%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW507_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:24:55 EDT 2023

% Result   : Theorem 43.32s 23.69s
% Output   : Refutation 44.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  153
% Syntax   : Number of formulae    :  263 ( 137 unt;  45 typ;   0 def)
%            Number of atoms       : 9408 ( 213 equ;   0 cnn)
%            Maximal formula atoms : 1884 (  43 avg)
%            Number of connectives : 25774 ( 123   ~;  13   |;  42   &;25476   @)
%                                         (  10 <=>; 110  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (  10 avg)
%            Number of types       :    9 (   8 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  39 usr;  12 con; 0-10 aty)
%            Number of variables   :  996 (   0   ^; 965   !;   2   ?; 996   :)
%                                         (  29  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(com1_type,type,
    com1: $tType ).

thf(loc_type,type,
    loc: $tType ).

thf(pname_type,type,
    pname: $tType ).

thf(state_type,type,
    state: $tType ).

thf(vname_type,type,
    vname: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(zero_type,type,
    zero: 
      !>[TA: $tType] : $o ).

thf(semiring_1_type,type,
    semiring_1: 
      !>[TA: $tType] : $o ).

thf(combb_type,type,
    combb: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).

thf(combc_type,type,
    combc: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).

thf(combs_type,type,
    combs: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( fun @ TC @ TB ) @ ( fun @ TC @ TA ) ) ) ).

thf(wt_type,type,
    wt: com1 > $o ).

thf(ass_type,type,
    ass: vname > ( fun @ state @ nat ) > com1 ).

thf(cond_type,type,
    cond: ( fun @ state @ bool ) > com1 > com1 > com1 ).

thf(local_type,type,
    local: loc > ( fun @ state @ nat ) > com1 > com1 ).

thf(skip_type,type,
    skip: com1 ).

thf(semi_type,type,
    semi: com1 > com1 > com1 ).

thf(while_type,type,
    while: ( fun @ state @ bool ) > com1 > com1 ).

thf(com_case_type,type,
    com_case: 
      !>[TA: $tType] : ( TA > ( fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) ) > ( fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ) ) > ( fun @ com1 @ ( fun @ com1 @ TA ) ) > ( fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ) ) > ( fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ) ) > ( fun @ pname @ TA ) > ( fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ) ) > com1 > TA ) ).

thf(com_rec_type,type,
    com_rec: 
      !>[TA: $tType] : ( TA > ( fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) ) > ( fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ) ) > ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) > ( fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) ) > ( fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ) > ( fun @ pname @ TA ) > ( fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ) ) > com1 > TA ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(hoare_1442473487ek_and_type,type,
    hoare_1442473487ek_and: 
      !>[TA: $tType] : ( ( fun @ TA @ ( fun @ state @ bool ) ) > ( fun @ state @ bool ) > TA > state > $o ) ).

thf(hoare_1841697145triple_type,type,
    hoare_1841697145triple: 
      !>[TA: $tType] : ( ( fun @ TA @ ( fun @ state @ bool ) ) > com1 > ( fun @ TA @ ( fun @ state @ bool ) ) > ( hoare_28830079triple @ TA ) ) ).

thf(hoare_376461865e_case_type,type,
    hoare_376461865e_case: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ TA ) ) ) > ( hoare_28830079triple @ TB ) > TA ) ).

thf(hoare_678420151le_rec_type,type,
    hoare_678420151le_rec: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ TA ) ) ) > ( hoare_28830079triple @ TB ) > TA ) ).

thf(hoare_47506394e_size_type,type,
    hoare_47506394e_size: 
      !>[TA: $tType] : ( ( fun @ TA @ nat ) > ( hoare_28830079triple @ TA ) > nat ) ).

thf(hoare_1633586161_valid_type,type,
    hoare_1633586161_valid: 
      !>[TA: $tType] : ( nat > ( hoare_28830079triple @ TA ) > $o ) ).

thf(suc_type,type,
    suc: nat > nat ).

thf(nat_case_type,type,
    nat_case: 
      !>[TA: $tType] : ( TA > ( fun @ nat @ TA ) > nat > TA ) ).

thf(nat_rec_type,type,
    nat_rec: 
      !>[TA: $tType] : ( TA > ( fun @ nat @ ( fun @ TA @ TA ) ) > nat > TA ) ).

thf(semiri532925092at_aux_type,type,
    semiri532925092at_aux: 
      !>[TA: $tType] : ( ( fun @ TA @ TA ) > nat > TA > TA ) ).

thf(size_size_type,type,
    size_size: 
      !>[TA: $tType] : ( TA > nat ) ).

thf(evaln_type,type,
    evaln: fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ).

thf(aa_type,type,
    aa: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).

thf(fAll_type,type,
    fAll: 
      !>[TA: $tType] : ( fun @ ( fun @ TA @ bool ) @ bool ) ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fimplies_type,type,
    fimplies: fun @ bool @ ( fun @ bool @ bool ) ).

thf(pp_type,type,
    pp: bool > $o ).

thf(com_type,type,
    com: com1 ).

thf(fun1_type,type,
    fun1: fun @ a @ ( fun @ state @ bool ) ).

thf(fun2_type,type,
    fun2: fun @ a @ ( fun @ state @ bool ) ).

thf(n_type,type,
    n: nat ).

thf(49,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool] :
      ( skip
     != ( cond @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_com_Osimps_I14_J) ).

thf(320,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool] :
      ( skip
     != ( cond @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(19,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: fun @ state @ bool] :
      ( ( while @ E @ D )
     != ( local @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_com_Osimps_I39_J) ).

thf(189,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: fun @ state @ bool] :
      ( ( while @ E @ D )
     != ( local @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(61,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
      | ~ ( pp @ B )
      | ( pp @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(355,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
      | ~ ( pp @ B )
      | ( pp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(96,axiom,
    ! [A: state,B: nat,C: state] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ skip ) @ C ) @ B ) @ A ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_evaln__elim__cases_I1_J) ).

thf(479,plain,
    ! [A: state,B: nat,C: state] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ skip ) @ C ) @ B ) @ A ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(109,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

thf(518,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(69,axiom,
    ! [TA: $tType,A: com1,B: fun @ state @ nat,C: loc,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),H: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( local @ C @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ com1 @ ( fun @ TA @ TA ) @ ( aa @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) @ ( aa @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ) @ I @ C ) @ B ) @ A ) @ ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_com_Orecs_I3_J) ).

thf(384,plain,
    ! [TA: $tType,A: com1,B: fun @ state @ nat,C: loc,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),H: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( local @ C @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ com1 @ ( fun @ TA @ TA ) @ ( aa @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) @ ( aa @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ) @ I @ C ) @ B ) @ A ) @ ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(94,axiom,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Suc__neq__Zero) ).

thf(472,plain,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(12,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: fun @ state @ nat,F: loc] :
      ( ( ( local @ F @ E @ D )
        = ( local @ C @ B @ A ) )
    <=> ( ( F = C )
        & ( E = B )
        & ( D = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_com_Osimps_I2_J) ).

thf(153,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: fun @ state @ nat,F: loc] :
      ( ( ( ( local @ F @ E @ D )
          = ( local @ C @ B @ A ) )
       => ( ( F = C )
          & ( E = B )
          & ( D = A ) ) )
      & ( ( ( F = C )
          & ( E = B )
          & ( D = A ) )
       => ( ( local @ F @ E @ D )
          = ( local @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(71,axiom,
    ! [A: state,B: nat,C: state,D: com1,E: state,F: nat,G: state,H: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ H ) @ G ) @ F ) @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ A ) )
       => ? [I: nat] :
            ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ H ) @ G ) @ I ) @ E ) )
            & ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ I ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_evaln__max2) ).

thf(389,plain,
    ! [A: state,B: nat,C: state,D: com1,E: state,F: nat,G: state,H: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ H ) @ G ) @ F ) @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ A ) )
       => ? [I: nat] :
            ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ H ) @ G ) @ I ) @ E ) )
            & ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ I ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(104,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
      ( ( hoare_376461865e_case @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_triple_Osimps_I2_J) ).

thf(504,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
      ( ( hoare_376461865e_case @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(1,conjecture,
    ( ~ ( pp @ ( hoare_376461865e_case @ a @ bool @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( combb @ ( fun @ a @ bool ) @ bool @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fAll @ a ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ a ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( 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fun @ state @ bool ) ) ) @ com1 ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun 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@ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ a ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ a ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ a ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ com1 ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ a ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) @ ( aa @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combc @ com1 @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ nat @ ( fun @ state @ bool ) ) ) @ evaln ) ) @ n ) ) ) ) ) ) ) ) ) @ ( hoare_1841697145triple @ a @ fun1 @ com @ fun2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ~ ( pp @ ( hoare_376461865e_case @ a @ bool @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( combb @ ( fun @ a @ bool ) @ bool @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fAll @ a ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ a ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combc @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun 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@ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ a ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ a ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ a ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ com1 ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ a ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) @ ( aa @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combc @ com1 @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ nat @ ( fun @ state @ bool ) ) ) @ evaln ) ) @ n ) ) ) ) ) ) ) ) ) @ ( hoare_1841697145triple @ a @ fun1 @ com @ fun2 ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(110,plain,
    ~ ( ~ ( pp @ ( hoare_376461865e_case @ a @ bool @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ bool ) ) @ ( combb @ ( fun @ a @ bool ) @ bool @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fAll @ a ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ a ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combc @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ com1 ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combs @ a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun 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@ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ a ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ com1 ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ a ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) @ ( aa @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combc @ com1 @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ nat @ ( fun @ state @ bool ) ) ) @ evaln ) ) @ n ) ) ) ) ) ) ) ) ) @ ( hoare_1841697145triple @ a @ fun1 @ com @ fun2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [A: fun @ state @ nat,B: vname,C: fun @ state @ nat,D: vname] :
      ( ( ( ass @ D @ C )
        = ( ass @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_com_Osimps_I1_J) ).

thf(125,plain,
    ! [A: fun @ state @ nat,B: vname,C: fun @ state @ nat,D: vname] :
      ( ( ( ( ass @ D @ C )
          = ( ass @ B @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( ass @ D @ C )
          = ( ass @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(62,axiom,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ ( fun @ state @ bool ),E: com1,F: fun @ TA @ ( fun @ state @ bool )] :
      ( ( ( hoare_1841697145triple @ TA @ F @ E @ D )
        = ( hoare_1841697145triple @ TA @ C @ B @ A ) )
    <=> ( ( F = C )
        & ( E = B )
        & ( D = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_triple_Oinject) ).

thf(357,plain,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ ( fun @ state @ bool ),E: com1,F: fun @ TA @ ( fun @ state @ bool )] :
      ( ( ( ( hoare_1841697145triple @ TA @ F @ E @ D )
          = ( hoare_1841697145triple @ TA @ C @ B @ A ) )
       => ( ( F = C )
          & ( E = B )
          & ( D = A ) ) )
      & ( ( ( F = C )
          & ( E = B )
          & ( D = A ) )
       => ( ( hoare_1841697145triple @ TA @ F @ E @ D )
          = ( hoare_1841697145triple @ TA @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(21,axiom,
    ! [A: com1,B: com1,C: com1,D: fun @ state @ bool] :
      ( ( while @ D @ C )
     != ( semi @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_com_Osimps_I47_J) ).

thf(196,plain,
    ! [A: com1,B: com1,C: com1,D: fun @ state @ bool] :
      ( ( while @ D @ C )
     != ( semi @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(26,axiom,
    ! [A: com1,B: com1] :
      ( ( wt @ ( semi @ B @ A ) )
     => ~ ( ( wt @ B )
         => ~ ( wt @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_WTs__elim__cases_I4_J) ).

thf(216,plain,
    ! [A: com1,B: com1] :
      ( ( wt @ ( semi @ B @ A ) )
     => ~ ( ( wt @ B )
         => ~ ( wt @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(16,axiom,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: fun @ state @ nat,E: loc] :
      ( ( local @ E @ D @ C )
     != ( while @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_com_Osimps_I38_J) ).

thf(179,plain,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: fun @ state @ nat,E: loc] :
      ( ( local @ E @ D @ C )
     != ( while @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(88,axiom,
    ! [A: state,B: nat,C: state,D: com1,E: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ E @ D ) ) @ C ) @ B ) @ A ) )
     => ( ( ( A = C )
         => ( pp @ ( aa @ state @ bool @ E @ C ) ) )
       => ~ ( ( pp @ ( aa @ state @ bool @ E @ C ) )
           => ! [F: state] :
                ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ F ) )
               => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_evaln__WHILE__case) ).

thf(443,plain,
    ! [A: state,B: nat,C: state,D: com1,E: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ E @ D ) ) @ C ) @ B ) @ A ) )
     => ( ( ( A = C )
         => ( pp @ ( aa @ state @ bool @ E @ C ) ) )
       => ~ ( ( pp @ ( aa @ state @ bool @ E @ C ) )
           => ! [F: state] :
                ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ F ) )
               => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(5,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool] :
      ( ( cond @ C @ B @ A )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_com_Osimps_I15_J) ).

thf(121,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool] :
      ( ( cond @ C @ B @ A )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(108,axiom,
    ! [A: nat] :
      ( ( suc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Suc__n__not__n) ).

thf(514,plain,
    ! [A: nat] :
      ( ( suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(74,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

thf(397,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(89,axiom,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool )] :
      ( ( size_size @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_triple_Osize_I2_J) ).

thf(453,plain,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool )] :
      ( ( size_size @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(105,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

thf(507,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(42,axiom,
    ! [A: com1,B: fun @ state @ bool] :
      ( skip
     != ( while @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_com_Osimps_I16_J) ).

thf(292,plain,
    ! [A: com1,B: fun @ state @ bool] :
      ( skip
     != ( while @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(107,axiom,
    ! [A: com1,B: state,C: nat,D: com1,E: state,F: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ F @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ E ) @ C ) @ B ) )
       => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( cond @ F @ D @ A ) ) @ E ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_evaln_OIfTrue) ).

thf(512,plain,
    ! [A: com1,B: state,C: nat,D: com1,E: state,F: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ F @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ E ) @ C ) @ B ) )
       => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( cond @ F @ D @ A ) ) @ E ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(68,axiom,
    ! [TA: $tType,A: fun @ state @ bool,B: fun @ TA @ ( fun @ state @ bool ),C: TA,D: state] :
      ( ( hoare_1442473487ek_and @ TA @ B @ A @ C @ D )
    <=> ( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ C ) @ D ) )
        & ( pp @ ( aa @ state @ bool @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_peek__and__def) ).

thf(380,plain,
    ! [TA: $tType,A: fun @ state @ bool,B: fun @ TA @ ( fun @ state @ bool ),C: TA,D: state] :
      ( ( ( hoare_1442473487ek_and @ TA @ B @ A @ C @ D )
       => ( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ C ) @ D ) )
          & ( pp @ ( aa @ state @ bool @ A @ D ) ) ) )
      & ( ( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ C ) @ D ) )
          & ( pp @ ( aa @ state @ bool @ A @ D ) ) )
       => ( hoare_1442473487ek_and @ TA @ B @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(4,axiom,
    ! [A: fun @ state @ nat,B: vname] :
      ( skip
     != ( ass @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_com_Osimps_I8_J) ).

thf(117,plain,
    ! [A: fun @ state @ nat,B: vname] :
      ( skip
     != ( ass @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(53,axiom,
    ! [A: state,B: state,C: nat,D: com1,E: state,F: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ F @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ E ) @ C ) @ B ) )
       => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ F @ D ) ) @ B ) @ C ) @ A ) )
         => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ F @ D ) ) @ E ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_evaln_OWhileTrue) ).

thf(334,plain,
    ! [A: state,B: state,C: nat,D: com1,E: state,F: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ F @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ E ) @ C ) @ B ) )
       => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ F @ D ) ) @ B ) @ C ) @ A ) )
         => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ F @ D ) ) @ E ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(72,axiom,
    ! [TA: $tType,A: fun @ nat @ ( fun @ TA @ TA ),B: TA,C: fun @ nat @ TA] :
      ( ! [D: nat] :
          ( ( aa @ nat @ TA @ C @ D )
          = ( nat_rec @ TA @ B @ A @ D ) )
     => ( ( aa @ nat @ TA @ C @ ( zero_zero @ nat ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_def__nat__rec__0) ).

thf(392,plain,
    ! [TA: $tType,A: fun @ nat @ ( fun @ TA @ TA ),B: TA,C: fun @ nat @ TA] :
      ( ! [D: nat] :
          ( ( aa @ nat @ TA @ C @ D )
          = ( nat_rec @ TA @ B @ A @ D ) )
     => ( ( aa @ nat @ TA @ C @ ( zero_zero @ nat ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(37,axiom,
    ! [A: com1,B: fun @ state @ bool] :
      ( ( wt @ ( while @ B @ A ) )
     => ( wt @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_WTs__elim__cases_I6_J) ).

thf(275,plain,
    ! [A: com1,B: fun @ state @ bool] :
      ( ( wt @ ( while @ B @ A ) )
     => ( wt @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(33,axiom,
    ! [A: com1,B: fun @ state @ bool] :
      ( ( while @ B @ A )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_com_Osimps_I17_J) ).

thf(260,plain,
    ! [A: com1,B: fun @ state @ bool] :
      ( ( while @ B @ A )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(58,axiom,
    ! [A: bool,B: bool] :
      ( ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(349,plain,
    ! [A: bool,B: bool] :
      ( ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(100,axiom,
    ! [TA: $tType,A: com1,B: fun @ state @ bool,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),G: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( while @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ com1 @ ( fun @ TA @ TA ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) @ E @ B ) @ A ) @ ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_com_Orecs_I6_J) ).

thf(493,plain,
    ! [TA: $tType,A: com1,B: fun @ state @ bool,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),G: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( while @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ com1 @ ( fun @ TA @ TA ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) @ E @ B ) @ A ) @ ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(90,axiom,
    ! [TA: $tType,A: hoare_28830079triple @ TA,B: nat] :
      ( ( hoare_1633586161_valid @ TA @ B @ A )
    <=> ( pp @ ( hoare_376461865e_case @ TA @ bool @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fAll @ TA ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ TA ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combc @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ com1 ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combs @ TA @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ TA ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ TA ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ com1 ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ TA ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) @ ( aa @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combc @ com1 @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ nat @ ( fun @ state @ bool ) ) ) @ evaln ) ) @ B ) ) ) ) ) ) ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_triple__valid__def) ).

thf(456,plain,
    ! [TA: $tType,A: hoare_28830079triple @ TA,B: nat] :
      ( ( ( hoare_1633586161_valid @ TA @ B @ A )
       => ( pp @ ( hoare_376461865e_case @ TA @ bool @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fAll @ TA ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ TA ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combc @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ com1 ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combs @ TA @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ TA ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ TA ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ com1 ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ TA ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) @ ( aa @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combc @ com1 @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ nat @ ( fun @ state @ bool ) ) ) @ evaln ) ) @ B ) ) ) ) ) ) ) ) ) @ A ) ) )
      & ( ( pp @ ( hoare_376461865e_case @ TA @ bool @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fAll @ TA ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) ) @ ( combb @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ TA ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combc @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ com1 ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combs @ TA @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ TA ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) @ TA ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ bool ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ bool ) ) @ ( combb @ ( fun @ state @ bool ) @ bool @ state ) @ ( fAll @ state ) ) ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ com1 ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ TA ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ state @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ state ) @ ( combs @ state @ bool @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ com1 ) @ ( aa @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ state ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ state ) @ fimplies ) ) ) @ ( aa @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ nat @ ( fun @ com1 @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( combc @ com1 @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ ( aa @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) @ ( fun @ ( fun @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) ) @ ( fun @ com1 @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) ) ) @ ( combb @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ ( fun @ nat @ ( fun @ state @ ( fun @ state @ bool ) ) ) @ com1 ) @ ( combc @ state @ nat @ ( fun @ state @ bool ) ) ) @ evaln ) ) @ B ) ) ) ) ) ) ) ) ) @ A ) )
       => ( hoare_1633586161_valid @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(50,axiom,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Zero__not__Suc) ).

thf(324,plain,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(47,axiom,
    ! [A: fun @ state @ nat,B: vname] : ( wt @ ( ass @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_WT_OAssign) ).

thf(317,plain,
    ! [A: fun @ state @ nat,B: vname] : ( wt @ ( ass @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(76,axiom,
    ! [TA: $tType,A: fun @ state @ nat,B: vname,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),G: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( ass @ B @ A ) )
      = ( aa @ ( fun @ state @ nat ) @ TA @ ( aa @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) @ I @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_com_Orecs_I2_J) ).

thf(403,plain,
    ! [TA: $tType,A: fun @ state @ nat,B: vname,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),G: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( ass @ B @ A ) )
      = ( aa @ ( fun @ state @ nat ) @ TA @ ( aa @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) @ I @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(81,axiom,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ nat] :
      ( ( hoare_47506394e_size @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_triple_Osize_I1_J) ).

thf(420,plain,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ nat] :
      ( ( hoare_47506394e_size @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(55,axiom,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Suc__not__Zero) ).

thf(339,plain,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(20,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc] :
      ( ( wt @ ( local @ C @ B @ A ) )
     => ( wt @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_WTs__elim__cases_I3_J) ).

thf(193,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc] :
      ( ( wt @ ( local @ C @ B @ A ) )
     => ( wt @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(95,axiom,
    ! [TA: $tType,A: fun @ nat @ ( fun @ TA @ TA ),B: TA] :
      ( ( nat_rec @ TA @ B @ A @ ( zero_zero @ nat ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_nat__rec__0) ).

thf(476,plain,
    ! [TA: $tType,A: fun @ nat @ ( fun @ TA @ TA ),B: TA] :
      ( ( nat_rec @ TA @ B @ A @ ( zero_zero @ nat ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(99,axiom,
    ! [A: nat] :
      ( A
     != ( suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_n__not__Suc__n) ).

thf(489,plain,
    ! [A: nat] :
      ( A
     != ( suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(25,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc] :
      ( skip
     != ( local @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_com_Osimps_I10_J) ).

thf(212,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc] :
      ( skip
     != ( local @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(51,axiom,
    ! [TA: $tType,A: com1,B: com1,C: fun @ state @ bool,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),H: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( cond @ C @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) @ G @ C ) @ B ) @ A ) @ ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ B ) ) @ ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_com_Orecs_I5_J) ).

thf(328,plain,
    ! [TA: $tType,A: com1,B: com1,C: fun @ state @ bool,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),H: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( cond @ C @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) @ G @ C ) @ B ) @ A ) @ ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ B ) ) @ ( com_rec @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(32,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: fun @ state @ bool] :
      ( ( while @ E @ D )
     != ( cond @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_com_Osimps_I53_J) ).

thf(256,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: fun @ state @ bool] :
      ( ( while @ E @ D )
     != ( cond @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(56,axiom,
    ! [A: state,B: nat,C: state,D: com1,E: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( semi @ E @ D ) ) @ C ) @ B ) @ A ) )
     => ~ ! [F: state] :
            ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ E ) @ C ) @ B ) @ F ) )
           => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ F ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_evaln__elim__cases_I4_J) ).

thf(343,plain,
    ! [A: state,B: nat,C: state,D: com1,E: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( semi @ E @ D ) ) @ C ) @ B ) @ A ) )
     => ~ ! [F: state] :
            ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ E ) @ C ) @ B ) @ F ) )
           => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ F ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(29,axiom,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: com1,E: fun @ state @ bool] :
      ( ( cond @ E @ D @ C )
     != ( ass @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_com_Osimps_I27_J) ).

thf(237,plain,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: com1,E: fun @ state @ bool] :
      ( ( cond @ E @ D @ C )
     != ( ass @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(79,axiom,
    ! [TA: $tType,A: hoare_28830079triple @ TA] :
      ~ ! [B: fun @ TA @ ( fun @ state @ bool ),C: com1,D: fun @ TA @ ( fun @ state @ bool )] :
          ( A
         != ( hoare_1841697145triple @ TA @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_triple_Oexhaust) ).

thf(412,plain,
    ! [TA: $tType,A: hoare_28830079triple @ TA] :
      ~ ! [B: fun @ TA @ ( fun @ state @ bool ),C: com1,D: fun @ TA @ ( fun @ state @ bool )] :
          ( A
         != ( hoare_1841697145triple @ TA @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(10,axiom,
    ! [TA: $tType,A: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),B: fun @ pname @ TA,C: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),D: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),E: fun @ com1 @ ( fun @ com1 @ TA ),F: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),G: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),H: TA] :
      ( ( com_case @ TA @ H @ G @ F @ E @ D @ C @ B @ A @ skip )
      = H ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_com_Osimps_I64_J) ).

thf(148,plain,
    ! [TA: $tType,A: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),B: fun @ pname @ TA,C: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),D: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),E: fun @ com1 @ ( fun @ com1 @ TA ),F: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),G: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),H: TA] :
      ( ( com_case @ TA @ H @ G @ F @ E @ D @ C @ B @ A @ skip )
      = H ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(34,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: com1] :
      ( ( semi @ E @ D )
     != ( local @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_com_Osimps_I35_J) ).

thf(264,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: com1] :
      ( ( semi @ E @ D )
     != ( local @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(43,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: fun @ state @ nat,F: loc] :
      ( ( local @ F @ E @ D )
     != ( cond @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_com_Osimps_I36_J) ).

thf(296,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: fun @ state @ nat,F: loc] :
      ( ( local @ F @ E @ D )
     != ( cond @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(82,axiom,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Zero__neq__Suc) ).

thf(423,plain,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(40,axiom,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: com1] :
      ( ( semi @ D @ C )
     != ( ass @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_com_Osimps_I25_J) ).

thf(286,plain,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: com1] :
      ( ( semi @ D @ C )
     != ( ass @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(23,axiom,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: fun @ state @ nat,E: loc] :
      ( ( local @ E @ D @ C )
     != ( ass @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_com_Osimps_I23_J) ).

thf(204,plain,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: fun @ state @ nat,E: loc] :
      ( ( local @ E @ D @ C )
     != ( ass @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(9,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: com1] :
      ( ( semi @ E @ D )
     != ( cond @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_com_Osimps_I44_J) ).

thf(144,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: com1] :
      ( ( semi @ E @ D )
     != ( cond @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(102,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

thf(498,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(18,axiom,
    ! [A: com1,B: com1] :
      ( ( wt @ B )
     => ( ( wt @ A )
       => ( wt @ ( semi @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_WT_OSemi) ).

thf(187,plain,
    ! [A: com1,B: com1] :
      ( ( wt @ B )
     => ( ( wt @ A )
       => ( wt @ ( semi @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(77,axiom,
    ! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA,D: fun @ nat @ TA] :
      ( ! [E: nat] :
          ( ( aa @ nat @ TA @ D @ E )
          = ( nat_rec @ TA @ C @ B @ E ) )
     => ( ( aa @ nat @ TA @ D @ ( suc @ A ) )
        = ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( aa @ nat @ TA @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_def__nat__rec__Suc) ).

thf(406,plain,
    ! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA,D: fun @ nat @ TA] :
      ( ! [E: nat] :
          ( ( aa @ nat @ TA @ D @ E )
          = ( nat_rec @ TA @ C @ B @ E ) )
     => ( ( aa @ nat @ TA @ D @ ( suc @ A ) )
        = ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( aa @ nat @ TA @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(3,axiom,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: com1] :
      ( ( semi @ D @ C )
     != ( while @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_com_Osimps_I46_J) ).

thf(113,plain,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: com1] :
      ( ( semi @ D @ C )
     != ( while @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(27,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: fun @ state @ nat,E: vname] :
      ( ( ass @ E @ D )
     != ( cond @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_com_Osimps_I26_J) ).

thf(219,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: fun @ state @ nat,E: vname] :
      ( ( ass @ E @ D )
     != ( cond @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(67,axiom,
    ! [TA: $tType,A: fun @ nat @ TA,B: TA] :
      ( ( nat_case @ TA @ B @ A @ ( zero_zero @ nat ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_nat__case__0) ).

thf(377,plain,
    ! [TA: $tType,A: fun @ nat @ TA,B: TA] :
      ( ( nat_case @ TA @ B @ A @ ( zero_zero @ nat ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(31,axiom,
    ! [A: com1,B: com1,C: com1,D: com1] :
      ( ( ( semi @ D @ C )
        = ( semi @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_com_Osimps_I3_J) ).

thf(245,plain,
    ! [A: com1,B: com1,C: com1,D: com1] :
      ( ( ( ( semi @ D @ C )
          = ( semi @ B @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( semi @ D @ C )
          = ( semi @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(85,axiom,
    ! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA] :
      ( ( nat_rec @ TA @ C @ B @ ( suc @ A ) )
      = ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( nat_rec @ TA @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_nat__rec__Suc) ).

thf(434,plain,
    ! [TA: $tType,A: nat,B: fun @ nat @ ( fun @ TA @ TA ),C: TA] :
      ( ( nat_rec @ TA @ C @ B @ ( suc @ A ) )
      = ( aa @ TA @ TA @ ( aa @ nat @ ( fun @ TA @ TA ) @ B @ A ) @ ( nat_rec @ TA @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(24,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: com1,F: fun @ state @ bool] :
      ( ( cond @ F @ E @ D )
     != ( local @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_com_Osimps_I37_J) ).

thf(208,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: com1,E: com1,F: fun @ state @ bool] :
      ( ( cond @ F @ E @ D )
     != ( local @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(70,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(387,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(63,axiom,
    semiring_1 @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).

thf(367,plain,
    semiring_1 @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(8,axiom,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: fun @ state @ bool] :
      ( ( while @ D @ C )
     != ( ass @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_com_Osimps_I29_J) ).

thf(140,plain,
    ! [A: fun @ state @ nat,B: vname,C: com1,D: fun @ state @ bool] :
      ( ( while @ D @ C )
     != ( ass @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(92,axiom,
    ! [A: nat,B: nat] :
      ( ( ( suc @ B )
        = ( suc @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat_Oinject) ).

thf(462,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( suc @ B )
          = ( suc @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( suc @ B )
          = ( suc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(38,axiom,
    ! [A: com1,B: com1,C: fun @ state @ nat,D: vname] :
      ( ( ass @ D @ C )
     != ( semi @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_com_Osimps_I24_J) ).

thf(278,plain,
    ! [A: com1,B: com1,C: fun @ state @ nat,D: vname] :
      ( ( ass @ D @ C )
     != ( semi @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(28,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: com1,F: fun @ state @ bool] :
      ( ( ( cond @ F @ E @ D )
        = ( cond @ C @ B @ A ) )
    <=> ( ( F = C )
        & ( E = B )
        & ( D = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_com_Osimps_I4_J) ).

thf(223,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool,D: com1,E: com1,F: fun @ state @ bool] :
      ( ( ( ( cond @ F @ E @ D )
          = ( cond @ C @ B @ A ) )
       => ( ( F = C )
          & ( E = B )
          & ( D = A ) ) )
      & ( ( ( F = C )
          & ( E = B )
          & ( D = A ) )
       => ( ( cond @ F @ E @ D )
          = ( cond @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(46,axiom,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: fun @ state @ bool] :
      ( ( ( while @ D @ C )
        = ( while @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_com_Osimps_I5_J) ).

thf(306,plain,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: fun @ state @ bool] :
      ( ( ( ( while @ D @ C )
          = ( while @ B @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( while @ D @ C )
          = ( while @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(30,axiom,
    ! [A: com1,B: com1,C: fun @ state @ bool] :
      ( ( wt @ ( cond @ C @ B @ A ) )
     => ~ ( ( wt @ B )
         => ~ ( wt @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_WTs__elim__cases_I5_J) ).

thf(241,plain,
    ! [A: com1,B: com1,C: fun @ state @ bool] :
      ( ( wt @ ( cond @ C @ B @ A ) )
     => ~ ( ( wt @ B )
         => ~ ( wt @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(13,axiom,
    ! [A: com1,B: com1,C: com1,D: fun @ state @ nat,E: loc] :
      ( ( local @ E @ D @ C )
     != ( semi @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_com_Osimps_I34_J) ).

thf(167,plain,
    ! [A: com1,B: com1,C: com1,D: fun @ state @ nat,E: loc] :
      ( ( local @ E @ D @ C )
     != ( semi @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(39,axiom,
    ! [A: fun @ state @ nat,B: vname] :
      ( ( ass @ B @ A )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_com_Osimps_I9_J) ).

thf(282,plain,
    ! [A: fun @ state @ nat,B: vname] :
      ( ( ass @ B @ A )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(78,axiom,
    ! [TA: $tType,A: com1,B: com1,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),G: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( semi @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ G @ B ) @ A ) @ ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ B ) ) @ ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_com_Orecs_I4_J) ).

thf(409,plain,
    ! [TA: $tType,A: com1,B: com1,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),G: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( semi @ B @ A ) )
      = ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ G @ B ) @ A ) @ ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ B ) ) @ ( com_rec @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(52,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
      ( ( hoare_678420151le_rec @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_triple_Orecs) ).

thf(331,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
      ( ( hoare_678420151le_rec @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
      = ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com1 @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(87,axiom,
    ! [A: com1,B: state,C: nat,D: com1,E: state,F: fun @ state @ bool] :
      ( ~ ( pp @ ( aa @ state @ bool @ F @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ E ) @ C ) @ B ) )
       => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( cond @ F @ A @ D ) ) @ E ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_evaln_OIfFalse) ).

thf(441,plain,
    ! [A: com1,B: state,C: nat,D: com1,E: state,F: fun @ state @ bool] :
      ( ~ ( pp @ ( aa @ state @ bool @ F @ E ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ E ) @ C ) @ B ) )
       => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( cond @ F @ A @ D ) ) @ E ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(65,axiom,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ! [A: TA,B: fun @ TA @ TA] :
          ( ( semiri532925092at_aux @ TA @ B @ ( zero_zero @ nat ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_of__nat__aux_Osimps_I1_J) ).

thf(370,plain,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ! [A: TA,B: fun @ TA @ TA] :
          ( ( semiri532925092at_aux @ TA @ B @ ( zero_zero @ nat ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(93,axiom,
    ! [A: state,B: nat,C: state,D: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ A ) )
     => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ ( suc @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_evaln__Suc) ).

thf(470,plain,
    ! [A: state,B: nat,C: state,D: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ A ) )
     => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ ( suc @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(54,axiom,
    ! [TA: $tType,A: com1,B: fun @ state @ nat,C: loc,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),H: fun @ com1 @ ( fun @ com1 @ TA ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_case @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( local @ C @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) @ ( aa @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ) @ I @ C ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_com_Osimps_I66_J) ).

thf(336,plain,
    ! [TA: $tType,A: com1,B: fun @ state @ nat,C: loc,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),H: fun @ com1 @ ( fun @ com1 @ TA ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_case @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( local @ C @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) @ ( aa @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ) @ I @ C ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(15,axiom,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: com1,E: fun @ state @ bool] :
      ( ( cond @ E @ D @ C )
     != ( while @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_com_Osimps_I52_J) ).

thf(175,plain,
    ! [A: com1,B: fun @ state @ bool,C: com1,D: com1,E: fun @ state @ bool] :
      ( ( cond @ E @ D @ C )
     != ( while @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(97,axiom,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nat_Osimps_I2_J) ).

thf(482,plain,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(64,axiom,
    ! [A: nat,B: state] : ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ skip ) @ B ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_evaln_OSkip) ).

thf(368,plain,
    ! [A: nat,B: state] : ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ skip ) @ B ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(48,axiom,
    wt @ skip,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_WT_OSkip) ).

thf(319,plain,
    wt @ skip,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(45,axiom,
    ! [A: fun @ state @ nat,B: loc,C: com1] :
      ( ( wt @ C )
     => ( wt @ ( local @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_WT_OLocal) ).

thf(304,plain,
    ! [A: fun @ state @ nat,B: loc,C: com1] :
      ( ( wt @ C )
     => ( wt @ ( local @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(59,axiom,
    ! [TA: $tType,A: fun @ state @ nat,B: vname,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),G: fun @ com1 @ ( fun @ com1 @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( ass @ B @ A ) )
      = ( aa @ ( fun @ state @ nat ) @ TA @ ( aa @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) @ I @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_com_Osimps_I65_J) ).

thf(351,plain,
    ! [TA: $tType,A: fun @ state @ nat,B: vname,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),G: fun @ com1 @ ( fun @ com1 @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( ass @ B @ A ) )
      = ( aa @ ( fun @ state @ nat ) @ TA @ ( aa @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) @ I @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(14,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: fun @ state @ nat,E: vname] :
      ( ( ass @ E @ D )
     != ( local @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_com_Osimps_I22_J) ).

thf(171,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc,D: fun @ state @ nat,E: vname] :
      ( ( ass @ E @ D )
     != ( local @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(41,axiom,
    ! [A: fun @ state @ bool,B: com1] :
      ( ( wt @ B )
     => ( wt @ ( while @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_While) ).

thf(290,plain,
    ! [A: fun @ state @ bool,B: com1] :
      ( ( wt @ B )
     => ( wt @ ( while @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(106,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).

thf(510,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(36,axiom,
    ! [TA: $tType,A: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),B: fun @ pname @ TA,C: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),D: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),E: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),F: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),G: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),H: TA] :
      ( ( com_rec @ TA @ H @ G @ F @ E @ D @ C @ B @ A @ skip )
      = H ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_com_Orecs_I1_J) ).

thf(272,plain,
    ! [TA: $tType,A: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),B: fun @ pname @ TA,C: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ),D: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ),E: fun @ com1 @ ( fun @ com1 @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),F: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ ( fun @ TA @ TA ) ) ),G: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),H: TA] :
      ( ( com_rec @ TA @ H @ G @ F @ E @ D @ C @ B @ A @ skip )
      = H ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(57,axiom,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ! [A: TA,B: nat,C: fun @ TA @ TA] :
          ( ( semiri532925092at_aux @ TA @ C @ ( suc @ B ) @ A )
          = ( semiri532925092at_aux @ TA @ C @ B @ ( aa @ TA @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_of__nat__aux_Osimps_I2_J) ).

thf(346,plain,
    ! [TA: $tType] :
      ( ( semiring_1 @ TA )
     => ! [A: TA,B: nat,C: fun @ TA @ TA] :
          ( ( semiri532925092at_aux @ TA @ C @ ( suc @ B ) @ A )
          = ( semiri532925092at_aux @ TA @ C @ B @ ( aa @ TA @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(11,axiom,
    ! [A: fun @ state @ bool,B: com1,C: com1] :
      ( ( wt @ C )
     => ( ( wt @ B )
       => ( wt @ ( cond @ A @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_WT_OIf) ).

thf(151,plain,
    ! [A: fun @ state @ bool,B: com1,C: com1] :
      ( ( wt @ C )
     => ( ( wt @ B )
       => ( wt @ ( cond @ A @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(44,axiom,
    ! [A: com1,B: fun @ state @ bool,C: fun @ state @ nat,D: vname] :
      ( ( ass @ D @ C )
     != ( while @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_com_Osimps_I28_J) ).

thf(300,plain,
    ! [A: com1,B: fun @ state @ bool,C: fun @ state @ nat,D: vname] :
      ( ( ass @ D @ C )
     != ( while @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(84,axiom,
    ! [A: nat,B: com1,C: state,D: fun @ state @ bool] :
      ( ~ ( pp @ ( aa @ state @ bool @ D @ C ) )
     => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ D @ B ) ) @ C ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_evaln_OWhileFalse) ).

thf(432,plain,
    ! [A: nat,B: com1,C: state,D: fun @ state @ bool] :
      ( ~ ( pp @ ( aa @ state @ bool @ D @ C ) )
     => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( while @ D @ B ) ) @ C ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(17,axiom,
    ! [A: com1,B: com1,C: com1,D: com1,E: fun @ state @ bool] :
      ( ( cond @ E @ D @ C )
     != ( semi @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_com_Osimps_I45_J) ).

thf(183,plain,
    ! [A: com1,B: com1,C: com1,D: com1,E: fun @ state @ bool] :
      ( ( cond @ E @ D @ C )
     != ( semi @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(66,axiom,
    ! [A: nat,B: nat] :
      ( ( ( suc @ B )
        = ( suc @ A ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Suc__inject) ).

thf(373,plain,
    ! [A: nat,B: nat] :
      ( ( ( suc @ B )
        = ( suc @ A ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(7,axiom,
    ! [A: com1,B: com1] :
      ( ( semi @ B @ A )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_com_Osimps_I13_J) ).

thf(136,plain,
    ! [A: com1,B: com1] :
      ( ( semi @ B @ A )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(35,axiom,
    ! [A: com1,B: fun @ state @ nat,C: loc] :
      ( ( local @ C @ B @ A )
     != skip ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_com_Osimps_I11_J) ).

thf(268,plain,
    ! [A: com1,B: fun @ state @ nat,C: loc] :
      ( ( local @ C @ B @ A )
     != skip ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(86,axiom,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat_Osimps_I3_J) ).

thf(437,plain,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(75,axiom,
    ! [TA: $tType,A: com1,B: com1,C: fun @ state @ bool,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),H: fun @ com1 @ ( fun @ com1 @ TA ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_case @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( cond @ C @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ com1 @ ( fun @ com1 @ TA ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ) @ G @ C ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_com_Osimps_I68_J) ).

thf(400,plain,
    ! [TA: $tType,A: com1,B: com1,C: fun @ state @ bool,D: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),E: fun @ pname @ TA,F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),G: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),H: fun @ com1 @ ( fun @ com1 @ TA ),I: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),J: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),K: TA] :
      ( ( com_case @ TA @ K @ J @ I @ H @ G @ F @ E @ D @ ( cond @ C @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ com1 @ ( fun @ com1 @ TA ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ) @ G @ C ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(80,axiom,
    ! [A: state,B: nat,C: state,D: com1,E: com1,F: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( cond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
     => ( ( ( pp @ ( aa @ state @ bool @ F @ C ) )
         => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ E ) @ C ) @ B ) @ A ) ) )
       => ~ ( ~ ( pp @ ( aa @ state @ bool @ F @ C ) )
           => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_evaln__elim__cases_I5_J) ).

thf(415,plain,
    ! [A: state,B: nat,C: state,D: com1,E: com1,F: fun @ state @ bool] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( cond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
     => ( ( ( pp @ ( aa @ state @ bool @ F @ C ) )
         => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ E ) @ C ) @ B ) @ A ) ) )
       => ~ ( ~ ( pp @ ( aa @ state @ bool @ F @ C ) )
           => ~ ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ D ) @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(73,axiom,
    ! [A: state,B: com1,C: state,D: nat,E: state,F: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ F ) @ E ) @ D ) @ C ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ B ) @ C ) @ D ) @ A ) )
       => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( semi @ F @ B ) ) @ E ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_evaln_OSemi) ).

thf(395,plain,
    ! [A: state,B: com1,C: state,D: nat,E: state,F: com1] :
      ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ F ) @ E ) @ D ) @ C ) )
     => ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ B ) @ C ) @ D ) @ A ) )
       => ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ ( semi @ F @ B ) ) @ E ) @ D ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(83,axiom,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: nat] :
      ( ( hoare_1633586161_valid @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
    <=> ! [E: TA,F: state] :
          ( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ C @ E ) @ F ) )
         => ! [G: state] :
              ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ B ) @ F ) @ D ) @ G ) )
             => ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_triple__valid__def2) ).

thf(427,plain,
    ! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com1,C: fun @ TA @ ( fun @ state @ bool ),D: nat] :
      ( ( ( hoare_1633586161_valid @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
       => ! [E: TA,F: state] :
            ( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ C @ E ) @ F ) )
           => ! [G: state] :
                ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ B ) @ F ) @ D ) @ G ) )
               => ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ G ) ) ) ) )
      & ( ! [E: TA,F: state] :
            ( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ C @ E ) @ F ) )
           => ! [G: state] :
                ( ( pp @ ( aa @ state @ bool @ ( aa @ nat @ ( fun @ state @ bool ) @ ( aa @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) @ ( aa @ com1 @ ( fun @ state @ ( fun @ nat @ ( fun @ state @ bool ) ) ) @ evaln @ B ) @ F ) @ D ) @ G ) )
               => ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ G ) ) ) )
       => ( hoare_1633586161_valid @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(91,axiom,
    ! [TA: $tType,A: nat,B: fun @ nat @ TA,C: TA] :
      ( ( nat_case @ TA @ C @ B @ ( suc @ A ) )
      = ( aa @ nat @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_nat__case__Suc) ).

thf(459,plain,
    ! [TA: $tType,A: nat,B: fun @ nat @ TA,C: TA] :
      ( ( nat_case @ TA @ C @ B @ ( suc @ A ) )
      = ( aa @ nat @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(22,axiom,
    ! [A: com1,B: com1] :
      ( skip
     != ( semi @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_com_Osimps_I12_J) ).

thf(200,plain,
    ! [A: com1,B: com1] :
      ( skip
     != ( semi @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(103,axiom,
    ! [TA: $tType,A: com1,B: fun @ state @ bool,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),G: fun @ com1 @ ( fun @ com1 @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( while @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ) @ E @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_com_Osimps_I69_J) ).

thf(501,plain,
    ! [TA: $tType,A: com1,B: fun @ state @ bool,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),G: fun @ com1 @ ( fun @ com1 @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( while @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ) @ E @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(98,axiom,
    ! [TA: $tType,A: com1,B: com1,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),G: fun @ com1 @ ( fun @ com1 @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( semi @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ com1 @ ( fun @ com1 @ TA ) @ G @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_com_Osimps_I67_J) ).

thf(486,plain,
    ! [TA: $tType,A: com1,B: com1,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com1 @ ( fun @ com1 @ TA ) ),G: fun @ com1 @ ( fun @ com1 @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com1 @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
      ( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( semi @ B @ A ) )
      = ( aa @ com1 @ TA @ ( aa @ com1 @ ( fun @ com1 @ TA ) @ G @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(60,axiom,
    zero @ nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

thf(354,plain,
    zero @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(101,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fAll @ TA ) @ B ) )
      | ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fAll_1_1_U) ).

thf(496,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fAll @ TA ) @ B ) )
      | ( pp @ ( aa @ TA @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(519,plain,
    $false,
    inference(e,[status(thm)],[320,189,355,479,518,384,472,153,389,504,110,125,357,196,216,179,443,121,514,397,453,507,292,512,380,117,334,392,275,260,349,493,456,324,317,403,420,339,193,476,489,212,328,256,343,237,412,148,264,296,423,286,204,144,498,187,406,113,219,377,245,434,208,387,367,140,462,278,223,306,241,167,282,409,331,441,370,470,336,175,482,368,319,304,351,171,290,510,272,346,151,300,432,183,373,136,268,437,400,415,395,427,459,200,501,486,354,496]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW507_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 22:45:49 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.82/1.10  % [INFO] 	 Parsing done (243ms). 
% 1.82/1.11  % [INFO] 	 Running in sequential loop mode. 
% 2.41/1.30  % [INFO] 	 eprover registered as external prover. 
% 2.41/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 2.41/1.31  % [INFO] 	 Scanning for conjecture ... 
% 3.15/1.53  % [INFO] 	 Found a conjecture and 107 axioms. Running axiom selection ... 
% 3.75/1.62  % [INFO] 	 Axiom selection finished. Selected 107 axioms (removed 0 axioms). 
% 4.03/1.76  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 4.03/1.78  % [INFO] 	 Type checking passed. 
% 4.03/1.78  % [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 ... 
% 43.32/23.68  % External prover 'e' found a proof!
% 43.32/23.68  % [INFO] 	 Killing All external provers ... 
% 43.32/23.68  % Time passed: 23175ms (effective reasoning time: 22573ms)
% 43.32/23.68  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 43.32/23.68  % Axioms used in derivation (107): fact_44_com_Osimps_I5_J, fact_77_com_Osimps_I25_J, fact_56_com_Osimps_I29_J, fact_62_nat_Osimps_I2_J, fact_70_com_Osimps_I26_J, fact_68_com_Osimps_I53_J, help_fimplies_2_1_U, help_COMBS_1_1_U, fact_11_peek__and__def, fact_40_WTs__elim__cases_I3_J, fact_57_com_Osimps_I28_J, fact_18_evaln__elim__cases_I5_J, fact_36_WTs__elim__cases_I5_J, fact_79_com_Osimps_I34_J, arity_Nat_Onat___Rings_Osemiring__1, fact_81_com_Osimps_I17_J, fact_95_evaln__WHILE__case, fact_63_Zero__not__Suc, fact_21_nat__rec__Suc, fact_5_evaln__Suc, fact_9_Suc__n__not__n, fact_4_triple_Orecs, fact_83_com_Osimps_I10_J, fact_74_com_Osimps_I46_J, fact_27_com_Osimps_I12_J, fact_76_com_Osimps_I24_J, fact_84_com_Osimps_I9_J, fact_37_WT_OIf, fact_30_com_Osimps_I45_J, fact_35_WTs__elim__cases_I4_J, fact_17_evaln_OSemi, fact_29_com_Osimps_I44_J, fact_23_com_Osimps_I3_J, fact_42_com_Orecs_I1_J, fact_88_com_Osimps_I66_J, fact_38_WT_OSemi, fact_52_com_Osimps_I23_J, fact_33_com_Osimps_I67_J, fact_78_com_Osimps_I35_J, fact_0_triple_Oinject, fact_58_Suc__neq__Zero, help_COMBB_1_1_U, fact_66_WT_OLocal, fact_54_com_Osimps_I39_J, fact_19_evaln_OIfTrue, fact_13_of__nat__aux_Osimps_I2_J, fact_61_Suc__not__Zero, fact_12_evaln__max2, help_fAll_1_1_U, fact_15_evaln__elim__cases_I1_J, fact_32_com_Osimps_I64_J, fact_31_com_Osimps_I14_J, fact_34_com_Osimps_I68_J, fact_75_com_Osimps_I47_J, fact_43_of__nat__aux_Osimps_I1_J, fact_47_evaln_OWhileTrue, fact_53_com_Osimps_I38_J, fact_93_triple_Osize_I2_J, fact_8_n__not__Suc__n, fact_51_com_Orecs_I2_J, fact_94_def__nat__rec__0, fact_65_While, fact_86_nat__rec__0, fact_39_WT_OSkip, arity_Nat_Onat___Groups_Ozero, fact_55_com_Osimps_I22_J, fact_73_com_Osimps_I36_J, fact_20_evaln_OIfFalse, fact_80_com_Osimps_I16_J, fact_64_nat__case__0, fact_49_com_Orecs_I3_J, fact_16_evaln_OSkip, help_COMBC_1_1_U, fact_14_nat__case__Suc, fact_3_nat_Oinject, fact_48_evaln_OWhileFalse, fact_6_triple_Oexhaust, fact_28_com_Osimps_I15_J, fact_22_evaln__elim__cases_I4_J, fact_91_com_Orecs_I4_J, fact_71_com_Osimps_I27_J, fact_1_triple_Osimps_I2_J, fact_72_com_Osimps_I37_J, fact_82_com_Osimps_I8_J, fact_67_WT_OAssign, fact_87_com_Osimps_I69_J, fact_7_triple__valid__def2, fact_41_WTs__elim__cases_I6_J, fact_10_Suc__inject, help_pp_1_1_U, fact_45_com_Osimps_I2_J, fact_24_com_Osimps_I4_J, fact_26_com_Osimps_I13_J, fact_92_triple_Osize_I1_J, help_fimplies_1_1_U, fact_46_com_Osimps_I1_J, fact_50_com_Orecs_I6_J, fact_60_nat_Osimps_I3_J, help_fimplies_3_1_U, fact_2_triple__valid__def, fact_69_com_Osimps_I52_J, help_pp_2_1_U, fact_25_def__nat__rec__Suc, fact_59_Zero__neq__Suc, fact_89_com_Osimps_I65_J, fact_85_com_Osimps_I11_J, fact_90_com_Orecs_I5_J
% 43.32/23.68  % No. of inferences in proof: 218
% 43.32/23.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23175 ms resp. 22573 ms w/o parsing
% 44.02/23.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.02/23.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------