Vampire---5.0.1.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SWW507_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 01:30:42 PM UTC 2026

% Result   : Theorem 10.32s 2.28s
% Output   : Refutation 11.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   61 (  14 unt;   0 typ;   6 def)
%            Number of atoms       :  144 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  142 (  59   ~;  60   |;  11   &)
%                                         (   9 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :   19 (   2 avg)
%            Number of types       :    9 (   8 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   7 prp; 0-5 aty)
%            Number of functors    :   44 (  44 usr;   9 con; 0-10 aty)
%            Number of variables   :   97 (   0 sgn  91   !;   6   ?;  97   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    a: $tType ).

tff(type_def_6,type,
    com1: $tType ).

tff(type_def_7,type,
    loc: $tType ).

tff(type_def_8,type,
    pname: $tType ).

tff(type_def_9,type,
    state: $tType ).

tff(type_def_10,type,
    vname: $tType ).

tff(type_def_11,type,
    bool: $tType ).

tff(type_def_12,type,
    hoare_28830079triple: $tType > $tType ).

tff(type_def_13,type,
    nat: $tType ).

tff(type_def_14,type,
    fun: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).

tff(func_def_1,type,
    combc: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).

tff(func_def_2,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).

tff(func_def_3,type,
    ass: ( vname * fun(state,nat) ) > com1 ).

tff(func_def_4,type,
    cond: ( fun(state,bool) * com1 * com1 ) > com1 ).

tff(func_def_5,type,
    local: ( loc * fun(state,nat) * com1 ) > com1 ).

tff(func_def_6,type,
    skip: com1 ).

tff(func_def_7,type,
    semi: ( com1 * com1 ) > com1 ).

tff(func_def_8,type,
    while: ( fun(state,bool) * com1 ) > com1 ).

tff(func_def_9,type,
    com_case: 
      !>[X0: $tType] : ( ( X0 * fun(vname,fun(fun(state,nat),X0)) * fun(loc,fun(fun(state,nat),fun(com1,X0))) * fun(com1,fun(com1,X0)) * fun(fun(state,bool),fun(com1,fun(com1,X0))) * fun(fun(state,bool),fun(com1,X0)) * fun(pname,X0) * fun(vname,fun(pname,fun(fun(state,nat),X0))) * com1 ) > X0 ) ).

tff(func_def_10,type,
    com_rec: 
      !>[X0: $tType] : ( ( X0 * fun(vname,fun(fun(state,nat),X0)) * fun(loc,fun(fun(state,nat),fun(com1,fun(X0,X0)))) * fun(com1,fun(com1,fun(X0,fun(X0,X0)))) * fun(fun(state,bool),fun(com1,fun(com1,fun(X0,fun(X0,X0))))) * fun(fun(state,bool),fun(com1,fun(X0,X0))) * fun(pname,X0) * fun(vname,fun(pname,fun(fun(state,nat),X0))) * com1 ) > X0 ) ).

tff(func_def_11,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_12,type,
    hoare_1841697145triple: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com1 * fun(X0,fun(state,bool)) ) > hoare_28830079triple(X0) ) ).

tff(func_def_13,type,
    hoare_376461865e_case: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).

tff(func_def_14,type,
    hoare_678420151le_rec: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).

tff(func_def_15,type,
    hoare_47506394e_size: 
      !>[X0: $tType] : ( ( fun(X0,nat) * hoare_28830079triple(X0) ) > nat ) ).

tff(func_def_16,type,
    suc: nat > nat ).

tff(func_def_17,type,
    nat_case: 
      !>[X0: $tType] : ( ( X0 * fun(nat,X0) * nat ) > X0 ) ).

tff(func_def_18,type,
    nat_rec: 
      !>[X0: $tType] : ( ( X0 * fun(nat,fun(X0,X0)) * nat ) > X0 ) ).

tff(func_def_19,type,
    semiri532925092at_aux: 
      !>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).

tff(func_def_20,type,
    size_size: 
      !>[X0: $tType] : ( X0 > nat ) ).

tff(func_def_21,type,
    evaln: fun(com1,fun(state,fun(nat,fun(state,bool)))) ).

tff(func_def_22,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_23,type,
    fAll: 
      !>[X0: $tType] : fun(fun(X0,bool),bool) ).

tff(func_def_24,type,
    fFalse: bool ).

tff(func_def_25,type,
    fTrue: bool ).

tff(func_def_26,type,
    fimplies: fun(bool,fun(bool,bool)) ).

tff(func_def_27,type,
    com: com1 ).

tff(func_def_28,type,
    fun1: fun(a,fun(state,bool)) ).

tff(func_def_29,type,
    fun2: fun(a,fun(state,bool)) ).

tff(func_def_30,type,
    n: nat ).

tff(func_def_31,type,
    sK0: 
      !>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).

tff(func_def_32,type,
    sK1: 
      !>[X0: $tType] : ( hoare_28830079triple(X0) > com1 ) ).

tff(func_def_33,type,
    sK2: 
      !>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).

tff(func_def_34,type,
    sK3: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com1 * fun(X0,fun(state,bool)) * nat ) > X0 ) ).

tff(func_def_35,type,
    sK4: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com1 * fun(X0,fun(state,bool)) * nat ) > state ) ).

tff(func_def_36,type,
    sK5: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com1 * fun(X0,fun(state,bool)) * nat ) > state ) ).

tff(func_def_37,type,
    sK6: ( state * state * com1 * state * state * com1 ) > nat ).

tff(func_def_38,type,
    sK7: ( state * nat * state * com1 * com1 ) > state ).

tff(func_def_39,type,
    sK8: 
      !>[X0: $tType] : ( ( fun(nat,fun(X0,X0)) * X0 * fun(nat,X0) ) > nat ) ).

tff(func_def_40,type,
    sK9: 
      !>[X0: $tType] : ( ( fun(nat,fun(X0,X0)) * X0 * fun(nat,X0) ) > nat ) ).

tff(func_def_41,type,
    sK10: ( state * nat * state * com1 * fun(state,bool) ) > state ).

tff(pred_def_1,type,
    zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    wt: com1 > $o ).

tff(pred_def_4,type,
    hoare_1442473487ek_and: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(state,bool) * X0 * state ) > $o ) ).

tff(pred_def_5,type,
    hoare_1633586161_valid: 
      !>[X0: $tType] : ( ( nat * hoare_28830079triple(X0) ) > $o ) ).

tff(pred_def_6,type,
    pp: bool > $o ).

tff(f3,axiom,
    ! [X0: $tType,X1: hoare_28830079triple(X0),X2: nat] :
      ( hoare_1633586161_valid(X0,X2,X1)
    <=> pp(hoare_376461865e_case(X0,bool,aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool)))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool)),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool),com1),aa(fun(fun(X0,bool),bool),fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),combb(fun(X0,bool),bool,fun(X0,fun(state,bool))),fAll(X0)))),aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool)),com1),aa(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),combb(fun(X0,fun(state,bool)),fun(X0,bool),fun(X0,fun(state,bool))),aa(fun(fun(state,bool),bool),fun(fun(X0,fun(state,bool)),fun(X0,bool)),combb(fun(state,bool),bool,X0),fAll(state))))),aa(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combc(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),aa(fun(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))))),combb(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(X0,fun(state,bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1)),aa(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(X0,fun(state,bool))),combb(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(X0,fun(state,bool))),combs(X0,fun(state,bool),fun(state,bool))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),aa(fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool))))),combb(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool))),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X0),combs(state,bool,bool))),aa(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1),aa(fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),combb(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),aa(fun(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(fun(com1,fun(fun(state,bool),fun(state,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))))),combb(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),com1),combb(fun(state,bool),fun(state,fun(state,bool)),X0)),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)),X2))))))))),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_triple__valid__def) ).

tff(f6,axiom,
    ! [X0: state,X1: nat,X2: state,X3: 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,X3),X2),X1),X0))
     => 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,X3),X2),suc(X1)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_evaln__Suc) ).

tff(f8,axiom,
    ! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com1,X3: fun(X0,fun(state,bool)),X4: nat] :
      ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
    <=> ! [X5: X0,X6: state] :
          ( pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6))
         => ! [X7: 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,X2),X6),X4),X7))
             => pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_triple__valid__def2) ).

tff(f108,conjecture,
    ( ~ 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    | 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tate,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/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f109,negated_conjecture,
    ~ ( ~ 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      | 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tate,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(negated_conjecture,[status(cth)],[f108]) ).

tff(f112,plain,
    ! [X0: state,X1: nat,X2: state,X3: 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,X3),X2),suc(X1)),X0))
      | ~ 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,X3),X2),X1),X0)) ),
    inference(ennf_transformation,[],[f6]) ).

tff(f114,plain,
    ! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com1,X3: fun(X0,fun(state,bool)),X4: nat] :
      ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
    <=> ! [X5: X0,X6: state] :
          ( ! [X7: state] :
              ( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
              | ~ 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,X2),X6),X4),X7)) )
          | ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) ) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f147,plain,
    ( 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    & ~ 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tate,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(ennf_transformation,[],[f109]) ).

tff(f150,plain,
    ! [X0: $tType,X1: hoare_28830079triple(X0),X2: nat] :
      ( ( hoare_1633586161_valid(X0,X2,X1)
        | ~ 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)
      & ( pp(hoare_376461865e_case(X0,bool,aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool)))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool)),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool),com1),aa(fun(fun(X0,bool),bool),fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),combb(fun(X0,bool),bool,fun(X0,fun(state,bool))),fAll(X0)))),aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool)),com1),aa(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),combb(fun(X0,fun(state,bool)),fun(X0,bool),fun(X0,fun(state,bool))),aa(fun(fun(state,bool),bool),fun(fun(X0,fun(state,bool)),fun(X0,bool)),combb(fun(state,bool),bool,X0),fAll(state))))),aa(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combc(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),aa(fun(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))))),combb(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(X0,fun(state,bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1)),aa(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(X0,fun(state,bool))),combb(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(X0,fun(state,bool))),combs(X0,fun(state,bool),fun(state,bool))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),aa(fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool))))),combb(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool))),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X0),combs(state,bool,bool))),aa(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1),aa(fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),combb(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),aa(fun(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(fun(com1,fun(fun(state,bool),fun(state,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))))),combb(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),com1),combb(fun(state,bool),fun(state,fun(state,bool)),X0)),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)),X2))))))))),X1))
        | ~ hoare_1633586161_valid(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f3]) ).

tff(f153,plain,
    ! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com1,X3: fun(X0,fun(state,bool)),X4: nat] :
      ( ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
        | ? [X5: X0,X6: state] :
            ( ? [X7: state] :
                ( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
                & 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,X2),X6),X4),X7)) )
            & pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) ) )
      & ( ! [X5: X0,X6: state] :
            ( ! [X7: state] :
                ( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
                | ~ 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,X2),X6),X4),X7)) )
            | ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) )
        | ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ) ),
    inference(nnf_transformation,[],[f114]) ).

tff(f154,plain,
    ! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com1,X3: fun(X0,fun(state,bool)),X4: nat] :
      ( ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
        | ? [X5: X0,X6: state] :
            ( ? [X7: state] :
                ( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,X5),X7))
                & 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,X2),X6),X4),X7)) )
            & pp(aa(state,bool,aa(X0,fun(state,bool),X3,X5),X6)) ) )
      & ( ! [X8: X0,X9: state] :
            ( ! [X10: state] :
                ( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X8),X10))
                | ~ 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,X2),X9),X4),X10)) )
            | ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X8),X9)) )
        | ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ) ),
    inference(rectify,[],[f153]) ).

tff(f155,plain,
    ! [X0: $tType,X1: fun(X0,fun(state,bool)),X2: com1,X3: fun(X0,fun(state,bool)),X4: nat] :
      ( ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
        | ( ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK3(X0,X1,X2,X3,X4)),sK5(X0,X1,X2,X3,X4)))
          & 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,X2),sK4(X0,X1,X2,X3,X4)),X4),sK5(X0,X1,X2,X3,X4)))
          & pp(aa(state,bool,aa(X0,fun(state,bool),X3,sK3(X0,X1,X2,X3,X4)),sK4(X0,X1,X2,X3,X4))) ) )
      & ( ! [X8: X0,X9: state] :
            ( ! [X10: state] :
                ( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X8),X10))
                | ~ 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,X2),X9),X4),X10)) )
            | ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X8),X9)) )
        | ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X5,sK3(X0,X1,X2,X3,X4)),skolemize(X6,sK4(X0,X1,X2,X3,X4)),skolemize(X7,sK5(X0,X1,X2,X3,X4))],[f154]) ).

tff(f176,plain,
    ! [X0: $tType,X2: nat,X1: hoare_28830079triple(X0)] :
      ( pp(hoare_376461865e_case(X0,bool,aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool)))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool)),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool),com1),aa(fun(fun(X0,bool),bool),fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),combb(fun(X0,bool),bool,fun(X0,fun(state,bool))),fAll(X0)))),aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool)),com1),aa(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),combb(fun(X0,fun(state,bool)),fun(X0,bool),fun(X0,fun(state,bool))),aa(fun(fun(state,bool),bool),fun(fun(X0,fun(state,bool)),fun(X0,bool)),combb(fun(state,bool),bool,X0),fAll(state))))),aa(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combc(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),aa(fun(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))))),combb(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(X0,fun(state,bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1)),aa(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(X0,fun(state,bool))),combb(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(X0,fun(state,bool))),combs(X0,fun(state,bool),fun(state,bool))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),aa(fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool))))),combb(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool))),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X0),combs(state,bool,bool))),aa(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1),aa(fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),combb(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),aa(fun(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(fun(com1,fun(fun(state,bool),fun(state,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))))),combb(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),com1),combb(fun(state,bool),fun(state,fun(state,bool)),X0)),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)),X2))))))))),X1))
      | ~ hoare_1633586161_valid(X0,X2,X1) ),
    inference(cnf_transformation,[],[f150]) ).

tff(f177,plain,
    ! [X0: $tType,X2: nat,X1: hoare_28830079triple(X0)] :
      ( hoare_1633586161_valid(X0,X2,X1)
      | ~ pp(hoare_376461865e_case(X0,bool,aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),bool)))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool)),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(com1,fun(fun(X0,fun(state,bool)),bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool),com1),aa(fun(fun(X0,bool),bool),fun(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(X0,fun(state,bool)),bool)),combb(fun(X0,bool),bool,fun(X0,fun(state,bool))),fAll(X0)))),aa(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),aa(fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))))),combb(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(X0,fun(state,bool))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,bool)))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool)),com1),aa(fun(fun(X0,fun(state,bool)),fun(X0,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,bool))),combb(fun(X0,fun(state,bool)),fun(X0,bool),fun(X0,fun(state,bool))),aa(fun(fun(state,bool),bool),fun(fun(X0,fun(state,bool)),fun(X0,bool)),combb(fun(state,bool),bool,X0),fAll(state))))),aa(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combc(fun(X0,fun(state,bool)),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),aa(fun(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(X0,fun(state,bool)),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))))),combb(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(X0,fun(state,bool))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1)),aa(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),fun(fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(X0,fun(state,bool))),combb(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(X0,fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),fun(X0,fun(state,bool))),combs(X0,fun(state,bool),fun(state,bool))),aa(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool)))),aa(fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(fun(state,bool),fun(state,bool))))),combb(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool))),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(X0,fun(state,fun(bool,bool))),fun(X0,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),X0),combs(state,bool,bool))),aa(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),aa(fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),fun(fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))))),combb(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),com1),aa(fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),fun(fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,bool)))),combb(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool)),fun(X0,fun(state,bool))),aa(fun(fun(state,fun(state,bool)),fun(state,bool)),fun(fun(X0,fun(state,fun(state,bool))),fun(X0,fun(state,bool))),combb(fun(state,fun(state,bool)),fun(state,bool),X0),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(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),aa(fun(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool))))),fun(fun(com1,fun(fun(state,bool),fun(state,fun(state,bool)))),fun(com1,fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))))),combb(fun(fun(state,bool),fun(state,fun(state,bool))),fun(fun(X0,fun(state,bool)),fun(X0,fun(state,fun(state,bool)))),com1),combb(fun(state,bool),fun(state,fun(state,bool)),X0)),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)),X2))))))))),X1)) ),
    inference(cnf_transformation,[],[f150]) ).

tff(f181,plain,
    ! [X2: state,X3: com1,X0: state,X1: 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,X3),X2),suc(X1)),X0))
      | ~ 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,X3),X2),X1),X0)) ),
    inference(cnf_transformation,[],[f112]) ).

tff(f183,plain,
    ! [X0: $tType,X2: com1,X3: fun(X0,fun(state,bool)),X10: state,X1: fun(X0,fun(state,bool)),X8: X0,X9: state,X4: nat] :
      ( pp(aa(state,bool,aa(X0,fun(state,bool),X1,X8),X10))
      | ~ 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,X2),X9),X4),X10))
      | ~ pp(aa(state,bool,aa(X0,fun(state,bool),X3,X8),X9))
      | ~ hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1)) ),
    inference(cnf_transformation,[],[f155]) ).

tff(f184,plain,
    ! [X0: $tType,X2: com1,X3: fun(X0,fun(state,bool)),X1: fun(X0,fun(state,bool)),X4: nat] :
      ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
      | pp(aa(state,bool,aa(X0,fun(state,bool),X3,sK3(X0,X1,X2,X3,X4)),sK4(X0,X1,X2,X3,X4))) ),
    inference(cnf_transformation,[],[f155]) ).

tff(f185,plain,
    ! [X0: $tType,X2: com1,X3: fun(X0,fun(state,bool)),X1: fun(X0,fun(state,bool)),X4: nat] :
      ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
      | 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,X2),sK4(X0,X1,X2,X3,X4)),X4),sK5(X0,X1,X2,X3,X4))) ),
    inference(cnf_transformation,[],[f155]) ).

tff(f186,plain,
    ! [X0: $tType,X2: com1,X3: fun(X0,fun(state,bool)),X1: fun(X0,fun(state,bool)),X4: nat] :
      ( hoare_1633586161_valid(X0,X4,hoare_1841697145triple(X0,X3,X2,X1))
      | ~ pp(aa(state,bool,aa(X0,fun(state,bool),X1,sK3(X0,X1,X2,X3,X4)),sK5(X0,X1,X2,X3,X4))) ),
    inference(cnf_transformation,[],[f155]) ).

tff(f308,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(f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tate,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(cnf_transformation,[],[f147]) ).

tff(f309,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(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)),suc(n)))))))))),hoare_1841697145triple(a,fun1,com,fun2))),
    inference(cnf_transformation,[],[f147]) ).

tff(f310,plain,
    ~ hoare_1633586161_valid(a,n,hoare_1841697145triple(a,fun1,com,fun2)),
    inference(forward_literal_rewriting,[],[f308,f176]) ).

tff(f311,plain,
    hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,fun1,com,fun2)),
    inference(forward_literal_rewriting,[],[f309,f177]) ).

tff(f313,definition,
    ( spl11_1
  <=> hoare_1633586161_valid(a,n,hoare_1841697145triple(a,fun1,com,fun2)) ),
    introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).

tff(f315,plain,
    ( ~ hoare_1633586161_valid(a,n,hoare_1841697145triple(a,fun1,com,fun2))
    | spl11_1 ),
    inference(avatar_component_clause,[],[f313]) ).

tff(f316,plain,
    ~ spl11_1,
    inference(avatar_split_clause,[],[f310,f313]) ).

tff(f318,definition,
    ( spl11_2
  <=> hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,fun1,com,fun2)) ),
    introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).

tff(f320,plain,
    ( hoare_1633586161_valid(a,suc(n),hoare_1841697145triple(a,fun1,com,fun2))
    | ~ spl11_2 ),
    inference(avatar_component_clause,[],[f318]) ).

tff(f321,plain,
    spl11_2,
    inference(avatar_split_clause,[],[f311,f318]) ).

tff(f322,plain,
    ( pp(aa(state,bool,aa(a,fun(state,bool),fun1,sK3(a,fun2,com,fun1,n)),sK4(a,fun2,com,fun1,n)))
    | spl11_1 ),
    inference(resolution,[],[f315,f184]) ).

tff(f323,plain,
    ( 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,com),sK4(a,fun2,com,fun1,n)),n),sK5(a,fun2,com,fun1,n)))
    | spl11_1 ),
    inference(resolution,[],[f315,f185]) ).

tff(f324,plain,
    ( ~ pp(aa(state,bool,aa(a,fun(state,bool),fun2,sK3(a,fun2,com,fun1,n)),sK5(a,fun2,com,fun1,n)))
    | spl11_1 ),
    inference(resolution,[],[f315,f186]) ).

tff(f330,definition,
    ( spl11_3
  <=> pp(aa(state,bool,aa(a,fun(state,bool),fun2,sK3(a,fun2,com,fun1,n)),sK5(a,fun2,com,fun1,n))) ),
    introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).

tff(f332,plain,
    ( ~ pp(aa(state,bool,aa(a,fun(state,bool),fun2,sK3(a,fun2,com,fun1,n)),sK5(a,fun2,com,fun1,n)))
    | spl11_3 ),
    inference(avatar_component_clause,[],[f330]) ).

tff(f333,plain,
    ( ~ spl11_3
    | spl11_1 ),
    inference(avatar_split_clause,[],[f324,f313,f330]) ).

tff(f335,definition,
    ( spl11_4
  <=> 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,com),sK4(a,fun2,com,fun1,n)),n),sK5(a,fun2,com,fun1,n))) ),
    introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).

tff(f337,plain,
    ( 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,com),sK4(a,fun2,com,fun1,n)),n),sK5(a,fun2,com,fun1,n)))
    | ~ spl11_4 ),
    inference(avatar_component_clause,[],[f335]) ).

tff(f338,plain,
    ( spl11_4
    | spl11_1 ),
    inference(avatar_split_clause,[],[f323,f313,f335]) ).

tff(f340,definition,
    ( spl11_5
  <=> pp(aa(state,bool,aa(a,fun(state,bool),fun1,sK3(a,fun2,com,fun1,n)),sK4(a,fun2,com,fun1,n))) ),
    introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).

tff(f342,plain,
    ( pp(aa(state,bool,aa(a,fun(state,bool),fun1,sK3(a,fun2,com,fun1,n)),sK4(a,fun2,com,fun1,n)))
    | ~ spl11_5 ),
    inference(avatar_component_clause,[],[f340]) ).

tff(f343,plain,
    ( spl11_5
    | spl11_1 ),
    inference(avatar_split_clause,[],[f322,f313,f340]) ).

tff(f344,plain,
    ( ! [X2: state,X0: a,X1: state] :
        ( pp(aa(state,bool,aa(a,fun(state,bool),fun2,X0),X1))
        | ~ 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,com),X2),suc(n)),X1))
        | ~ pp(aa(state,bool,aa(a,fun(state,bool),fun1,X0),X2)) )
    | ~ spl11_2 ),
    inference(resolution,[],[f320,f183]) ).

tff(f375,plain,
    ( 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,com),sK4(a,fun2,com,fun1,n)),suc(n)),sK5(a,fun2,com,fun1,n)))
    | ~ spl11_4 ),
    inference(resolution,[],[f337,f181]) ).

tff(f395,definition,
    ( spl11_7
  <=> 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,com),sK4(a,fun2,com,fun1,n)),suc(n)),sK5(a,fun2,com,fun1,n))) ),
    introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).

tff(f398,plain,
    ( spl11_7
    | ~ spl11_4 ),
    inference(avatar_split_clause,[],[f375,f335,f395]) ).

tff(f399,plain,
    ( ! [X0: state] :
        ( ~ pp(aa(state,bool,aa(a,fun(state,bool),fun1,sK3(a,fun2,com,fun1,n)),X0))
        | ~ 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,com),X0),suc(n)),sK5(a,fun2,com,fun1,n))) )
    | ~ spl11_2
    | spl11_3 ),
    inference(resolution,[],[f344,f332]) ).

tff(f526,plain,
    ( ~ 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,com),sK4(a,fun2,com,fun1,n)),suc(n)),sK5(a,fun2,com,fun1,n)))
    | ~ spl11_2
    | spl11_3
    | ~ spl11_5 ),
    inference(resolution,[],[f399,f342]) ).

tff(f545,plain,
    ( ~ spl11_7
    | ~ spl11_2
    | spl11_3
    | ~ spl11_5 ),
    inference(avatar_split_clause,[],[f526,f340,f330,f318,f395]) ).

cnf(s1,plain,
    ~ spl11_1,
    inference(sat_conversion,[],[f316]) ).

cnf(s2,plain,
    spl11_2,
    inference(sat_conversion,[],[f321]) ).

cnf(s3,plain,
    ( spl11_1
    | ~ spl11_3 ),
    inference(sat_conversion,[],[f333]) ).

cnf(s4,plain,
    ( spl11_1
    | spl11_4 ),
    inference(sat_conversion,[],[f338]) ).

cnf(s5,plain,
    ( spl11_1
    | spl11_5 ),
    inference(sat_conversion,[],[f343]) ).

cnf(s7,plain,
    ( ~ spl11_4
    | spl11_7 ),
    inference(sat_conversion,[],[f398]) ).

cnf(s14,plain,
    ( ~ spl11_2
    | spl11_3
    | ~ spl11_5
    | ~ spl11_7 ),
    inference(sat_conversion,[],[f545]) ).

cnf(s15,plain,
    spl11_5,
    inference(rat,[],[s5,s1]) ).

cnf(s16,plain,
    spl11_4,
    inference(rat,[],[s4,s1]) ).

cnf(s17,plain,
    ~ spl11_3,
    inference(rat,[],[s3,s1]) ).

cnf(s18,plain,
    spl11_7,
    inference(rat,[],[s7,s16]) ).

cnf(s19,plain,
    $false,
    inference(rat,[],[s14,s15,s2,s18,s17]) ).

tff(f546,plain,
    $false,
    inference(avatar_sat_refutation,[],[s19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW507_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26  % Computer : n008.cluster.edu
% 0.11/0.26  % Model    : x86_64 x86_64
% 0.11/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26  % Memory   : 8046.5625MB
% 0.11/0.26  % OS       : Linux 6.8.0-71-generic
% 0.11/0.26  % CPULimit : 300
% 0.11/0.26  % WCLimit  : 300
% 0.11/0.26  % DateTime : Mon Sep 28 14:16:09 UTC 2026
% 0.11/0.26  % CPUTime  : 
% 0.11/0.26  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31  Running first-order theorem proving
% 0.25/0.31  Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.32/2.28  % (2276298)Detected formulas, will run a generic FOF schedule.
% 10.32/2.28  % (2276304)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1924468621:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.32/2.28  % (2276308)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1961824555:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.32/2.28  % (2276306)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2219253593:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.32/2.28  % (2276305)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=331897363:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.32/2.28  % (2276306)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.32/2.28  % (2276308)Instruction limit reached! 
% 10.32/2.28  % (2276308)------------------------------
% 10.32/2.28  % (2276308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276308)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276308)Termination reason: Instruction limit
% 10.32/2.28  % (2276308)Termination phase: Saturation
% 10.32/2.28  % (2276308)Time elapsed: 0.101 s
% 10.32/2.28  % (2276308)Peak memory usage: 89 MB
% 10.32/2.28  % (2276308)Instructions burned: 120 (million)
% 10.32/2.28  % (2276307)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=266521275:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.32/2.28  % (2276309)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1133442054:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.32/2.28  % (2276310)dis-21_1_sil=8000:lcm=predicate:random_seed=559660632:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.32/2.28  % (2276307)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 10.32/2.28  % (2276307)Instruction limit reached! 
% 10.32/2.28  % (2276307)------------------------------
% 10.32/2.28  % (2276307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276307)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276307)Termination reason: Instruction limit
% 10.32/2.28  % (2276307)Termination phase: Saturation
% 10.32/2.28  % (2276307)Time elapsed: 0.076 s
% 10.32/2.28  % (2276307)Peak memory usage: 88 MB
% 10.32/2.28  % (2276307)Instructions burned: 110 (million)
% 10.32/2.28  % (2276310)Instruction limit reached! 
% 10.32/2.28  % (2276310)------------------------------
% 10.32/2.28  % (2276310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276310)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276310)Termination reason: Instruction limit
% 10.32/2.28  % (2276310)Termination phase: Saturation
% 10.32/2.28  % (2276310)Time elapsed: 0.099 s
% 10.32/2.28  % (2276310)Peak memory usage: 90 MB
% 10.32/2.28  % (2276310)Instructions burned: 129 (million)
% 10.32/2.28  % (2276309)Instruction limit reached! 
% 10.32/2.28  % (2276309)------------------------------
% 10.32/2.28  % (2276309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276309)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276309)Termination reason: Instruction limit
% 10.32/2.28  % (2276309)Termination phase: Saturation
% 10.32/2.28  % (2276309)Time elapsed: 0.138 s
% 10.32/2.28  % (2276309)Peak memory usage: 90 MB
% 10.32/2.28  % (2276309)Instructions burned: 139 (million)
% 10.32/2.28  % Exception at run slice level
% 10.32/2.28  User error: GNN currently only supports monomorphic FOL.
% 10.32/2.28  % (2276315)lrs+10_1_sil=8000:sp=occurrence:random_seed=127826028:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.32/2.28  % (2276319)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2206126243:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 10.32/2.28  % (2276320)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3950423258:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 10.32/2.28  % (2276321)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3128954410:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.32/2.28  % (2276322)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3705316004:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 10.32/2.28  % (2276319)Instruction limit reached! 
% 10.32/2.28  % (2276319)------------------------------
% 10.32/2.28  % (2276319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276319)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276319)Termination reason: Instruction limit
% 10.32/2.28  % (2276319)Termination phase: Saturation
% 10.32/2.28  % (2276319)Time elapsed: 0.148 s
% 10.32/2.28  % (2276319)Peak memory usage: 90 MB
% 10.32/2.28  % (2276319)Instructions burned: 157 (million)
% 10.32/2.28  % (2276315)Instruction limit reached! 
% 10.32/2.28  % (2276315)------------------------------
% 10.32/2.28  % (2276315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276315)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276315)Termination reason: Instruction limit
% 10.32/2.28  % (2276315)Termination phase: Saturation
% 10.32/2.28  % (2276315)Time elapsed: 0.277 s
% 10.32/2.28  % (2276315)Peak memory usage: 91 MB
% 10.32/2.28  % (2276315)Instructions burned: 286 (million)
% 10.32/2.28  % (2276322)Instruction limit reached! 
% 10.32/2.28  % (2276322)------------------------------
% 10.32/2.28  % (2276322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276322)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276322)Termination reason: Instruction limit
% 10.32/2.28  % (2276322)Termination phase: Saturation
% 10.32/2.28  % (2276322)Time elapsed: 0.103 s
% 10.32/2.28  % (2276322)Peak memory usage: 89 MB
% 10.32/2.28  % (2276322)Instructions burned: 296 (million)
% 10.32/2.28  % Exception at run slice level
% 10.32/2.28  User error: GNN currently only supports monomorphic FOL.
% 10.32/2.28  % Exception at run slice level
% 10.32/2.28  User error: GNN currently only supports monomorphic FOL.
% 10.32/2.28  % (2276321)Instruction limit reached! 
% 10.32/2.28  % (2276321)------------------------------
% 10.32/2.28  % (2276321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276321)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276321)Termination reason: Instruction limit
% 10.32/2.28  % (2276321)Termination phase: Saturation
% 10.32/2.28  % (2276321)Time elapsed: 0.197 s
% 10.32/2.28  % (2276321)Peak memory usage: 89 MB
% 10.32/2.28  % (2276321)Instructions burned: 249 (million)
% 10.32/2.28  % (2276320)Instruction limit reached! 
% 10.32/2.28  % (2276320)------------------------------
% 10.32/2.28  % (2276320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276320)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276320)Termination reason: Instruction limit
% 10.32/2.28  % (2276320)Termination phase: Saturation
% 10.32/2.28  % (2276320)Time elapsed: 0.309 s
% 10.32/2.28  % (2276320)Peak memory usage: 92 MB
% 10.32/2.28  % (2276320)Instructions burned: 325 (million)
% 10.32/2.28  % (2276330)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=33394893:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 10.32/2.28  % (2276333)lrs+10_1_sil=8000:sp=occurrence:random_seed=40843252:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.32/2.28  % (2276328)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=716912322:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 10.32/2.28  % (2276329)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1895815918:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 10.32/2.28  % (2276330)Instruction limit reached! 
% 10.32/2.28  % (2276330)------------------------------
% 10.32/2.28  % (2276330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276330)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276330)Termination reason: Instruction limit
% 10.32/2.28  % (2276330)Termination phase: Saturation
% 10.32/2.28  % (2276330)Time elapsed: 0.055 s
% 10.32/2.28  % (2276330)Peak memory usage: 88 MB
% 10.32/2.28  % (2276330)Instructions burned: 129 (million)
% 10.32/2.28  % (2276329)First to succeed.
% 10.32/2.28  % (2276329)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2276298"
% 10.32/2.28  % (2276332)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3755300799:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 10.32/2.28  % (2276336)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=70387806:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 10.32/2.28  % (2276336)Refutation not found, incomplete strategy
% 10.32/2.28  % (2276336)------------------------------
% 10.32/2.28  % (2276336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276336)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276336)Termination reason: Refutation not found, incomplete strategy
% 10.32/2.28  % (2276336)Time elapsed: 0.038 s
% 10.32/2.28  % (2276336)Peak memory usage: 89 MB
% 10.32/2.28  % (2276336)Instructions burned: 44 (million)
% 10.32/2.28  % (2276332)Instruction limit reached! 
% 10.32/2.28  % (2276332)------------------------------
% 10.32/2.28  % (2276332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276332)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276332)Termination reason: Instruction limit
% 10.32/2.28  % (2276332)Termination phase: Saturation
% 10.32/2.28  % (2276332)Time elapsed: 0.112 s
% 10.32/2.28  % (2276332)Peak memory usage: 89 MB
% 10.32/2.28  % (2276332)Instructions burned: 115 (million)
% 10.32/2.28  % (2276338)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3238500582:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 10.32/2.28  % (2276343)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=851224343:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 10.32/2.28  % (2276343)Instruction limit reached! 
% 10.32/2.28  % (2276343)------------------------------
% 10.32/2.28  % (2276343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.28  % (2276343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.28  % (2276343)CaDiCaL version: 2.1.3
% 10.32/2.28  % (2276343)Termination reason: Instruction limit
% 10.32/2.28  % (2276343)Termination phase: Saturation
% 10.32/2.28  % (2276343)Time elapsed: 0.065 s
% 10.32/2.28  % (2276343)Peak memory usage: 91 MB
% 10.32/2.28  % (2276343)Instructions burned: 135 (million)
% 10.32/2.28  % (2276333)Also succeeded, but the first one will report.
% 10.32/2.28  % (2276329)Refutation found. Thanks to Tanya!
% 10.32/2.28  % SZS status Theorem for theBenchmark
% 10.32/2.28  % SZS output start Proof for theBenchmark
% See solution above
% 11.30/2.59  % (2276329)------------------------------
% 11.30/2.59  % (2276329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.30/2.59  % (2276329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.30/2.59  % (2276329)CaDiCaL version: 2.1.3
% 11.30/2.59  % (2276329)Termination reason: Refutation
% 11.30/2.59  % (2276329)Time elapsed: 0.054 s
% 11.30/2.59  % (2276329)Peak memory usage: 90 MB
% 11.30/2.59  % (2276329)Instructions burned: 60 (million)
% 11.30/2.59  % (2276329)------------------------------
% 11.30/2.59  % (2276329)------------------------------
% 11.30/2.59  % (2276298)Success in time 1.507 s
% 11.30/2.59  % Vampire exiting
%------------------------------------------------------------------------------