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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV962-1 : 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 : n005.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 09:01:08 AM UTC 2026

% Result   : Unsatisfiable 12.50s 3.92s
% Output   : Refutation 13.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  407
% Syntax   : Number of formulae    :  815 ( 561 unt;   0 typ;   0 def)
%            Number of atoms       : 1214 ( 695 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 11321 ( 804   ~; 399   |;   0   &;10118   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   67 (  65 usr;  21 con; 0-21 aty)
%            Number of variables   : 5316 (   0   ^;5316   !;   0   ?;5316   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_v_____decl,type,
    v_v____: $i ).

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

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

thf(v_e_092_060_094isub_0622_H_____decl,type,
    v_e_092_060_094isub_0622_H____: $i ).

thf(c_DefAss_O_092_060D_062_decl,type,
    c_DefAss_O_092_060D_062: $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

thf(c_Expr_Oexp_OVar_decl,type,
    c_Expr_Oexp_OVar: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Expr_Oexp_Oexp__rec__1_decl,type,
    c_Expr_Oexp_Oexp__rec__1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

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

thf(c_Expr_Oexp_Oexp__case_decl,type,
    c_Expr_Oexp_Oexp__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $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__4_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4: $i > $i > $i > $i > $i ).

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3: $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(c_TypeRel_Ohas__field_decl,type,
    c_TypeRel_Ohas__field: $i > $i > $i > $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

thf(c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1_decl,type,
    c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(v_T_092_060_094isub_0622_H_____decl,type,
    v_T_092_060_094isub_0622_H____: $i ).

thf(130,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_0) ).

thf(809,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(318,axiom,
    c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622_H____ @ ( v_D____ @ ( v_F____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1337,plain,
    c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622_H____ @ ( v_D____ @ ( v_F____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_DefAss_O_092_060D_062 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I3_J_0) ).

thf(1168,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_DefAss_O_092_060D_062 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(368,axiom,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( T @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OFAss ) ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( S @ ( R @ ( Q @ ( P @ ( H @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I233_J_0) ).

thf(1454,plain,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( T @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OFAss ) ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( S @ ( R @ ( Q @ ( P @ ( H @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedSeq_0) ).

thf(1237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(214,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I122_J_0) ).

thf(1083,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(170,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I224_J_0) ).

thf(941,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ c_Objects_Otypeof__h ) )
        = ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) )
      | ~ ( D @ ( A @ c_Objects_Ohext ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__typeof__mono_0) ).

thf(555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ c_Objects_Otypeof__h ) )
        = ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) )
      | ~ ( D @ ( A @ c_Objects_Ohext ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(332,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( F @ ( E @ ( G @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Seq_0) ).

thf(1369,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ c_Expr_Oexp_OVal ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( F @ ( E @ ( G @ ( C @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( E @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I91_J_0) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622_H____ @ ( v_D____ @ ( v_F____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( v_T____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(408,plain,
    ! [A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622_H____ @ ( v_D____ @ ( v_F____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( v_T____ @ ( A @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(262,axiom,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OVal ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( C @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I228_J_0) ).

thf(1211,plain,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OVal ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( C @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(396,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__2 ) ) ) ) ) ) @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_13) ).

thf(1522,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__2 ) ) ) ) ) ) @ ( G @ ( B @ ( D @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_ONT @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(364,axiom,
    ! [X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( X @ ( V @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OFAss ) ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( X @ ( V @ ( W @ ( U @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X @ ( V @ ( W @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( U @ ( T @ ( S @ ( R @ ( H @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I8_J_0) ).

thf(1443,plain,
    ! [X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( X @ ( V @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OFAss ) ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( X @ ( V @ ( W @ ( U @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X @ ( V @ ( W @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( U @ ( T @ ( S @ ( R @ ( H @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(353,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_ORedTry_0) ).

thf(1422,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(260,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(1205,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)],[260]) ).

thf(235,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(1142,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)],[235]) ).

thf(80,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I203_J_0) ).

thf(655,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(201,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_1) ).

thf(1041,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I11_J_0) ).

thf(523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OSeq ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I151_J_0) ).

thf(762,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(355,axiom,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_OVar ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( E @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I5_J_0) ).

thf(1426,plain,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_OVar ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(30,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I184_J_0) ).

thf(500,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(131,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I141_J_0) ).

thf(814,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(285,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I170_J_0) ).

thf(1260,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(325,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( E @ c_Expr_Oexp_OSeq ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OSeqRed_0) ).

thf(1354,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( E @ c_Expr_Oexp_OSeq ) ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(370,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I172_J_0) ).

thf(1458,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(86,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I191_J_0) ).

thf(670,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(268,axiom,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OSeq ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( K @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I236_J_0) ).

thf(1222,plain,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OSeq ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( K @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(167,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I124_J_0) ).

thf(930,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(218,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I59_J_0) ).

thf(1095,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I4_J_0) ).

thf(1196,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ c_WellType_OWT ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(189,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I109_J_0) ).

thf(1001,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(229,axiom,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OWhile ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( V @ ( T @ ( U @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( M @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I13_J_0) ).

thf(1127,plain,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OWhile ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( V @ ( T @ ( U @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( M @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(341,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(1391,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)],[341]) ).

thf(202,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I145_J_0) ).

thf(1046,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(331,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I87_J_0) ).

thf(1366,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(400,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I76_J_0) ).

thf(1529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(287,axiom,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1265,plain,
    ( ( t_a @ ( v_P @ c_COMBI ) )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(380,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(1482,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)],[380]) ).

thf(122,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I143_J_0) ).

thf(782,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(363,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( H @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 ) ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_2) ).

thf(1441,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( E @ ( B @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( H @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 ) ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I23_J_0) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(298,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 @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Try_0) ).

thf(1287,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 @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_OVal ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(357,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(1430,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)],[357]) ).

thf(123,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I218_J_0) ).

thf(785,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(316,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(1330,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)],[316]) ).

thf(309,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_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I79_J_0) ).

thf(1313,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_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OThrowThrow_0) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(173,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I135_J_0) ).

thf(949,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(313,axiom,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OBinOp ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I229_J_0) ).

thf(1323,plain,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OBinOp ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(70,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I215_J_0) ).

thf(619,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(163,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_1) ).

thf(917,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I95_J_0) ).

thf(702,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(113,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( B @ ( A @ ( D @ c_Conform_Oconf ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typeof__conf_0) ).

thf(751,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( C @ ( B @ ( A @ ( D @ c_Conform_Oconf ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(407,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCond_0) ).

thf(1545,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(337,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I78_J_0) ).

thf(1379,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OSeqThrow_0) ).

thf(1247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(6,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_0) ).

thf(421,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(379,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I77_J_0) ).

thf(1479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(322,axiom,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OCall ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( I @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I234_J_0) ).

thf(1347,plain,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OCall ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( I @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(344,axiom,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OVar ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( E @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I230_J_0) ).

thf(1398,plain,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OVar ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( E @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(329,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OBoolean @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I2_J_0) ).

thf(1362,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OBoolean @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(272,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_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I101_J_0) ).

thf(1232,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_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(132,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I110_J_0) ).

thf(817,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I211_J_0) ).

thf(902,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(193,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I186_J_0) ).

thf(1013,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(118,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).

thf(770,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_1) ).

thf(448,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(384,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( E @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCond_2) ).

thf(1494,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( E @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I19_J_0) ).

thf(1465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(304,axiom,
    v_T_092_060_094isub_0622____ @ ( v_T_092_060_094isub_0622_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_HsubT_0) ).

thf(1302,plain,
    v_T_092_060_094isub_0622____ @ ( v_T_092_060_094isub_0622_H____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(55,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I65_J_0) ).

thf(574,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(129,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I21_J_0) ).

thf(806,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(159,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I152_J_0) ).

thf(905,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(382,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I93_J_0) ).

thf(1489,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(349,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_2) ).

thf(1415,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(334,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__elim__cases_I5_J_0) ).

thf(1373,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I117_J_0) ).

thf(443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(25,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I129_J_0) ).

thf(485,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I18_J_0) ).

thf(1136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(251,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__trans_0) ).

thf(1183,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ~ ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) )
      | ( tc_Type_Oty @ ( tc_Type_Oty @ ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(296,axiom,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_Othrow ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( N @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I239_J_0) ).

thf(1283,plain,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_Othrow ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( N @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(336,axiom,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( T @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( S @ ( R @ ( Q @ ( P @ ( O @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I240_J_0) ).

thf(1377,plain,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( T @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( S @ ( R @ ( Q @ ( P @ ( O @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(264,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OThrowThrow_0) ).

thf(1215,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(108,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I6_J_0) ).

thf(734,plain,
    c_Type_Oty_OVoid != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(148,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(866,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)],[148]) ).

thf(16,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I105_J_0) ).

thf(453,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(324,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I71_J_0) ).

thf(1351,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I66_J_0) ).

thf(660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(188,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I94_J_0) ).

thf(998,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(346,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(1405,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)],[346]) ).

thf(65,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I206_J_0) ).

thf(602,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(183,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(981,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)],[183]) ).

thf(246,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(1169,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)],[246]) ).

thf(92,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I219_J_0) ).

thf(687,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(211,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_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I107_J_0) ).

thf(1074,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_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(34,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_0) ).

thf(512,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(361,axiom,
    v_T_092_060_094isub_0622_H____ @ ( v_e_092_060_094isub_0622_H____ @ ( 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(1438,plain,
    v_T_092_060_094isub_0622_H____ @ ( v_e_092_060_094isub_0622_H____ @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I202_J_0) ).

thf(546,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(165,axiom,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I7_J_0) ).

thf(925,plain,
    c_Type_Oty_ONT != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(306,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( H @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( C @ ( H @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( 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_9) ).

thf(1306,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( H @ c_Expr_Oexp_OFAss ) ) ) ) @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( C @ ( H @ ( B @ ( G @ ( D @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(258,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I180_J_0) ).

thf(1199,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(239,axiom,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OBlock ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( J @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I235_J_0) ).

thf(1153,plain,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OBlock ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( J @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I85_J_0) ).

thf(1338,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(376,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I45_J_0) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I49_J_0) ).

thf(534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(101,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I112_J_0) ).

thf(714,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(242,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__trans_0) ).

thf(1163,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(291,axiom,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OLAss ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( F @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I231_J_0) ).

thf(1274,plain,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OLAss ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( F @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(156,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_1) ).

thf(894,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(120,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I115_J_0) ).

thf(778,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(174,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(952,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)],[174]) ).

thf(395,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I182_J_0) ).

thf(1519,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(283,axiom,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OFAcc ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( G @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I7_J_0) ).

thf(1255,plain,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OFAcc ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( G @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(227,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I146_J_0) ).

thf(1123,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(265,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I10_J_0) ).

thf(1217,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_Progress_OWTrt_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(381,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(1487,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)],[381]) ).

thf(8,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I128_J_0) ).

thf(429,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(124,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(788,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)],[124]) ).

thf(275,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( E @ ( A @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtVal_0) ).

thf(1238,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( E @ ( A @ ( D @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(388,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I176_J_0) ).

thf(1502,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(133,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I114_J_0) ).

thf(820,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(94,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I57_J_0) ).

thf(693,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(73,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I137_J_0) ).

thf(630,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(354,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_1) ).

thf(1423,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I9_J_0) ).

thf(467,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCall ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

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

thf(583,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I149_J_0) ).

thf(1027,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(115,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).

thf(757,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I74_J_0) ).

thf(1291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(221,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I7_J_0) ).

thf(1106,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I125_J_0) ).

thf(847,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(52,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I7_J_1) ).

thf(566,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_DefAss_O_092_060D_062 ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
       != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I14_J_0) ).

thf(852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
       != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

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

thf(435,plain,
    c_Type_Oty_ONT != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(17,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I157_J_0) ).

thf(456,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(140,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(842,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)],[140]) ).

thf(216,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I42_J_0) ).

thf(1089,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(289,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssThrow1_0) ).

thf(1270,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(315,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(1328,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)],[315]) ).

thf(335,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OBoolean @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I2_J_0) ).

thf(1375,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( c_Type_Oty_OBoolean @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I13_J_0) ).

thf(1064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( D @ ( A @ c_Expr_Oexp_OWhile ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I44_J_0) ).

thf(1227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(105,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I197_J_0) ).

thf(725,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(386,axiom,
    ! [X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( X @ ( V @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( X @ ( V @ ( W @ ( U @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X @ ( V @ ( W @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( U @ ( T @ ( S @ ( R @ ( O @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I15_J_0) ).

thf(1498,plain,
    ! [X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( X @ ( V @ ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( X @ ( V @ ( W @ ( U @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( X @ ( V @ ( W @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( U @ ( T @ ( S @ ( R @ ( O @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(405,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I181_J_0) ).

thf(1540,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I48_J_0) ).

thf(593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(149,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I188_J_0) ).

thf(869,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(145,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I69_J_0) ).

thf(857,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I90_J_0) ).

thf(1160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(26,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I47_J_0) ).

thf(488,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(328,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCondThrow_0) ).

thf(1361,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(168,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(933,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)],[168]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I2_J_1) ).

thf(679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(240,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(1155,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)],[240]) ).

thf(351,axiom,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OCond ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( L @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I237_J_0) ).

thf(1419,plain,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OCond ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( L @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( A @ c_BigStep_Oeval ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Val_0) ).

thf(1461,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( A @ c_BigStep_Oeval ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I210_J_0) ).

thf(537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(194,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I199_J_0) ).

thf(1016,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(61,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I36_J_0) ).

thf(590,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(71,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(622,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)],[71]) ).

thf(238,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I120_J_0) ).

thf(1150,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(302,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 @ c_Expr_Oexp_Othrow ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow1_0) ).

thf(1297,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 @ c_Expr_Oexp_Othrow ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

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

thf(1451,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I72_J_0) ).

thf(1131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) ) ) )
      | ~ ( D @ ( F @ ( E @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__widen_0) ).

thf(1525,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) ) ) )
      | ~ ( D @ ( F @ ( E @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
       != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I5_J_0) ).

thf(647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
       != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(286,axiom,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OFAcc ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( G @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I232_J_0) ).

thf(1263,plain,
    ! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( S @ ( T @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OFAcc ) ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( Q @ ( P @ ( G @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(404,axiom,
    v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( 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(1539,plain,
    v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_h_Ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(369,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OCondThrow_0) ).

thf(1456,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ c_Expr_Oexp_Othrow ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I88_J_0) ).

thf(1382,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I126_J_0) ).

thf(984,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(161,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I213_J_0) ).

thf(911,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(342,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed1_0) ).

thf(1393,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(31,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I192_J_0) ).

thf(503,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(66,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I190_J_0) ).

thf(605,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(359,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(1434,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)],[359]) ).

thf(311,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I173_J_0) ).

thf(1318,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(259,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(1202,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)],[259]) ).

thf(276,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I80_J_0) ).

thf(1241,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(74,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(633,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)],[74]) ).

thf(117,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(765,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)],[117]) ).

thf(199,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I205_J_0) ).

thf(1035,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(393,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(1515,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)],[393]) ).

thf(252,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_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I178_J_0) ).

thf(1185,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I37_J_0) ).

thf(586,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(154,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(888,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)],[154]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I41_J_0) ).

thf(1086,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(169,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I198_J_0) ).

thf(938,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I6_J_0) ).

thf(558,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(210,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(1071,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)],[210]) ).

thf(294,axiom,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_Onew ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I1_J_0) ).

thf(1278,plain,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_Onew ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(3,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I43_J_0) ).

thf(412,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(281,axiom,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_Othrow ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( U @ ( S @ ( T @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( R @ ( N @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I14_J_0) ).

thf(1251,plain,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_Othrow ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( U @ ( S @ ( T @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( R @ ( N @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(266,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( I @ ( E @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OFAssThrow2_0) ).

thf(1219,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( I @ ( tc_String_Ochar @ tc_List_Olist @ ( J @ c_Expr_Oexp_OVal ) @ ( F @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( I @ ( E @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(181,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I3_J_0) ).

thf(975,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_OVoid,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(191,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I216_J_0) ).

thf(1007,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(340,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_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I121_J_0) ).

thf(1388,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_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(111,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(743,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)],[111]) ).

thf(402,axiom,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OCast ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( B @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I227_J_0) ).

thf(1535,plain,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OCast ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( B @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I167_J_0) ).

thf(958,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Option_Ooption_OSome ) )
       != ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Option_Ooption_OSome ) )
       != ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(135,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I4_J_0) ).

thf(826,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OBinOp ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(56,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I159_J_0) ).

thf(577,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(100,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I163_J_0) ).

thf(711,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(234,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I83_J_0) ).

thf(1139,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(308,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(1312,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)],[308]) ).

thf(206,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I217_J_0) ).

thf(1058,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(217,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(1092,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)],[217]) ).

thf(128,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I12_J_0) ).

thf(804,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( E @ ( D @ ( A @ c_Expr_Oexp_OCond ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I6_J_1) ).

thf(947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(269,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(1224,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)],[269]) ).

thf(326,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_1) ).

thf(1356,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).

thf(540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I67_J_0) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(356,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCond_1) ).

thf(1428,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( E @ ( D @ ( C @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(290,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(1271,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)],[290]) ).

thf(333,axiom,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_OVal ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( C @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I3_J_0) ).

thf(1371,plain,
    ! [U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( U @ ( S @ ( T @ ( S @ ( R @ c_Expr_Oexp_OVal ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( R @ ( C @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(256,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__evals_OSeqThrow_0) ).

thf(1194,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( B @ ( A @ c_BigStep_Oeval ) ) ) ) )
      | ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ ( B @ c_Expr_Oexp_OSeq ) ) @ ( A @ c_BigStep_Oeval ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(225,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I207_J_0) ).

thf(1117,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(397,axiom,
    v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_092_060_094isub_0621_0) ).

thf(1524,plain,
    v_C____ @ c_Type_Oty_OClass @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(323,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(1349,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)],[323]) ).

thf(186,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(990,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)],[186]) ).

thf(383,axiom,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_Onew ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I226_J_0) ).

thf(1492,plain,
    ! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( Q @ ( R @ ( Q @ ( P @ c_Expr_Oexp_Onew ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( P @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(109,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(737,plain,
    ! [A: $i] :
      ( c_Type_Oty_ONT
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I132_J_0) ).

thf(616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(90,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I209_J_0) ).

thf(681,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(347,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(1408,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)],[347]) ).

thf(33,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_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I46_J_0) ).

thf(509,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_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(152,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I185_J_0) ).

thf(880,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(64,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I62_J_0) ).

thf(599,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(362,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtFAss_0) ).

thf(1439,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( J @ c_Type_Oty_OClass @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( F @ ( I @ ( E @ ( J @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ~ ( H @ ( G @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( I @ ( H @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(147,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I20_J_0) ).

thf(863,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(248,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_14) ).

thf(1175,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(23,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I10_J_2) ).

thf(477,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I39_J_0) ).

thf(552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(36,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I30_J_0) ).

thf(520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I75_J_0) ).

thf(1325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I38_J_0) ).

thf(964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(321,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I177_J_0) ).

thf(1344,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(196,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_0) ).

thf(1022,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(249,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(1177,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)],[249]) ).

thf(28,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I189_J_0) ).

thf(494,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I133_J_0) ).

thf(1080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(19,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_1) ).

thf(462,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = G )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(207,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(1061,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)],[207]) ).

thf(263,axiom,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OCast ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I2_J_0) ).

thf(1213,plain,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OCast ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(153,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(883,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)],[153]) ).

thf(67,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(608,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)],[67]) ).

thf(330,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(1364,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)],[330]) ).

thf(385,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( B @ ( D @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( 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_10) ).

thf(1496,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E @ ( B @ ( D @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( E @ ( 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)],[385]) ).

thf(11,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(438,plain,
    ! [A: $i] :
      ( c_Type_Oty_OVoid
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I148_J_0) ).

thf(922,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(81,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(658,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)],[81]) ).

thf(75,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_2) ).

thf(636,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(278,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(1245,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)],[278]) ).

thf(209,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I6_J_0) ).

thf(1066,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OLAss ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(365,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(1445,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)],[365]) ).

thf(223,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I144_J_0) ).

thf(1113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(51,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I134_J_0) ).

thf(563,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( F @ ( E @ ( D @ ( C @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(104,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I201_J_0) ).

thf(722,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(83,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(663,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__Class_2) ).

thf(1277,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ c_Type_Oty_OClass @ ( c_Type_Oty_ONT @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(232,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OThrowRed_0) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ c_Expr_Oexp_Othrow ) @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_Othrow ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(391,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 ) ) ) ) )
      | ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = c_Type_Oty_OVoid ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_12) ).

thf(1509,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 ) ) ) ) )
      | ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( H @ ( G @ ( F @ ( B @ ( E @ ( D @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( B @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = c_Type_Oty_OVoid ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(236,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I183_J_0) ).

thf(1145,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(114,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(754,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OBoolean ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(134,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I51_J_0) ).

thf(823,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(138,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I153_J_0) ).

thf(836,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I116_J_0) ).

thf(1049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(7,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I96_J_0) ).

thf(426,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(244,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I8_J_0) ).

thf(1166,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(261,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(1208,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)],[261]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Onew ) @ c_DefAss_O_092_060D_062 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I1_J_0) ).

thf(589,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Onew ) @ c_DefAss_O_092_060D_062 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I220_J_0) ).

thf(531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(171,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I200_J_0) ).

thf(944,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(38,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I194_J_0) ).

thf(525,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(57,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I204_J_0) ).

thf(580,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(93,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I63_J_0) ).

thf(690,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(150,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I187_J_0) ).

thf(872,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(98,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I118_J_0) ).

thf(705,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(345,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(1400,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)],[345]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(271,axiom,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OSeq ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( V @ ( T @ ( U @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( K @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I11_J_0) ).

thf(1230,plain,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OSeq ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( V @ ( T @ ( U @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( K @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(219,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(1098,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)],[219]) ).

thf(87,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I58_J_0) ).

thf(673,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(358,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( E @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_5) ).

thf(1432,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( F @ ( G @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( E @ ( A @ ( G @ ( C @ ( F @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ c_Type_Oty_OClass @ ( E @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(125,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_3) ).

thf(791,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = I )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(253,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(1188,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)],[253]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(441,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_COMBI ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(200,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I103_J_0) ).

thf(1038,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(102,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I169_J_0) ).

thf(717,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(273,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( E @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCond_0) ).

thf(1235,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( F @ ( G @ c_Expr_Oexp_OCond ) ) ) @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( G @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( F @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( E @ ( D @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(297,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( H @ ( D @ ( G @ ( F @ ( A @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 ) ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I5_J_0) ).

thf(1285,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( H @ ( G @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( B @ ( H @ ( D @ ( G @ ( F @ ( A @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__5__1 ) ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(327,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( E @ ( A @ ( D @ c_Progress_OWTrt_H ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I3_J_0) ).

thf(1358,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( E @ ( A @ ( D @ c_Progress_OWTrt_H ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(406,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OTryRed_0) ).

thf(1543,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( G @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( B @ c_Expr_Oexp_OTryCatch ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(284,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).

thf(1257,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(68,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I111_J_0) ).

thf(613,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(267,axiom,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wt_0) ).

thf(1221,plain,
    v_T____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_e_092_060_094isub_0622____ @ ( v_D____ @ ( v_F____ @ ( tc_String_Ochar @ tc_List_Olist @ ( v_v____ @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( v_E____ @ ( v_ha____ @ ( v_P @ c_WellTypeRT_OWTrt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(182,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I104_J_0) ).

thf(978,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

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

thf(497,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(204,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I165_J_0) ).

thf(1052,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I84_J_0) ).

thf(1506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(14,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I15_J_0) ).

thf(446,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( F @ ( E @ ( D @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I127_J_0) ).

thf(571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(352,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1421,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I150_J_0) ).

thf(627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(310,axiom,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OCond ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( T @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( W @ ( U @ ( V @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( W @ ( U @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( L @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I12_J_0) ).

thf(1316,plain,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OCond ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( T @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( W @ ( U @ ( V @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( W @ ( U @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( L @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(250,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I171_J_0) ).

thf(1180,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I22_J_0) ).

thf(482,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(312,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt_H__WTrts_H_Ointros_I19_J_0) ).

thf(1321,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_Progress_OWTrt_H ) ) ) ) )
      | ~ ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(394,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(1517,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)],[394]) ).

thf(155,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I99_J_0) ).

thf(891,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widen__refl_0) ).

thf(1126,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(366,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A
        = ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__cases_I1_J_0) ).

thf(1448,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ ( C @ c_BigStep_Oeval ) ) ) ) )
      | ( A
        = ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(192,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I225_J_0) ).

thf(1010,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( F @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(222,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(1108,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)],[222]) ).

thf(299,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrtCond_2) ).

thf(1289,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( F @ ( G @ ( H @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( H @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( G @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( C @ ( F @ ( E @ ( D @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ~ ( B @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(141,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I168_J_0) ).

thf(844,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(292,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(1276,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)],[292]) ).

thf(35,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I142_J_0) ).

thf(517,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(378,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I89_J_0) ).

thf(1476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(220,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I13_J_0) ).

thf(1101,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
       != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(79,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I140_J_0) ).

thf(652,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(277,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_BigStep_Ofinal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_final__def_1) ).

thf(1244,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Expr_Oexp_OVal ) @ c_BigStep_Ofinal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(121,axiom,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).

thf(781,plain,
    ! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(187,axiom,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I12_J_0) ).

thf(995,plain,
    c_Type_Oty_OBoolean != c_Type_Oty_ONT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(282,axiom,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OLAss ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( F @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I6_J_0) ).

thf(1253,plain,
    ! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( V @ ( T @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OLAss ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V @ ( T @ ( U @ ( S @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( S @ ( R @ ( F @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(96,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I119_J_0) ).

thf(699,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(177,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I223_J_0) ).

thf(961,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(339,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(1385,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)],[339]) ).

thf(320,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I70_J_0) ).

thf(1341,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(112,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_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I164_J_0) ).

thf(748,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_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(107,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(731,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)],[107]) ).

thf(5,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I162_J_0) ).

thf(418,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(198,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I12_J_1) ).

thf(1030,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(53,axiom,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ty_Osimps_I2_J_0) ).

thf(568,plain,
    c_Type_Oty_OVoid != c_Type_Oty_OBoolean,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(162,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I156_J_0) ).

thf(914,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(255,axiom,
    v_TF____ @ ( v_T_092_060_094isub_0622____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_TsubTF_0) ).

thf(1193,plain,
    v_TF____ @ ( v_T_092_060_094isub_0622____ @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( v_P @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(212,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(1077,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)],[212]) ).

thf(157,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I193_J_0) ).

thf(899,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(91,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I147_J_0) ).

thf(684,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(307,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(1309,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)],[307]) ).

thf(46,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I106_J_0) ).

thf(549,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(85,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(667,plain,
    ! [A: $i] :
      ( c_Type_Oty_OBoolean
     != ( A @ c_Type_Oty_OClass ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(301,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I73_J_0) ).

thf(1294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(224,axiom,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hext__refl_0) ).

thf(1116,plain,
    ! [A: $i] : ( A @ ( A @ c_Objects_Ohext ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(392,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I139_J_0) ).

thf(1512,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAss ) ) ) ) )
     != ( E @ ( G @ ( F @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(295,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I86_J_0) ).

thf(1280,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(9,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I136_J_0) ).

thf(432,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(343,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I138_J_0) ).

thf(1395,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(305,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(1303,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)],[305]) ).

thf(280,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I100_J_0) ).

thf(1248,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( H @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I24_J_0) ).

thf(833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OLAss ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_DefAss_O_092_060D_062 ) ) )
      | ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I14_J_1) ).

thf(410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_DefAss_O_092_060D_062 ) ) )
      | ( B @ ( C @ ( B @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(179,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I15_J_2) ).

thf(967,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = H )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
       != ( E @ ( I @ ( H @ ( G @ ( F @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(399,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_11) ).

thf(1527,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__3 ) ) ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(237,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OCondRed_0) ).

thf(1148,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( B @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( G @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( C @ ( B @ c_Expr_Oexp_OCond ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(360,axiom,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OWhile ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( M @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I238_J_0) ).

thf(1436,plain,
    ! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( R @ ( S @ ( R @ ( Q @ ( P @ c_Expr_Oexp_OWhile ) ) @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__case ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( Q @ ( P @ ( M @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(127,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I108_J_0) ).

thf(801,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCond ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(32,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(506,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_ONT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(317,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(1335,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)],[317]) ).

thf(84,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(664,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)],[84]) ).

thf(136,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I4_J_2) ).

thf(828,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBinOp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(377,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_2) ).

thf(1473,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( H @ ( G @ ( F @ c_Expr_Oexp_OFAss ) ) ) ) @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) )
      | ( E = c_Type_Oty_OVoid )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(95,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(696,plain,
    ! [A: $i] :
      ( ( A @ c_Type_Oty_OClass )
     != c_Type_Oty_OVoid ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(175,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I56_J_0) ).

thf(955,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(126,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).

thf(796,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(247,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( F @ ( D @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( B @ ( A @ ( D @ c_Conform_Oconf ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__def_2) ).

thf(1172,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( F @ ( D @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( B @ ( A @ ( D @ c_Conform_Oconf ) ) ) ) )
      | ( ( B @ ( A @ c_Objects_Otypeof__h ) )
       != ( tc_Type_Oty @ ( C @ c_Option_Ooption_OSome ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(22,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I196_J_0) ).

thf(474,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBlock ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OSeq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
       != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).

thf(1410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
       != ( B @ ( C @ c_Expr_Oexp_OVal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I14_J_0) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ c_Expr_Oexp_Othrow ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(243,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssThrow2_0) ).

thf(1165,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ c_Expr_Oexp_Othrow ) @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(166,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conf__hext_0) ).

thf(928,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( F @ c_Objects_Ohext ) )
      | ~ ( E @ ( D @ ( C @ ( F @ ( A @ c_Conform_Oconf ) ) ) ) )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Conform_Oconf ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I40_J_0) ).

thf(415,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( C @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(139,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I123_J_0) ).

thf(839,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(185,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I102_J_0) ).

thf(987,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(230,axiom,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OBlock ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( T @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( J @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I10_J_0) ).

thf(1129,plain,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OBlock ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( T @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( J @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(403,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ 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 @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTrt__elim__cases_I8_J_8) ).

thf(1537,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ ( G @ 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 @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__2 ) ) ) ) ) ) @ ( F @ ( D @ ( B @ ( G @ ( A @ ( F @ ( C @ ( E @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__1 ) ) ) ) ) ) @ ( A @ c_TypeRel_Ohas__field ) ) ) ) ) )
      | ( D @ ( B @ ( A @ ( C @ c_WellTypeRT_Osko__WellTypeRT__XWTrt__elim__cases__8__4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_WellTypeRT_OWTrt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I221_J_0) ).

thf(596,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(195,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I97_J_0) ).

thf(1019,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( F @ ( E @ ( D @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(39,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I214_J_0) ).

thf(528,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCond ) ) ) )
     != ( D @ ( F @ ( E @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

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

thf(644,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(18,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I208_J_0) ).

thf(459,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( E @ ( D @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I131_J_0) ).

thf(908,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( D @ c_Expr_Oexp_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(387,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( E @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_redp__redsp_OFAssRed2_0) ).

thf(1500,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( H @ ( G @ ( F @ ( E @ ( A @ c_SmallStep_Oredp ) ) ) ) )
      | ( H @ ( tc_String_Ochar @ tc_List_Olist @ ( G @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( F @ ( tc_String_Ochar @ tc_List_Olist @ ( E @ ( D @ ( C @ ( tc_String_Ochar @ tc_List_Olist @ ( B @ c_Expr_Oexp_OVal ) @ c_Expr_Oexp_OFAss ) ) ) ) @ ( A @ c_SmallStep_Oredp ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls__092_060D_062___092_060D_062s_Osimps_I2_J_0) ).

thf(850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ ( D @ c_Expr_Oexp_OCast ) ) @ c_DefAss_O_092_060D_062 ) ) )
      | ( C @ ( B @ ( A @ c_DefAss_O_092_060D_062 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(190,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I32_J_0) ).

thf(1004,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Onew ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I82_J_0) ).

thf(1299,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVal ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_widens__refl_0) ).

thf(1505,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Type_Oty @ ( tc_Type_Oty @ ( C @ ( C @ ( B @ ( A @ c_TypeRel_Owiden ) @ c_List_Olist__all2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(226,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I166_J_0) ).

thf(1120,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Othrow ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I130_J_0) ).

thf(728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_OVar ) )
     != ( B @ ( D @ ( C @ c_Expr_Oexp_OWhile ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(110,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I195_J_0) ).

thf(740,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OTryCatch ) ) ) ) )
     != ( E @ ( H @ ( G @ ( F @ c_Expr_Oexp_OCall ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(401,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I179_J_0) ).

thf(1532,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OFAss ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(146,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I31_J_0) ).

thf(860,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OCall ) ) ) )
     != ( D @ ( E @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(21,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(469,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)],[21]) ).

thf(373,axiom,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OBinOp ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( T @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( W @ ( U @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Orecs_I4_J_0) ).

thf(1463,plain,
    ! [W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( W @ ( U @ ( V @ ( U @ ( T @ ( S @ ( R @ c_Expr_Oexp_OBinOp ) ) ) @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( W @ ( U @ ( V @ ( T @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( W @ ( U @ ( V @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_Oexp__rec__1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( T @ ( S @ ( R @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(44,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I113_J_0) ).

thf(543,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Expr_Oexp_Othrow ) )
     != ( B @ ( E @ ( D @ ( C @ c_Expr_Oexp_OBinOp ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I25_J_0) ).

thf(676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OLAss ) ) )
     != ( C @ ( D @ c_Expr_Oexp_Onew ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(27,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I98_J_0) ).

thf(491,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OBinOp ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OFAcc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(375,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( F @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( E @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTCond_1) ).

thf(1468,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_String_Ochar @ tc_List_Olist @ ( D @ ( E @ ( F @ c_Expr_Oexp_OCond ) ) ) @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( c_Type_Oty_OBoolean @ ( F @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( E @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( D @ ( C @ ( A @ c_WellType_OWT ) ) ) )
      | ~ ( B @ ( B @ ( tc_String_Ochar @ tc_List_Olist @ tc_Expr_Oexp @ ( tc_String_Ochar @ tc_List_Olist @ tc_List_Olist @ tc_prod ) @ ( A @ c_TypeRel_Owiden ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(99,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I212_J_0) ).

thf(708,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OSeq ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(119,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I68_J_0) ).

thf(775,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OCast ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(50,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I222_J_0) ).

thf(560,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Expr_Oexp_OWhile ) ) )
     != ( C @ ( G @ ( F @ ( E @ ( D @ c_Expr_Oexp_OTryCatch ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTThrow_0) ).

thf(1417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Type_Oty_OClass @ ( C @ ( B @ ( A @ c_WellType_OWT ) ) ) )
      | ( c_Type_Oty_OVoid @ ( tc_String_Ochar @ tc_List_Olist @ ( C @ c_Expr_Oexp_Othrow ) @ ( B @ ( A @ c_WellType_OWT ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(180,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp_Osimps_I158_J_0) ).

thf(972,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Expr_Oexp_OFAcc ) ) ) )
     != ( D @ ( G @ ( F @ ( E @ c_Expr_Oexp_OBlock ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(1551,plain,
    $false,
    inference(e,[status(thm)],[809,1337,1168,1454,1237,1083,941,555,1369,1190,408,1211,1522,1443,1422,1205,1142,655,1041,523,762,1426,500,814,1260,1354,1458,670,1222,930,1095,1196,1001,1127,1391,1046,1366,1529,1265,1482,782,1441,1055,1287,1430,785,1330,1313,1462,949,1323,619,917,702,751,1545,1379,1247,421,1479,1347,1398,1362,1232,817,902,1013,770,448,1494,1465,1302,574,806,905,1489,1415,1373,443,485,1136,1183,1283,1377,1215,734,866,453,1351,660,998,1405,602,981,1169,687,1074,512,1438,546,925,1306,1199,1153,1338,1470,534,714,1163,1274,894,778,952,1519,1255,1123,1217,1487,429,788,1238,1502,820,693,630,1423,467,583,1027,757,1291,1106,847,566,852,435,456,842,1089,1270,1328,1375,1064,1227,725,1498,1540,593,869,857,1160,488,1361,933,679,1155,1419,1461,537,1016,590,622,1150,1297,1451,1131,1525,647,1263,1539,1456,1382,984,911,1393,503,605,1434,1318,1202,1241,633,765,1035,1515,1185,586,888,1086,938,558,1071,1278,412,1251,1219,975,1007,1388,743,1535,958,875,826,577,711,1139,1312,1058,1092,804,947,1224,1356,540,641,1428,1271,1371,1194,1117,1524,1349,990,1492,737,616,681,1408,509,880,599,1439,863,1175,477,552,520,1325,964,1344,1022,1177,494,1080,462,1061,1213,883,608,1364,1496,438,922,658,636,1245,1066,1445,1113,563,722,663,1277,1134,1509,1145,754,823,836,1049,426,1166,1208,589,531,944,525,580,690,872,705,1400,1267,1230,1098,673,1432,791,1188,441,1038,717,1235,1285,1358,1543,1257,613,1221,978,497,1052,1506,446,571,1421,627,1316,1180,482,1321,1517,891,1126,1448,1010,1108,1289,844,1276,517,1476,1101,652,1244,781,995,1253,699,961,1385,1341,748,731,418,1030,568,914,1193,1077,899,684,1309,549,667,1294,1116,1512,1280,432,1395,1303,1248,833,410,967,1527,1148,1436,801,506,1335,664,828,1473,696,955,796,1172,474,1410,720,1165,928,415,839,987,1129,1537,596,1019,528,644,459,908,1500,850,1004,1299,1505,1120,728,740,1532,860,469,1463,543,676,491,1468,708,775,560,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV962-1 : 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
% 0.15/0.41  % Computer : n005.cluster.edu
% 0.15/0.41  % Model    : x86_64 x86_64
% 0.15/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41  % Memory   : 8046.5625MB
% 0.15/0.41  % OS       : Linux 6.8.0-71-generic
% 0.15/0.41  % CPULimit : 300
% 0.15/0.41  % WCLimit  : 300
% 0.15/0.41  % DateTime : Sat Sep 26 15:15:17 UTC 2026
% 0.15/0.41  % CPUTime  : 
% 0.15/0.41  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
% 0.82/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.44/1.26  % [INFO] 	 Parsing done (275ms). 
% 1.44/1.27  % [INFO] 	 Running in sequential loop mode. 
% 2.32/1.47  % [INFO] 	 eprover registered as external prover. 
% 2.32/1.47  % [INFO] 	 Scanning for conjecture ... 
% 2.73/1.57  % [INFO] 	 Found a conjecture (or negated_conjecture) and 406 axioms. Running axiom selection ... 
% 3.20/1.68  % [INFO] 	 Axiom selection finished. Selected 406 axioms (removed 0 axioms). 
% 4.19/1.86  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.19/1.88  % [INFO] 	 Type checking passed. 
% 4.19/1.88  % [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 ... 
% 12.50/3.91  % External prover 'e' found a proof!
% 12.50/3.92  % [INFO] 	 Killing All external provers ... 
% 12.50/3.92  % Time passed: 3363ms (effective reasoning time: 2645ms)
% 12.50/3.92  % Axioms used in derivation (406): cls_WTrt__elim__cases_I8_J_3, cls_option_Oinject_0, cls_exp_Osimps_I56_J_0, cls_exp_Osimps_I118_J_0, cls_exp_Osimps_I156_J_0, cls_exp_Osimps_I9_J_1, cls_WTSeq_0, cls_exp_Osimps_I92_J_0, cls_WTrt__elim__cases_I8_J_9, cls_exp_Osimps_I184_J_0, cls_exp_Osimps_I195_J_0, cls_exp_Osimps_I103_J_0, cls_conf__def_2, cls_exp_Orecs_I1_J_0, cls_redp__redsp_OThrowRed_0, cls_exp_Osimps_I218_J_0, cls_exp_Osimps_I213_J_0, cls_exp_Orecs_I12_J_0, cls_list__all2__eq_1, cls_exp_Osimps_I193_J_0, cls_exp_Osimps_I72_J_0, cls_exp_Osimps_I137_J_0, cls_exp_Osimps_I128_J_0, cls_eval__evals_OFAssThrow2_0, cls_map__le__trans_0, cls_eval__cases_I1_J_1, cls_redp__redsp_OFAssRed1_0, cls_exp_Osimps_I10_J_1, cls_exp_Osimps_I225_J_0, cls_exp_Osimps_I138_J_0, cls_exp_Osimps_I81_J_0, cls__092_060D_062___092_060D_062s_Osimps_I7_J_1, cls_exp_Osimps_I165_J_0, cls_exp_Osimps_I7_J_2, cls_redp__redsp_OThrowThrow_0, cls_redp__redsp_OSeqRed_0, cls_exp_Osimps_I219_J_0, cls_exp_Osimps_I149_J_0, cls_exp_Osimps_I20_J_0, cls_exp_Osimps_I42_J_0, cls_exp_Osimps_I190_J_0, cls_WTrtCond_0, cls_exp_Osimps_I204_J_0, cls_has_0, cls_CHAINED_0, cls_eval__evals_OCondThrow_0, cls_WT__elim__cases_I8_J_0, cls_exp_Osimps_I221_J_0, cls_exp_Osimps_I227_J_0, cls_exp_Osimps_I11_J_0, cls_WTrt__elim__cases_I8_J_14, cls_exp_Osimps_I15_J_1, cls_ty_Osimps_I8_J_0, cls_exp_Osimps_I28_J_0, cls_exp_Orecs_I4_J_0, cls_exp_Osimps_I25_J_0, cls_exp_Osimps_I211_J_0, cls__092_060D_062___092_060D_062s_Osimps_I15_J_0, cls_exp_Osimps_I36_J_0, cls__092_060D_062___092_060D_062s_Osimps_I6_J_1, cls_exp_Osimps_I22_J_0, cls_exp_Osimps_I19_J_0, cls_widen__Class_2, cls_exp_Osimps_I115_J_0, cls_WTCond_2, cls_exp_Osimps_I154_J_0, cls_exp_Osimps_I199_J_0, cls_COMBI__def__raw_0, cls_exp_Osimps_I185_J_0, cls_ty_Osimps_I20_J_0, cls_exp_Osimps_I141_J_0, cls_exp_Osimps_I49_J_0, cls_exp_Osimps_I109_J_0, cls_WTrt__elim__cases_I8_J_10, cls_ty_Osimps_I13_J_0, cls_exp_Osimps_I13_J_0, cls_exp_Osimps_I97_J_0, cls_exp_Osimps_I238_J_0, cls_exp_Osimps_I170_J_0, cls_exp_Osimps_I208_J_0, cls_exp_Osimps_I188_J_0, cls_WTrt__elim__cases_I8_J_7, cls_exp_Osimps_I212_J_0, cls_typeof__conf_0, cls_exp_Orecs_I14_J_0, cls_exp_Osimps_I178_J_0, cls_exp_Osimps_I8_J_3, cls_redp__redsp_OCondThrow_0, cls_WTrt__elim__cases_I8_J_2, cls_exp_Osimps_I2_J_1, cls_exp_Osimps_I79_J_0, cls_exp_Osimps_I206_J_0, cls_exp_Osimps_I194_J_0, cls_exp_Osimps_I223_J_0, cls_exp_Osimps_I233_J_0, cls_exp_Osimps_I11_J_1, cls_widens__trans_0, cls_exp_Osimps_I40_J_0, cls_exp_Osimps_I124_J_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_2, cls_exp_Osimps_I226_J_0, cls_WTThrow_0, cls_exp_Osimps_I4_J_1, cls_exp_Osimps_I171_J_0, cls__092_060D_062___092_060D_062s_Osimps_I4_J_0, cls_exp_Osimps_I157_J_0, cls_exp_Osimps_I113_J_0, cls_exp_Osimps_I236_J_0, cls_exp_Osimps_I136_J_0, cls_exp_Osimps_I175_J_0, cls_exp_Orecs_I8_J_0, cls_exp_Osimps_I231_J_0, cls_WTrt__elim__cases_I5_J_2, cls_eval__evals_OSeqThrow_0, cls_exp_Osimps_I4_J_0, cls_widen__refl_0, cls_exp_Osimps_I5_J_0, cls_exp_Osimps_I17_J_0, cls_exp_Orecs_I5_J_0, cls_hext__trans_0, cls__092_060D_062___092_060D_062s_Osimps_I2_J_0, cls_exp_Osimps_I160_J_0, cls_exp_Osimps_I228_J_0, cls_exp_Osimps_I84_J_0, cls_exp_Osimps_I67_J_0, cls_exp_Osimps_I131_J_0, cls_WTrt__elim__cases_I8_J_6, cls_WT__elim__cases_I4_J_0, cls_exp_Osimps_I209_J_0, cls_exp_Osimps_I116_J_0, cls_hext__refl_0, cls__092_060D_062___092_060D_062s_Osimps_I12_J_0, cls_exp_Osimps_I142_J_0, cls_exp_Osimps_I24_J_0, cls_exp_Osimps_I74_J_0, cls_exp_Osimps_I110_J_0, cls_exp_Osimps_I229_J_0, cls_exp_Osimps_I205_J_0, cls_exp_Osimps_I29_J_0, cls_redp__redsp_OFAssThrow1_0, cls_redp__redsp_OFAssRed2_0, cls_exp_Osimps_I21_J_0, cls_exp_Osimps_I123_J_0, cls_exp_Osimps_I134_J_0, cls_exp_Osimps_I9_J_0, cls_exp_Osimps_I85_J_0, cls_exp_Osimps_I176_J_0, cls__092_060D_062___092_060D_062s_Osimps_I7_J_0, cls_exp_Osimps_I146_J_0, cls_exp_Osimps_I174_J_0, cls_ty_Osimps_I3_J_0, cls_conf__widen_0, cls_WTrtFAssNT_0, cls_exp_Osimps_I172_J_0, cls_exp_Osimps_I139_J_0, cls_exp_Osimps_I10_J_2, cls_exp_Osimps_I43_J_0, cls_exp_Orecs_I10_J_0, cls_exp_Osimps_I143_J_0, cls_widens__refl_0, cls_ty_Osimps_I9_J_0, cls_redp__redsp_OTryRed_0, cls_exp_Osimps_I148_J_0, cls_exp_Osimps_I46_J_0, cls_map__le__refl_0, cls_exp_Osimps_I99_J_0, cls_eval__evals_OFAssThrow1_0, cls_wt_092_060_094isub_0621_0, cls_WTrt__hext__mono_0, cls_exp_Osimps_I23_J_0, cls_WTrt_H__WTrts_H_Ointros_I11_J_0, cls_WTrtFAss_0, cls__092_060D_062___092_060D_062s_Osimps_I1_J_0, cls_redp__redsp_ORedTry_0, cls_ty_Osimps_I12_J_0, cls_exp_Osimps_I69_J_0, cls_WTrt__elim__cases_I8_J_13, cls_exp_Orecs_I13_J_0, cls_WTrt__env__mono_0, cls_exp_Osimps_I180_J_0, cls_exp_Osimps_I239_J_0, cls_exp_Osimps_I132_J_0, cls_exp_Osimps_I77_J_0, cls_exp_Osimps_I98_J_0, cls_exp_Osimps_I61_J_0, cls_exp_Osimps_I15_J_0, cls_exp_Osimps_I183_J_0, cls_exp_Osimps_I26_J_0, cls_exp_Osimps_I207_J_0, cls_exp_Osimps_I83_J_0, cls_exp_Osimps_I2_J_0, cls_exp_Osimps_I12_J_2, cls_exp_Osimps_I8_J_2, cls_exp_Osimps_I177_J_0, cls_Seq_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_ty_Osimps_I15_J_0, cls_exp_Osimps_I76_J_0, cls_exp_Osimps_I70_J_0, cls_exp_Osimps_I27_J_0, cls_exp_Osimps_I89_J_0, cls_exp_Osimps_I159_J_0, cls_exp_Orecs_I7_J_0, cls_exp_Osimps_I62_J_0, cls_exp_Osimps_I186_J_0, cls_exp_Osimps_I210_J_0, cls_exp_Osimps_I105_J_0, cls_exp_Osimps_I220_J_0, cls_ty_Osimps_I7_J_0, cls_TsubTF_0, cls_exp_Osimps_I112_J_0, cls_exp_Osimps_I60_J_0, cls_exp_Osimps_I122_J_0, cls_exp_Osimps_I162_J_0, cls_exp_Osimps_I135_J_0, cls__092_060D_062___092_060D_062s_Osimps_I2_J_1, cls_exp_Osimps_I158_J_0, cls_redp__redsp_OSeqThrow_0, cls_exp_Osimps_I15_J_3, cls_eval__evals_OThrowThrow_0, cls_exp_Osimps_I169_J_0, cls_exp_Osimps_I201_J_0, cls_exp_Osimps_I166_J_0, cls_exp_Orecs_I3_J_0, cls_exp_Osimps_I55_J_0, cls_exp_Osimps_I47_J_0, cls_exp_Osimps_I7_J_1, cls_WTrtSeq_0, cls_exp_Orecs_I6_J_0, cls_exp_Osimps_I189_J_0, cls_WTrt__elim__cases_I8_J_5, cls_exp_Osimps_I75_J_0, cls_exp_Osimps_I101_J_0, cls_exp_Osimps_I102_J_0, cls_exp_Osimps_I30_J_0, cls_exp_Osimps_I224_J_0, cls_wt_092_060_094isub_0622_0, cls_exp_Osimps_I80_J_0, cls_exp_Osimps_I16_J_0, cls_exp_Osimps_I1_J_0, cls_exp_Osimps_I145_J_0, cls_exp_Osimps_I59_J_0, cls_exp_Osimps_I129_J_0, cls_exp_Osimps_I35_J_0, cls_final__def_1, cls_exp_Osimps_I39_J_0, cls_T_HsubT_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_0, cls_exp_Osimps_I182_J_0, cls_WT__implies__WTrt_0, cls_wt_0, cls_WTrt__elim__cases_I2_J_0, cls_exp_Osimps_I133_J_0, cls_redp__redsp_OCondRed_0, cls_exp_Osimps_I68_J_0, cls_map__le__antisym_0, cls_ty_Oinject_0, cls__092_060D_062___092_060D_062s_Osimps_I14_J_1, cls_exp_Osimps_I4_J_2, cls_exp_Osimps_I114_J_0, cls_exp_Osimps_I121_J_0, cls_exp_Osimps_I216_J_0, cls_exp_Osimps_I203_J_0, cls_exp_Osimps_I235_J_0, cls_exp_Osimps_I57_J_0, cls_exp_Osimps_I41_J_0, cls_wt_092_060_094isub_0621_H_0, cls_exp_Osimps_I230_J_0, cls_WTrt_H__WTrts_H_Ointros_I18_J_0, cls_exp_Osimps_I191_J_0, cls_exp_Osimps_I215_J_0, cls_WTCond_0, cls_exp_Osimps_I93_J_0, cls_exp_Osimps_I53_J_0, cls_exp_Osimps_I73_J_0, cls_exp_Osimps_I126_J_0, cls_exp_Osimps_I152_J_0, cls_exp_Osimps_I50_J_0, cls_exp_Osimps_I95_J_0, cls_exp_Osimps_I117_J_0, cls_exp_Osimps_I179_J_0, cls_WTrt_H__WTrts_H_Ointros_I3_J_0, cls_conf__hext_0, cls_exp_Osimps_I54_J_0, cls_exp_Osimps_I86_J_0, cls_exp_Osimps_I144_J_0, cls_exp_Osimps_I150_J_0, cls_exp_Osimps_I37_J_0, cls_exp_Osimps_I8_J_1, cls_exp_Orecs_I11_J_0, cls_exp_Osimps_I58_J_0, cls_exp_Osimps_I106_J_0, cls_exp_Osimps_I127_J_0, cls_exp_Osimps_I66_J_0, cls_exp_Osimps_I34_J_0, cls_exp_Osimps_I6_J_0, cls_exp_Osimps_I108_J_0, cls_exp_Osimps_I222_J_0, cls_WTrt__elim__cases_I8_J_12, cls_wt_H__wt_0, cls_wt_092_060_094isub_0622_H_0, cls_exp_Osimps_I90_J_0, cls_ty_Osimps_I21_J_0, cls_widen__trans_0, cls_ty_Osimps_I6_J_0, cls_exp_Osimps_I155_J_0, cls_exp_Osimps_I232_J_0, cls_eval__cases_I1_J_0, cls_exp_Osimps_I71_J_0, cls_exp_Osimps_I12_J_1, cls_redp__redsp_OFAssThrow2_0, cls_exp_Osimps_I82_J_0, cls_WT__elim__cases_I5_J_0, cls_exp_Osimps_I125_J_0, cls__092_060D_062___092_060D_062s_Osimps_I8_J_0, cls_exp_Osimps_I14_J_0, cls_WTrtVal_0, cls_exp_Osimps_I107_J_0, cls_exp_Osimps_I167_J_0, cls__092_060D_062___092_060D_062s_Osimps_I11_J_0, cls_exp_Osimps_I161_J_0, cls_exp_Osimps_I120_J_0, cls_exp_Osimps_I9_J_2, cls_exp_Osimps_I7_J_0, cls_exp_Osimps_I217_J_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_exp_Osimps_I45_J_0, cls_exp_Osimps_I8_J_0, cls_exp_Osimps_I192_J_0, cls_exp_Osimps_I151_J_0, cls__092_060D_062___092_060D_062s_Osimps_I14_J_0, cls_exp_Osimps_I153_J_0, cls_WTrt__elim__cases_I8_J_4, cls_exp_Osimps_I44_J_0, cls_exp_Osimps_I18_J_0, cls_exp_Osimps_I164_J_0, cls_exp_Osimps_I32_J_0, cls_exp_Osimps_I6_J_1, cls_exp_Osimps_I65_J_0, cls_Try_0, cls_exp_Osimps_I51_J_0, cls__092_060D_062___092_060D_062s_Osimps_I3_J_0, cls_exp_Osimps_I52_J_0, cls_WTrt__elim__cases_I8_J_0, cls_Val_0, cls_exp_Osimps_I187_J_0, cls_exp_Osimps_I15_J_2, cls_list__all2__eq_0, cls_exp_Osimps_I10_J_0, cls_wt__env__mono_0, cls_WTrt__elim__cases_I5_J_0, cls_exp_Osimps_I111_J_0, cls_ty_Osimps_I2_J_0, cls_exp_Osimps_I130_J_0, cls_exp_Osimps_I31_J_0, cls_exp_Osimps_I64_J_0, cls_exp_Osimps_I88_J_0, cls_WTrtCond_1, cls_exp_Osimps_I96_J_0, cls_wt__wt_H_0, cls_exp_Osimps_I91_J_0, cls_exp_Osimps_I234_J_0, cls_exp_Osimps_I181_J_0, cls_exp_Osimps_I200_J_0, cls_exp_Osimps_I196_J_0, cls_WT__elim__cases_I2_J_0, cls_exp_Osimps_I214_J_0, cls_exp_Osimps_I168_J_0, cls_exp_Orecs_I2_J_0, cls_exp_Osimps_I119_J_0, cls_ty_Osimps_I14_J_0, cls_WTrtCond_2, cls_exp_Osimps_I63_J_0, cls_WTrt__elim__cases_I8_J_11, cls_exp_Osimps_I140_J_0, cls_exp_Osimps_I87_J_0, cls__092_060D_062___092_060D_062s_Osimps_I9_J_0, cls_COMBI__def_0, cls_WTrt_H__WTrts_H_Ointros_I19_J_1, cls_exp_Osimps_I78_J_0, cls_exp_Osimps_I202_J_0, cls_exp_Osimps_I94_J_0, cls_exp_Osimps_I12_J_0, cls_exp_Osimps_I33_J_0, cls_exp_Osimps_I100_J_0, cls_exp_Osimps_I163_J_0, cls_exp_Osimps_I173_J_0, cls_exp_Osimps_I48_J_0, cls_exp_Osimps_I104_J_0, cls_hext__typeof__mono_0, cls_exp_Osimps_I198_J_0, cls__092_060D_062___092_060D_062s_Osimps_I13_J_0, cls_exp_Orecs_I15_J_0, cls_exp_Osimps_I240_J_0, cls_WTrt__elim__cases_I8_J_1, cls_exp_Osimps_I38_J_0, cls_exp_Osimps_I147_J_0, cls_WTrt_H__WTrts_H_Ointros_I10_J_0, cls_exp_Osimps_I3_J_0, cls_WTrt__elim__cases_I8_J_8, cls_exp_Osimps_I197_J_0, cls__092_060D_062___092_060D_062s_Osimps_I6_J_0, cls_exp_Osimps_I237_J_0, cls_redp__redsp_ORedSeq_0, cls_WTCond_1, cls_exp_Osimps_I13_J_1
% 12.50/3.92  % No. of inferences in proof: 815
% 12.50/3.92  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3363 ms resp. 2645 ms w/o parsing
% 13.70/4.23  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.70/4.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------