__reds_OBinOpThrow1_0, cls_exp_Osimps_I172_J_0, cls_exp_Osimps_I139_J_0, cls_CHAINED_1, cls_WTBinOpAdd_0, cls_exp_Osimps_I174_J_0, cls_exp_Osimps_I10_J_2, cls_WTrt__elim__cases_I9_J_14, cls_ThrowReds_0, cls_subject__reduction_1, cls_WT__elim__cases_I5_J_2, cls_map__le__refl_0, cls_exp_Osimps_I99_J_0, cls_WTrt__hext__mono_0, cls_exp_Osimps_I46_J_0, cls_CHAINED_0_01, cls_red__reds_OTryRed_0, cls_exp_Osimps_I69_J_0, cls_in__lex__prod_2, cls_WTrt__env__mono_0, cls_exp_Osimps_I180_J_0, cls_red__reds_ORedBlock_0, cls_FAccReds_0, cls_exp_Osimps_I77_J_0, cls_exp_Osimps_I98_J_0, cls_exp_Osimps_I61_J_0, cls_exp_Osimps_I15_J_0, cls_exp_Osimps_I183_J_0, cls_red__preserves__sconf_0, cls_WTrt__elim__cases_I3_J_0, cls_exp_Osimps_I207_J_0, cls_exp_Osimps_I83_J_0, cls_exp_Osimps_I2_J_0, cls_WT__elim__cases_I2_J_2, cls_exp_Osimps_I12_J_2, cls_exp_Osimps_I8_J_2, cls_list__all2__Cons_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_exp_Osimps_I76_J_0, cls_exp_Osimps_I70_J_0, cls_red__reds_ORedWhile_0, cls_exp_Osimps_I177_J_0, cls_FAssRedsThrow2_0, cls_confs__Cons2_2, cls_CastRedsNull_0, cls_exp_Osimps_I89_J_0, cls_exp_Osimps_I159_J_0, cls_rel__list__all2__Cons_1, cls_exp_Osimps_I62_J_0, cls_red__reds_OBinOpRed2_0, cls_TryReds_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_exp_Osimps_I105_J_0, cls_exp_Osimps_I220_J_0, cls_exp_Osimps_I158_J_0, cls_val_Osimps_I16_J_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I60_J_0, cls_exp_Osimps_I162_J_0, cls_CondRedsThrow_0, cls_step_I1_J_0, cls_WTWhile_0, cls_refl__onD2_0, cls_map__add__le__mapE_0, cls_widens__Cons_0, cls_not__Cons__self_0, cls_exp_Osimps_I15_J_3, cls_red__reds_OBinOpRed1_0, cls_exp_Osimps_I169_J_0, cls_exp_Osimps_I201_J_0, cls_exp_Osimps_I166_J_0, cls_mem__def_0, cls_red__reds_OFAssThrow1_0, cls_TryRedsVal_0, cls_exp_Osimps_I47_J_0, cls_exp_Osimps_I7_J_1, cls_red__reds_OBlockThrow_0, cls_exp_Osimps_I189_J_0, cls_Red__preserves__sconf_0, cls_rtrancl__eq__or__trancl_1, cls_exp_Osimps_I55_J_0, cls_WTrt__elim__cases_I2_J_4, cls_WTrtSeq_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_CastRedsThrow_0, cls_exp_Osimps_I75_J_0, cls_exp_Osimps_I224_J_0, cls_WT__elim__cases_I9_J_0, cls_SeqRedsThrow_0, cls_red__reds_OSeqRed_0, cls_WT__elim__cases_I1_J_0, cls_exp_Osimps_I80_J_0, cls_refl__onD_0, cls_exp_Osimps_I145_J_0, cls_Pair__eq_0, cls_in__lex__prod_3, cls_exp_Osimps_I59_J_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_0, cls_exp_Osimps_I182_J_0, cls_exp_Osimps_I68_J_0, cls_map__le__antisym_0, cls_WT__implies__WTrt_0, cls_LAssRedsThrow_0, cls_WTrt__elim__cases_I2_J_0, cls_step_I5_J_0, cls_exp_Osimps_I4_J_2, cls_exp_Osimps_I216_J_0, cls_exp_Osimps_I203_J_0, cls_exp_Osimps_I57_J_0, cls_red__reds_OCastThrow_0, cls_WTBinOpEq_1, cls_exp_Osimps_I114_J_0, cls_WTrt__elim__cases_I9_J_13, cls_WTrt_H__WTrts_H_Ointros_I18_J_0, cls_exp_Osimps_I191_J_0, cls_rel__list__all2__Cons2_3, cls_WT__elim__cases_I9_J_16, cls_exp_Osimps_I215_J_0, cls_WTCond_0, cls_exp_Osimps_I93_J_0, cls_SeqReds_0, cls_exp_Osimps_I53_J_0, cls_exp_Osimps_I152_J_0, cls_exp_Osimps_I50_J_0, cls_red__reds_OThrowRed_0, cls_val_Osimps_I17_J_0, cls_WTrt__elim__cases_I3_J_1, cls_exp_Osimps_I179_J_0, cls_red__reds_OFAccRed_0, cls_conf__hext_0, cls_exp_Osimps_I54_J_0, cls_refl__onD1_0, cls_exp_Osimps_I8_J_1, cls_CHAINED_0_02, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, cls_val_Osimps_I11_J_0, cls_exp_Osimps_I86_J_0, cls_exp_Osimps_I58_J_0, cls_list__all2__Cons1_3, cls_exp_Osimps_I106_J_0, cls_wt_H__wt_0, cls_exp_Osimps_I66_J_0, cls_exp_Osimps_I6_J_0, cls_exp_Osimps_I108_J_0, cls_exp_Osimps_I222_J_0, cls_red__reds_OBinOpThrow2_0, cls_exp_Osimps_I90_J_0, cls_FAssRedsThrow1_0, cls_exp_Osimps_I12_J_1, cls_WTrtWhile_0, cls_subject__reduction2_1, cls_FAccRedsThrow_0, cls_confs__Cons2_0, cls_widens__Cons_1, cls_widen__trans_0, cls_confs__Cons2_1, cls_exp_Osimps_I155_J_0, cls_red__reds_OCondThrow_0, cls_WTrt_H__WTrts_H_Ointros_I6_J_0, cls_rtrancl_Ortrancl__refl_0, cls_exp_Osimps_I71_J_0, cls_WTrt__elim__cases_I9_J_1, cls_exp_Osimps_I82_J_0, cls_WT__elim__cases_I9_J_1, cls_WT__elim__cases_I5_J_0, cls_exp_Osimps_I14_J_0, cls_confs__hext_0, cls_exp_Osimps_I107_J_0, cls_WTrt__elim__cases_I2_J_3, cls_exp_Osimps_I9_J_2, cls_exp_Osimps_I161_J_0, cls_exp_Osimps_I167_J_0, cls_confs__widens_0, cls_red__reds_ORedCastNull_0, cls_exp_Osimps_I7_J_0, cls_WT__elim__cases_I9_J_18, cls_exp_Osimps_I217_J_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_WTBinOpEq_0, cls_list_Oinject_1, cls_exp_Osimps_I153_J_0, cls_exp_Osimps_I45_J_0, cls_bop_Osimps_I1_J_0, cls_exp_Osimps_I8_J_0, cls_ThrowRedsThrow_0, cls_exp_Osimps_I192_J_0, cls_exp_Osimps_I151_J_0, cls_same__fstI_0, cls_WTrt__elim__cases_I9_J_12, cls_exp_Osimps_I44_J_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_exp_Osimps_I164_J_0, cls_exp_Osimps_I6_J_1, cls_exp_Osimps_I65_J_0, cls_exp_Osimps_I51_J_0, cls_WTrt__elim__cases_I1_J_0, cls_BinOp1Reds_0, cls_red__hext__incr_0, cls_conf__def_1, cls_red__reds_OSeqThrow_0, cls_exp_Osimps_I52_J_0, cls_red__reds_OCastRed_0, cls_WTrt__elim__cases_I8_J_0, cls_exp_Osimps_I187_J_0, cls_FAssReds1_0, cls_exp_Osimps_I15_J_2, cls_list__all2__eq_0, cls_r__into__rtrancl_0, cls_red__reds_OFAccThrow_0, cls_wf_0, cls_exp_Osimps_I10_J_0, cls_wt__env__mono_0, cls_WTrt__elim__cases_I5_J_0, cls_exp_Osimps_I111_J_0, cls_ty_Osimps_I2_J_0, cls_exp_Osimps_I64_J_0, cls_exp_Osimps_I88_J_0, cls_WTrtCond_1, cls_exp_Osimps_I96_J_0, cls_CHAINED_0_03, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I181_J_0, cls_exp_Osimps_I200_J_0, cls_WTrtBinOpAdd_0, cls_ty_Osimps_I10_J_0, cls_WT__elim__cases_I2_J_5, cls_wt__wt_H_0, cls_exp_Osimps_I196_J_0, cls_WT__elim__cases_I2_J_0, cls_exp_Osimps_I214_J_0, cls_exp_Osimps_I168_J_0, cls_WTrtCond_2, cls_exp_Osimps_I63_J_0, cls_conjI__realizer_0, cls_step_I2_J_0, cls_ty_Osimps_I4_J_0, cls_map__le__map__add_0, cls_exp_Osimps_I140_J_0, cls_red__preserves__lconf_0, cls_red__reds_OCondRed_0, cls_map__le__iff__map__add__commute_1, cls_COMBI__def_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_1, cls_Red__lcl__add_0, cls_exp_Osimps_I87_J_0, cls_exp_Osimps_I78_J_0, cls_exp_Osimps_I198_J_0, cls_widens__Cons_3, cls_exp_Osimps_I12_J_0, cls_Pair__eq_1, cls_WTrt__elim__cases_I9_J_2, cls_exp_Osimps_I104_J_0, cls_list__all2__Cons2_3, cls_exp_Osimps_I202_J_0, cls_exp_Osimps_I100_J_0, cls_WT__elim__cases_I3_J_1, cls_exp_Osimps_I163_J_0, cls_red__reds_ORedSeq_0, cls_exp_Osimps_I173_J_0, cls_bop_Osimps_I2_J_0, cls_map__add__le__mapI_0, cls_in__lex__prod_0, cls_exp_Osimps_I147_J_0, cls_red__reds_ORedTry_0, cls_step_Ohyps_I3_J_0, cls_WTrt_H__WTrts_H_Ointros_I20_J_0, cls_fst__conv_0, cls_rel__list__all2__Cons1_3, cls_exp_Osimps_I3_J_0, cls_exp_Osimps_I197_J_0, cls_WT__elim__cases_I6_J_2, cls_WTCond_1, cls_exp_Osimps_I13_J_1
% 44.91/9.79  % No. of inferences in proof: 871
% 44.91/9.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9260 ms resp. 8674 ms w/o parsing
% 46.06/10.21  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 46.06/10.21  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------