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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV957-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:01:07 AM UTC 2026

% Result   : Unsatisfiable 10.07s 3.84s
% Output   : Refutation 11.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  254
% Syntax   : Number of formulae    :  509 ( 145 unt;   0 typ;   0 def)
%            Number of atoms       : 1640 ( 801 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 9815 ( 696   ~;1131   |;   0   &;7988   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   71 (  69 usr;  26 con; 0-8 aty)
%            Number of variables   : 2886 (   0   ^;2886   !;   0   ?;2886   :)

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

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

thf(v_h_Ha_____decl,type,
    v_h_Ha____: $i ).

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

thf(v_e_Ha_____decl,type,
    v_e_Ha____: $i ).

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

thf(v_C_H_____decl,type,
    v_C_H____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_TypeRel_Osees__field_decl,type,
    c_TypeRel_Osees__field: $i > $i > $i > $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_WellType_Osko__WellType__XWT__elim__cases__7__1_decl,type,
    c_WellType_Osko__WellType__XWT__elim__cases__7__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2: $i > $i > $i > $i > $i > $i > $i > $i ).

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

thf(v_ea_____decl,type,
    v_ea____: $i ).

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

thf(v_sko__Type__Xty__Xinducts__1_decl,type,
    v_sko__Type__Xty__Xinducts__1: $i > $i ).

thf(v_sko__local__XIH__1_decl,type,
    v_sko__local__XIH__1: $i > $i > $i > $i > $i > $i ).

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

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

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

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

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

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

thf(v_U_____decl,type,
    v_U____: $i ).

thf(v_F_____decl,type,
    v_F____: $i ).

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

thf(v_e_092_060_094isub_0622_____decl,type,
    v_e_092_060_094isub_0622____: $i ).

thf(v_sko__local__XFAssRed1__2__1_decl,type,
    v_sko__local__XFAssRed1__2__1: $i > $i > $i > $i > $i > $i ).

thf(v_TF_____decl,type,
    v_TF____: $i ).

thf(v_T_092_060_094isub_0622_____decl,type,
    v_T_092_060_094isub_0622____: $i ).

thf(v_sko__local__XFAssRed1__Xhyps__2__1_decl,type,
    v_sko__local__XFAssRed1__Xhyps__2__1: $i > $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xty__Xexhaust__1__1_decl,type,
    c_Type_Osko__Type__Xty__Xexhaust__1__1: $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_Type_Osko__Type__Xty__Xnchotomy__1__1_decl,type,
    c_Type_Osko__Type__Xty__Xnchotomy__1__1: $i > $i ).

thf(v_sko__Value__Xdefault__val__Xinduct__1_decl,type,
    v_sko__Value__Xdefault__val__Xinduct__1: $i > $i ).

thf(v_sko__unknown__thm__BwWZ__1_decl,type,
    v_sko__unknown__thm__BwWZ__1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(v_sko__Type__Xty__Xinduct__1_decl,type,
    v_sko__Type__Xty__Xinduct__1: $i > $i ).

thf(236,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_35) ).

thf(892,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(129,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_28) ).

thf(629,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(128,axiom,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(628,plain,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(189,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I7_J_0) ).

thf(777,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).

thf(481,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(94,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I10_J_0) ).

thf(523,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(19,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_34) ).

thf(308,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(174,axiom,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_TF____ @ ( v_T_092_060_094isub_0622____ @ ( v_P @ c_TypeRel_Owiden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sub_0) ).

thf(741,plain,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_TF____ @ ( v_T_092_060_094isub_0622____ @ ( v_P @ c_TypeRel_Owiden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(69,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I9_J_0) ).

thf(449,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_0) ).

thf(878,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(118,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_6) ).

thf(597,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_I2_J_1) ).

thf(730,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(9,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__field__fun_0) ).

thf(276,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( H @ ( B @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( A @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(124,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_12) ).

thf(614,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(146,axiom,
    ! [A: $i] : ( A @ c_Type_Oty_OClass @ c_Type_Ois__refT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__refT__def_2) ).

thf(677,plain,
    ! [A: $i] : ( A @ c_Type_Oty_OClass @ c_Type_Ois__refT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(98,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has__visible__field_0) ).

thf(533,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(104,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I11_J_0) ).

thf(550,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OBoolean ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I15_J_0) ).

thf(797,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OBoolean ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(162,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IH_1) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(77,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_12) ).

thf(472,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I1_J_0) ).

thf(698,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(177,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_29) ).

thf(747,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(238,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__env__mono_0) ).

thf(898,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( F @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ v_sko__Type__Xty__Xinducts__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oinducts_0) ).

thf(709,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ v_sko__Type__Xty__Xinducts__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(59,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I174_J_0) ).

thf(417,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(233,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_Ohyps_I2_J_0) ).

thf(885,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(109,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Ois__refT )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__refTE_0) ).

thf(565,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Ois__refT )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_1) ).

thf(257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(44,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_27) ).

thf(372,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OInteger ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I19_J_0) ).

thf(934,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OInteger ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(101,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( H @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__field__fun_1) ).

thf(542,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( H @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(246,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_25) ).

thf(917,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( A @ c_Type_Osko__Type__Xty__Xexhaust__1__1 @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oexhaust_0) ).

thf(751,plain,
    ! [A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( A @ c_Type_Osko__Type__Xty__Xexhaust__1__1 @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(199,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( F @ ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I7_J_1) ).

thf(802,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( F @ ( B @ ( D @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__7__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(33,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I24_J_0) ).

thf(344,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(205,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ v_sko__Value__Xdefault__val__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_default__val_Oinduct_0) ).

thf(817,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ v_sko__Value__Xdefault__val__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(107,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I3_J_0) ).

thf(559,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(132,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_4) ).

thf(638,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(227,axiom,
    ( v_U____
    = ( v_C_H____ @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UClass_0) ).

thf(870,plain,
    ( v_U____
    = ( v_C_H____ @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(186,axiom,
    v_T_092_060_094isub_0622____ @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_092_060_094isub_0622_0) ).

thf(770,plain,
    v_T_092_060_094isub_0622____ @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(231,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_9) ).

thf(881,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(13,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_8) ).

thf(289,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(22,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_17) ).

thf(316,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(78,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_16) ).

thf(475,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(194,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_15) ).

thf(789,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(24,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I154_J_0) ).

thf(321,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(253,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_17) ).

thf(937,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(35,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I175_J_0) ).

thf(348,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(37,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I2_J_0) ).

thf(353,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(207,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_0) ).

thf(821,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( B @ c_Expr_Oexp_OCast ) ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(82,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I29_J_0) ).

thf(485,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(212,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).

thf(834,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(71,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I17_J_0) ).

thf(453,plain,
    c_Type_Oty_ONT != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(188,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( J @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( J @ ( I @ ( H @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_24) ).

thf(774,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( J @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( J @ ( I @ ( H @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(62,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_3) ).

thf(428,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(5,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( B @ c_Expr_Oexp_OCast ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I6_J_2) ).

thf(265,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( B @ c_Expr_Oexp_OCast ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(51,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_13) ).

thf(397,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(151,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_0) ).

thf(687,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( E @ ( D @ ( C @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(14,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( D @ ( C @ ( F @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sees__field__idemp_0) ).

thf(292,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( D @ ( C @ ( F @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(247,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_7) ).

thf(920,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(147,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( F @ ( D @ ( G @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTFAcc_0) ).

thf(678,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( F @ ( D @ ( G @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(183,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_35) ).

thf(761,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(202,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_21) ).

thf(810,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(91,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_3) ).

thf(512,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(66,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_2) ).

thf(439,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(7,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I155_J_0) ).

thf(270,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(96,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I11_J_0) ).

thf(529,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(243,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAssNT_0) ).

thf(910,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(224,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAccNT_0) ).

thf(862,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(16,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_28) ).

thf(297,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(153,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_11) ).

thf(693,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(204,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).

thf(815,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

thf(467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(218,axiom,
    ( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_T____ @ ( v_h_Ha____ @ ( v_e_092_060_094isub_0622____ @ ( v_e_Ha____ @ ( v_T____ @ ( v_P @ ( v_F____ @ ( v_E____ @ ( v_D____ @ v_sko__unknown__thm__BwWZ__1 ) ) ) ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) )
    | ( v_U____ != c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_1) ).

thf(847,plain,
    ( ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_T____ @ ( v_h_Ha____ @ ( v_e_092_060_094isub_0622____ @ ( v_e_Ha____ @ ( v_T____ @ ( v_P @ ( v_F____ @ ( v_E____ @ ( v_D____ @ v_sko__unknown__thm__BwWZ__1 ) ) ) ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) )
    | ( v_U____ != c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(40,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I4_J_0) ).

thf(361,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OInteger,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(127,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( L @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_1) ).

thf(625,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( L @ ( K @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(220,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_15) ).

thf(852,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(27,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_32) ).

thf(329,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(141,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( H @ ( C @ ( E @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_3) ).

thf(665,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( H @ ( C @ ( E @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(114,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_15) ).

thf(583,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(235,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_13) ).

thf(889,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(85,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_16) ).

thf(493,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(181,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I6_J_3) ).

thf(757,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( B @ c_Expr_Oexp_OCast ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(149,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_11) ).

thf(682,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(25,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I54_J_0) ).

thf(324,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(72,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_22) ).

thf(456,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(215,axiom,
    v_T_092_060_094isub_0622____ @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_092_060_094isub_0622_H_0) ).

thf(842,plain,
    v_T_092_060_094isub_0622____ @ ( v_e_092_060_094isub_0622____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_Ohyps_I2_J_1) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__Xhyps__2__1 ) ) ) ) @ ( v_P @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(136,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_6) ).

thf(650,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( D @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(168,axiom,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(725,plain,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(54,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I27_J_0) ).

thf(403,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(48,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_10) ).

thf(388,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(38,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_10) ).

thf(356,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(192,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_5) ).

thf(783,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(60,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_2) ).

thf(420,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(232,axiom,
    v_U____ @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(884,plain,
    v_U____ @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(83,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(488,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).

thf(669,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(95,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I7_J_0) ).

thf(526,plain,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(103,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I60_J_0) ).

thf(547,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(158,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_23) ).

thf(706,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(126,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_32) ).

thf(622,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(135,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I8_J_0) ).

thf(647,plain,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(173,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_0) ).

thf(738,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(165,axiom,
    v_U____ @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_092_060_094isub_0621_H_0) ).

thf(721,plain,
    v_U____ @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(190,axiom,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf_0) ).

thf(779,plain,
    tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( v_E____ @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(121,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I160_J_0) ).

thf(605,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(195,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I5_J_0) ).

thf(792,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(20,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I22_J_0) ).

thf(311,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(145,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( E @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_2) ).

thf(674,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( E @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(140,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( C @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( G @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( E @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( B @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_6) ).

thf(662,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( C @ ( E @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( G @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( E @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( B @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(249,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F
        = ( G @ ( H @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( H @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_30) ).

thf(926,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F
        = ( G @ ( H @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( H @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(196,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_27) ).

thf(794,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(115,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I53_J_0) ).

thf(586,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ v_sko__Type__Xty__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oinduct_0) ).

thf(906,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Type_Oty_OVoid @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OBoolean @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_OInteger @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Type_Oty_ONT @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ v_sko__Type__Xty__Xinduct__1 @ c_Type_Oty_OClass @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(57,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I28_J_0) ).

thf(412,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(178,axiom,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_C____ @ c_Type_Oty_OClass @ ( v_U____ @ ( v_P @ c_TypeRel_Owiden ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UsubC_0) ).

thf(750,plain,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_C____ @ c_Type_Oty_OClass @ ( v_U____ @ ( v_P @ c_TypeRel_Owiden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I34_J_0) ).

thf(425,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(208,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_4) ).

thf(824,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(279,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(111,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I12_J_0) ).

thf(573,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(67,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_36) ).

thf(444,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(45,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_24) ).

thf(375,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Oty_OClass )
       != ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).

thf(733,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Type_Oty_OClass )
       != ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(206,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I10_J_0) ).

thf(819,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(108,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I52_J_0) ).

thf(562,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(402,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(171,axiom,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_D____ @ ( v_TF____ @ ( v_F____ @ ( v_C____ @ ( v_P @ c_TypeRel_Ohas__field ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_has_0) ).

thf(732,plain,
    tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_D____ @ ( v_TF____ @ ( v_F____ @ ( v_C____ @ ( v_P @ c_TypeRel_Ohas__field ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(216,axiom,
    ( v_U____
    = ( v_C_H____ @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(843,plain,
    ( v_U____
    = ( v_C_H____ @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(12,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_20) ).

thf(286,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(11,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_1) ).

thf(281,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(102,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OBoolean @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_1) ).

thf(545,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OBoolean @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(3,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_14) ).

thf(259,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(229,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_5) ).

thf(875,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(209,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCast_0) ).

thf(826,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtNew_0) ).

thf(711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Onew ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(133,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( I @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_18) ).

thf(641,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( I @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(49,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_26) ).

thf(391,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(21,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_8) ).

thf(313,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I61_J_0) ).

thf(611,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(29,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I1_J_0) ).

thf(335,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OVoid @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(200,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_17) ).

thf(804,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(100,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I2_J_0) ).

thf(540,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(144,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_7) ).

thf(672,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IH_0) ).

thf(713,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XIH__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I35_J_0) ).

thf(498,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OVoid ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I9_J_0) ).

thf(764,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OVoid ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(211,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_19) ).

thf(831,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(70,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I18_J_0) ).

thf(451,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(239,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_8) ).

thf(900,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( K @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( K @ ( J @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(55,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_25) ).

thf(406,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( I @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(90,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I161_J_0) ).

thf(509,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(64,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_24) ).

thf(434,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(99,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_1) ).

thf(535,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(117,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I5_J_0) ).

thf(594,plain,
    c_Type_Oty_OInteger != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(237,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_9) ).

thf(895,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(142,axiom,
    v_C____ @ c_Type_Oty_OClass @ ( v_ea____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_092_060_094isub_0621_0) ).

thf(668,plain,
    v_C____ @ c_Type_Oty_OClass @ ( v_ea____ @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(251,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I8_J_0) ).

thf(932,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(222,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).

thf(858,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt__env__mono_0) ).

thf(367,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(156,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_7) ).

thf(700,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(93,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_5) ).

thf(520,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( A @ c_Type_Osko__Type__Xty__Xnchotomy__1__1 @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Onchotomy_0) ).

thf(780,plain,
    ! [A: $i] :
      ( ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OBoolean )
      | ( A = c_Type_Oty_OInteger )
      | ( A = c_Type_Oty_ONT )
      | ( A
        = ( A @ c_Type_Osko__Type__Xty__Xnchotomy__1__1 @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I26_J_0) ).

thf(608,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(50,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_23) ).

thf(394,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(6,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I13_J_0) ).

thf(267,plain,
    c_Type_Oty_ONT != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(63,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_14) ).

thf(431,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(137,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( I @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( I @ ( H @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_28) ).

thf(653,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( I @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( I @ ( H @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(244,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).

thf(912,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(150,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I2_J_0) ).

thf(685,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( F @ c_Type_Ois__refT )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( D @ ( A @ c_Decl_Ois__class ) ) )
      | ( D @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(166,axiom,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_ea____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).

thf(722,plain,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_ea____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(84,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_21) ).

thf(490,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( J @ ( G @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(116,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

thf(589,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(97,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I4_J_0) ).

thf(531,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(148,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( C @ ( F @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I7_J_0) ).

thf(680,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( C @ c_Expr_Oexp_OFAcc ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( C @ ( F @ ( A @ ( E @ ( B @ ( D @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(1,negated_conjecture,
    ~ ( v_C_H____ @ c_Type_Oty_OClass @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(255,plain,
    ~ ( v_C_H____ @ c_Type_Oty_OClass @ ( v_e_Ha____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(125,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_1) ).

thf(617,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(180,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OBoolean
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I14_J_0) ).

thf(754,plain,
    ! [A: $i] :
      ( c_Type_Oty_OBoolean
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(105,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_20) ).

thf(553,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(213,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_33) ).

thf(836,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(221,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_14) ).

thf(855,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(152,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_21) ).

thf(690,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(228,axiom,
    ( ( v_h_Ha____ @ ( v_e_092_060_094isub_0622____ @ ( v_e_Ha____ @ ( v_T____ @ ( v_P @ ( v_F____ @ ( v_E____ @ ( v_D____ @ v_sko__unknown__thm__BwWZ__1 ) ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_e_Ha____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
    | ( v_U____ != c_Type_Oty_ONT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_0) ).

thf(872,plain,
    ( ( v_h_Ha____ @ ( v_e_092_060_094isub_0622____ @ ( v_e_Ha____ @ ( v_T____ @ ( v_P @ ( v_F____ @ ( v_E____ @ ( v_D____ @ v_sko__unknown__thm__BwWZ__1 ) ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( v_e_Ha____ @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
    | ( v_U____ != c_Type_Oty_ONT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(234,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( H @ ( G @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTFAss_0) ).

thf(887,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( E @ ( H @ ( D @ ( I @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) )
      | ~ ( G @ ( F @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( H @ ( G @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(26,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I25_J_0) ).

thf(327,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_ONT @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(56,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_6) ).

thf(409,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(163,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_31) ).

thf(717,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(31,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I55_J_0) ).

thf(338,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(39,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OVoid @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_0) ).

thf(359,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OVoid @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(76,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Orecs_I3_J_0) ).

thf(470,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OInteger @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__rec ) ) ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(112,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I8_J_0) ).

thf(576,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(176,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_23) ).

thf(744,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(157,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_20) ).

thf(703,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(138,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_25) ).

thf(656,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I17_J_0) ).

thf(600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(225,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OVoid )
      | ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( L @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( L @ ( K @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_0) ).

thf(864,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OVoid )
      | ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( L @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( L @ ( K @ ( J @ ( I @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(169,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_10) ).

thf(727,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( E @ ( I @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(68,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I6_J_0) ).

thf(446,plain,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(217,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtSeq_0) ).

thf(845,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( F @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(106,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_30) ).

thf(556,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(81,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_34) ).

thf(482,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(240,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( K @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( K @ ( J @ ( I @ ( H @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_16) ).

thf(903,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = c_Type_Oty_OBoolean )
      | ( F = c_Type_Oty_OInteger )
      | ( F = c_Type_Oty_ONT )
      | ( F
        = ( G @ ( K @ ( E @ ( F @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( F @ ( K @ ( J @ ( I @ ( H @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(113,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ ( F @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I7_J_1) ).

thf(581,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ ( D @ ( F @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( A @ ( D @ ( C @ ( B @ c_WellType_Osko__WellType__XWT__elim__cases__7__1 ) ) ) ) ) @ ( A @ c_TypeRel_Osees__field ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(182,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I26_J_0) ).

thf(759,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ c_Type_Oty_OClass @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = ( F @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(187,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_33) ).

thf(771,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_FAssRed1_I2_J_0) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ tc_fun ) @ ( tc_Value_Oval @ tc_Option_Ooption @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_prod ) @ tc_Option_Ooption @ ( tc_nat @ tc_fun ) @ ( v_la____ @ ( v_ha____ @ c_Pair ) ) ) @ ( A @ ( v_P @ c_TypeSafe__Mirabelle_Osconf ) ) )
      | ~ ( B @ ( v_ea____ @ ( A @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( v_h_Ha____ @ ( v_e_Ha____ @ ( B @ ( v_P @ ( A @ v_sko__local__XFAssRed1__2__1 ) ) ) ) @ ( v_e_Ha____ @ ( A @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(92,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I8_J_0) ).

thf(517,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(23,axiom,
    v_T____ = c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_void_0) ).

thf(319,plain,
    v_T____ = c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(36,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OInteger @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_2) ).

thf(351,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_OInteger @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I16_J_0) ).

thf(632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(193,axiom,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I20_J_0) ).

thf(786,plain,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I2_J_0) ).

thf(568,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(250,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_31) ).

thf(929,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(79,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_22) ).

thf(478,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(47,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_0) ).

thf(383,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(34,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_36) ).

thf(346,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(198,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_4) ).

thf(800,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(245,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_19) ).

thf(914,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(46,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

thf(378,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(17,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I11_J_0) ).

thf(300,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(4,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_26) ).

thf(262,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(120,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I23_J_0) ).

thf(603,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( c_Type_Oty_OBoolean @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(226,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_1) ).

thf(867,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( F @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(8,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_30) ).

thf(273,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(18,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_31) ).

thf(305,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(15,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_9) ).

thf(294,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( K @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(32,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( I @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_29) ).

thf(341,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( I @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_ONT )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(89,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_18) ).

thf(506,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(201,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_13) ).

thf(807,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(65,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTSeq_0) ).

thf(437,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( E @ ( D @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(185,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( H @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OInteger ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_26) ).

thf(767,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( H @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OInteger ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Objects_Ohext ) )
      | ~ ( B @ ( C @ c_Objects_Ohext ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__trans_0) ).

thf(400,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Objects_Ohext ) )
      | ~ ( B @ ( C @ c_Objects_Ohext ) )
      | ( B @ ( A @ c_Objects_Ohext ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(210,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_27) ).

thf(828,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OBoolean )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ hAPP ) @ hBOOL )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__asm__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(131,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_18) ).

thf(635,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G = c_Type_Oty_OVoid )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_ONT )
      | ~ ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(154,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I10_J_1) ).

thf(696,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ ( A @ c_Decl_Ois__class ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( A @ c_TypeRel_Owiden ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_2) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( A @ c_TypeRel_Owiden ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(58,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_ONT @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_3) ).

thf(415,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( c_Type_Oty_ONT @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(214,axiom,
    ! [A: $i] :
      ( c_Type_Oty_OInteger
     != ( A @ c_Type_Oty_OClass ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I18_J_0) ).

thf(839,plain,
    ! [A: $i] :
      ( c_Type_Oty_OInteger
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(74,axiom,
    c_Type_Oty_OInteger != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I16_J_0) ).

thf(464,plain,
    c_Type_Oty_OInteger != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(28,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_11) ).

thf(332,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( J @ ( F @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Decl_Ois__class ) ) )
      | ( C @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Onew ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTNew_0) ).

thf(860,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( C @ ( A @ c_Decl_Ois__class ) ) )
      | ( C @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Onew ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(134,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_22) ).

thf(644,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( G @ ( I @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( I @ ( E @ ( D @ ( H @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OBoolean ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(73,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I7_J_1) ).

thf(459,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(242,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit__asm_4) ).

thf(908,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( G @ ( F @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( G @ c_Type_Oty_OClass @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(167,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAss_0) ).

thf(723,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( I @ ( H @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(219,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAcc_0) ).

thf(850,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( G @ ( E @ ( H @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
       != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I1_J_0) ).

thf(501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
       != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(43,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_7) ).

thf(369,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( G @ ( J @ ( I @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OVoid )
      | ( B = c_Type_Oty_OBoolean )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(30,axiom,
    c_Type_Oty_ONT @ c_Type_Ois__refT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_is__refT__def_1) ).

thf(337,plain,
    c_Type_Oty_ONT @ c_Type_Ois__refT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(254,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osplit_29) ).

thf(940,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( G = c_Type_Oty_OInteger )
      | ( G = c_Type_Oty_ONT )
      | ( G
        = ( G @ ( F @ ( A @ v_sko__Type__Xty__Xsplit__1 ) ) @ c_Type_Oty_OClass ) )
      | ( t_a @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I10_J_0) ).

thf(923,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Onew ) @ ( D @ ( C @ c_WellType_OWT ) ) ) )
      | ( A
        = ( B @ c_Type_Oty_OClass ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(139,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_12) ).

thf(659,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = c_Type_Oty_ONT )
      | ( A
        = ( G @ ( J @ ( F @ ( A @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ c_Type_Oty_OClass ) )
      | ( ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( G @ ( A @ ( J @ ( I @ ( D @ ( C @ ( H @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(86,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).

thf(496,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( A @ c_TypeRel_Owiden ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(41,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Ocase__cong_19) ).

thf(364,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) )
        = ( D @ ( B @ ( C @ ( H @ ( J @ ( I @ ( E @ c_Type_Oty_Oty__case ) ) ) ) ) ) ) )
      | ( B = c_Type_Oty_OBoolean )
      | ( B = c_Type_Oty_OInteger )
      | ( ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( A @ ( B @ c_Type_Osko__Type__Xty__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(943,plain,
    $false,
    inference(e,[status(thm)],[892,629,628,777,481,523,308,741,449,878,597,730,276,614,677,533,550,797,715,472,698,747,898,709,417,885,565,257,372,934,542,917,751,802,344,817,559,638,870,770,881,289,316,475,789,321,937,348,353,821,485,834,453,774,428,265,397,687,292,920,678,761,810,512,439,270,529,910,862,297,693,815,467,847,361,625,852,329,665,583,889,493,757,682,324,456,842,742,650,725,403,388,356,783,420,884,488,669,526,547,706,622,647,738,721,779,605,792,311,674,662,926,794,586,906,412,750,425,824,279,573,444,375,733,819,562,402,732,843,286,281,545,259,875,826,711,641,391,313,611,335,804,540,672,713,498,764,831,451,900,406,509,434,535,594,895,668,932,858,367,700,520,780,608,394,267,431,653,912,685,722,490,589,531,680,255,617,754,553,836,855,690,872,887,327,409,717,338,359,470,576,744,703,656,600,864,727,446,845,556,482,903,581,759,771,813,517,319,351,632,786,568,929,478,383,346,800,914,378,300,262,603,867,273,305,294,341,506,807,437,767,400,828,635,696,720,415,839,464,332,860,644,459,908,723,850,501,369,337,940,923,659,496,364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV957-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39  % Computer : n015.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8046.5625MB
% 0.13/0.39  % OS       : Linux 6.8.0-71-generic
% 0.13/0.39  % CPULimit : 300
% 0.13/0.39  % WCLimit  : 300
% 0.13/0.39  % DateTime : Sat Sep 26 15:17:58 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.83/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.81/1.30  % [INFO] 	 Parsing done (306ms). 
% 1.81/1.31  % [INFO] 	 Running in sequential loop mode. 
% 2.41/1.69  % [INFO] 	 eprover registered as external prover. 
% 2.62/1.70  % [INFO] 	 Scanning for conjecture ... 
% 2.83/1.86  % [INFO] 	 Found a conjecture (or negated_conjecture) and 255 axioms. Running axiom selection ... 
% 3.06/2.02  % [INFO] 	 Axiom selection finished. Selected 253 axioms (removed 2 axioms). 
% 4.26/2.22  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.26/2.24  % [INFO] 	 Type checking passed. 
% 4.26/2.24  % [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 ... 
% 10.07/3.84  % External prover 'e' found a proof!
% 10.07/3.84  % [INFO] 	 Killing All external provers ... 
% 10.07/3.84  % Time passed: 3293ms (effective reasoning time: 2518ms)
% 10.07/3.84  % Axioms used in derivation (253): cls_ty_Osplit__asm_29, cls_WTrt__elim__cases_I8_J_3, cls_WTFAcc_0, cls_IH_0, cls_WTSeq_0, cls_ty_Osplit__asm_23, cls_ty_Osplit__asm_12, cls_ty_Osplit_9, cls_ty_Osplit_4, cls_ty_Osplit__asm_30, cls_ty_Osplit_24, cls_UClass_0, cls_default__val_Oinduct_0, cls_FAssRed1_I2_J_1, cls_ty_Ocase__cong_5, cls_ty_Osimps_I22_J_0, cls_ty_Ocase__cong_14, cls_ty_Ocase__cong_4, cls_exp_Osimps_I7_J_2, cls_map__le__trans_0, cls_ty_Osplit_5, cls_ty_Osimps_I17_J_0, cls_ty_Osimps_I25_J_0, cls_WTrt__elim__cases_I10_J_0, cls_ty_Osplit__asm_34, cls_CHAINED_0, cls_WT__elim__cases_I8_J_0, cls_exp_Osimps_I11_J_0, cls_WT__elim__cases_I10_J_1, cls_ty_Ocase__cong_25, cls_ty_Osplit_0, cls_has_0, cls_ty_Osplit_11, cls_ty_Ocase__cong_28, cls_has__visible__field_0, cls_ty_Osimps_I8_J_0, cls_ty_Ocase__cong_20, cls_ty_Osplit_27, cls_exp_Osimps_I28_J_0, cls_ty_Osplit__asm_28, cls_ty_Ocase__cong_18, cls_ty_Osimps_I5_J_0, cls_not__refTE_0, cls_widen__Class_2, cls_ty_Ocase__cong_8, cls_ty_Osplit_32, cls_exp_Osimps_I154_J_0, cls_WTrt__elim__cases_I6_J_0, cls_COMBI__def__raw_0, cls_WTrt__elim__cases_I10_J_1, cls_ty_Osplit_16, cls_ty_Osimps_I20_J_0, cls_ty_Osplit__asm_5, cls_ty_Osplit_21, cls_ty_Osimps_I13_J_0, cls_WT__elim__cases_I7_J_1, cls_WTrt__elim__cases_I8_J_7, cls_ty_Osplit_14, cls_ty_Osplit_36, cls_exp_Osimps_I2_J_1, cls_ty_Ocase__cong_31, cls_exp_Osimps_I8_J_3, cls_ty_Osplit_10, cls_ty_Osimps_I24_J_0, cls_exp_Osimps_I11_J_1, cls_exp_Osimps_I175_J_0, cls_WTrt_H__WTrts_H_Ointros_I9_J_0, cls_WTrt__elim__cases_I6_J_3, cls_ty_Osplit__asm_17, cls_ty_Osplit_25, cls_ty_Onchotomy_0, cls_ty_Osplit__asm_9, cls_ty_Osplit__asm_26, cls_ty_Ocase__cong_13, cls_widen__refl_0, cls_exp_Osimps_I17_J_0, cls_WTrt__elim__cases_I8_J_6, cls_hext__trans_0, cls_exp_Osimps_I160_J_0, cls_ty_Ocase__cong_29, cls_ty_Osplit__asm_15, cls_hext__refl_0, cls_exp_Osimps_I29_J_0, cls_ty_Osimps_I11_J_0, cls_ty_Osplit_12, cls_ty_Osplit_6, cls_exp_Osimps_I174_J_0, cls_ty_Osimps_I9_J_0, cls_ty_Osimps_I3_J_0, cls_ty_Ocase__cong_26, cls_WTrtFAssNT_0, cls_ty_Osplit__asm_19, cls_void_0, cls_ty_Ocase__cong_3, cls_conf_0, cls_CHAINED_0_01, cls_map__le__refl_0, cls_WTrtFAccNT_0, cls_wt_092_060_094isub_0621_0, cls_WTrt__hext__mono_0, cls_WTrtFAss_0, cls_WTFAss_0, cls_WTrt_H__WTrts_H_Ointros_I11_J_0, cls_ty_Osimps_I12_J_0, cls_ty_Osplit__asm_18, cls_ty_Osplit_13, cls_exp_Osimps_I61_J_0, cls_WTrt__env__mono_0, cls_ty_Osplit_1, cls_exp_Osimps_I26_J_0, cls_WT__elim__cases_I6_J_0, cls_ty_Osplit__asm_33, cls_ty_Osimps_I19_J_0, cls_exp_Osimps_I8_J_2, cls_WTrtNew_0, cls_ty_Osimps_I18_J_0, cls_ty_Osimps_I15_J_0, cls_calculation_0, cls_ty_Ocase__cong_7, cls_exp_Osimps_I2_J_0, cls_ty_Osplit__asm_6, cls_ty_Ocase__cong_17, cls_ty_Osplit_22, cls_sub_0, cls_ty_Osplit_33, cls_exp_Osimps_I27_J_0, cls_WTrt_H__WTrts_H_Ointros_I2_J_0, cls_ty_Osplit__asm_22, cls_is__refT__def_1, cls_ty_Osimps_I7_J_0, cls_ty_Osplit__asm_11, cls_ty_Osplit_35, cls_ty_Ocase__cong_30, cls_exp_Osimps_I60_J_0, cls_ty_Orecs_I1_J_0, cls_ty_Osplit_19, cls_ty_Osimps_I16_J_0, cls_ty_Osplit_2, cls_ty_Ocase__cong_9, cls_exp_Osimps_I7_J_1, cls_WTrtSeq_0, cls_wt_092_060_094isub_0622_0, cls_ty_Osimps_I26_J_0, cls_exp_Osimps_I55_J_0, cls_ty_Osplit_29, cls_exp_Osimps_I16_J_0, cls_ty_Osplit__asm_25, cls_ty_Osplit__asm_10, cls_Pair__eq_0, cls_ty_Osplit_30, cls_ty_Ocase__cong_12, cls_ty_Osplit_7, cls_exp_Osimps_I1_J_0, cls_exp_Osimps_I35_J_0, cls_ty_Osplit__asm_36, cls_WT__implies__WTrt_0, cls_wt_0, cls_ty_Oinject_0, cls_map__le__antisym_0, cls_ty_Osplit_18, cls_calculation_1, cls_wt_092_060_094isub_0621_H_0, cls_FAssRed1_Ohyps_I2_J_0, cls_ty_Ocase__cong_10, cls_WTrt_H__WTrts_H_Ointros_I18_J_0, cls_ty_Osplit__asm_14, cls_FAssRed1_Ohyps_I2_J_1, cls_ty_Osplit__asm_32, cls_ty_Ocase__cong_2, cls_WTrt_H__WTrts_H_Ointros_I8_J_0, cls_ty_Orecs_I2_J_0, cls_exp_Osimps_I53_J_0, cls_ty_Orecs_I3_J_0, cls_ty_Ocase__cong_22, cls_WTrtFAcc_0, cls_ty_Oinduct_0, cls_exp_Osimps_I54_J_0, cls_exp_Osimps_I8_J_1, cls_ty_Orecs_I4_J_0, cls_WTNew_0, cls_exp_Osimps_I34_J_0, cls_ty_Osimps_I21_J_0, cls_wt_H__wt_0, cls_wt_092_060_094isub_0622_H_0, cls_ty_Osplit__asm_7, cls_ty_Osplit_8, cls_ty_Osplit_23, cls_ty_Osimps_I23_J_0, cls_widen__trans_0, cls_WTrt__elim__cases_I7_J_1, cls_is__refT__def_2, cls_ty_Osimps_I6_J_0, cls_exp_Osimps_I155_J_0, cls_ty_Ocase__cong_16, cls_ty_Osplit_34, cls_sees__field__fun_1, cls_ty_Osplit__asm_21, cls_ty_Osplit__asm_8, cls_ty_Osplit__asm_13, cls_exp_Osimps_I161_J_0, cls_ty_Osplit__asm_24, cls_exp_Osimps_I7_J_0, cls_ty_Orecs_I5_J_0, cls_WTrt__elim__cases_I8_J_4, cls_ty_Ocase__cong_24, cls_ty_Osplit__asm_35, cls_exp_Osimps_I8_J_0, cls_ty_Ocase__cong_0, cls_ty_Ocase__cong_27, cls_ty_Ocase__cong_11, cls_WTrt_H__WTrts_H_Ointros_I1_J_0, cls_ty_Osplit_17, cls_ty_Osimps_I2_J_0, cls_exp_Osimps_I52_J_0, cls_ty_Ocase__cong_15, cls_WTrt__elim__cases_I8_J_0, cls_ty_Oexhaust_0, cls_ty_Osplit__asm_20, cls_ty_Ocase__cong_6, cls_WT__elim__cases_I10_J_0, cls_ty_Osplit_28, cls_wt__env__mono_0, cls_sees__field__idemp_0, cls_sees__field__fun_0, cls_ty_Osplit_26, cls_WT__elim__cases_I7_J_0, cls_ty_Osimps_I14_J_0, cls_ty_Osimps_I10_J_0, cls_ty_Osplit__asm_4, cls_wt__wt_H_0, cls_ty_Ocase__cong_19, cls_ty_Osimps_I4_J_0, cls_ty_Osplit_15, cls_UsubC_0, cls_ty_Ocase__cong_1, cls_COMBI__def_0, cls_ty_Osplit__asm_27, cls_ty_Osplit_31, cls_Pair__eq_1, cls_ty_Oinducts_0, cls_FAssRed1_I2_J_0, cls_WTrt__elim__cases_I7_J_0, cls_WTrtCast_0, cls_ty_Osplit__asm_16, cls_WTrt_H__WTrts_H_Ointros_I10_J_0, cls_ty_Ocase__cong_21, cls_WT__elim__cases_I6_J_2, cls_ty_Osplit_3, cls_ty_Osplit__asm_31, cls_ty_Ocase__cong_23, cls_IH_1, cls_WTrt__elim__cases_I8_J_1, cls_ty_Osplit_20
% 10.07/3.84  % No. of inferences in proof: 509
% 10.07/3.84  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3293 ms resp. 2518 ms w/o parsing
% 11.02/4.07  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.02/4.08  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------