TSTP Solution File: LCL807_5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL807_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May  1 03:20:17 EDT 2024

% Result   : Theorem 0.56s 0.74s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   69
% Syntax   : Number of formulae    :   86 (   8 unt;  63 typ;   0 def)
%            Number of atoms       :   53 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   50 (  20   ~;  14   |;   5   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   32 (  18   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   4 prp; 0-3 aty)
%            Number of functors    :   55 (  55 usr;  29 con; 0-5 aty)
%            Number of variables   :   66 (  26   !;   5   ?;  66   :)
%                                         (  35  !>;   0  ?*;   0  @-;   0  @+)

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

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

tff(type_def_7,type,
    list: $tType > $tType ).

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

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

tff(type_def_10,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,
    combi: 
      !>[X0: $tType] : fun(X0,X0) ).

tff(func_def_3,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).

tff(func_def_4,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_5,type,
    it: fun(dB,bool) ).

tff(func_def_6,type,
    abs: dB > dB ).

tff(func_def_7,type,
    app: fun(dB,fun(dB,dB)) ).

tff(func_def_8,type,
    var: nat > dB ).

tff(func_def_9,type,
    dB_size: dB > nat ).

tff(func_def_10,type,
    lift: fun(dB,fun(nat,dB)) ).

tff(func_def_11,type,
    subst: fun(dB,fun(dB,fun(nat,dB))) ).

tff(func_def_12,type,
    foldl: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).

tff(func_def_13,type,
    foldr: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).

tff(func_def_14,type,
    cons: 
      !>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).

tff(func_def_15,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_16,type,
    listset: 
      !>[X0: $tType] : ( list(fun(X0,bool)) > fun(list(X0),bool) ) ).

tff(func_def_17,type,
    map: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).

tff(func_def_18,type,
    set_Cons: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(list(X0),bool) ) > fun(list(X0),bool) ) ).

tff(func_def_19,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

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

tff(func_def_21,type,
    fun1: fun(type,fun(type,type)) ).

tff(func_def_22,type,
    typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).

tff(func_def_23,type,
    typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).

tff(func_def_24,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_25,type,
    fAll: 
      !>[X0: $tType] : fun(fun(X0,bool),bool) ).

tff(func_def_26,type,
    fEx: 
      !>[X0: $tType] : fun(fun(X0,bool),bool) ).

tff(func_def_27,type,
    fFalse: bool ).

tff(func_def_28,type,
    fTrue: bool ).

tff(func_def_29,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_30,type,
    fequal: 
      !>[X0: $tType] : fun(X0,fun(X0,bool)) ).

tff(func_def_31,type,
    fimplies: fun(bool,fun(bool,bool)) ).

tff(func_def_32,type,
    member: 
      !>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).

tff(func_def_33,type,
    t2: type ).

tff(func_def_34,type,
    t1: type ).

tff(func_def_35,type,
    t_a: type ).

tff(func_def_36,type,
    t: type ).

tff(func_def_37,type,
    ts: list(type) ).

tff(func_def_38,type,
    a: dB ).

tff(func_def_39,type,
    as: list(dB) ).

tff(func_def_40,type,
    b: dB ).

tff(func_def_41,type,
    bs: list(dB) ).

tff(func_def_42,type,
    e: fun(nat,type) ).

tff(func_def_43,type,
    ea: fun(nat,type) ).

tff(func_def_44,type,
    i: nat ).

tff(func_def_45,type,
    ia: nat ).

tff(func_def_46,type,
    n: nat ).

tff(func_def_47,type,
    rs: list(dB) ).

tff(func_def_48,type,
    t3: dB ).

tff(func_def_49,type,
    u: dB ).

tff(func_def_50,type,
    ua: dB ).

tff(func_def_51,type,
    sK0: type ).

tff(func_def_52,type,
    sK1: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

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

tff(pred_def_2,type,
    listsp: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_3,type,
    pp: bool > $o ).

tff(pred_def_5,type,
    sQ2_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f181,plain,
    $false,
    inference(avatar_sat_refutation,[],[f177,f178,f180]) ).

tff(f180,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f179]) ).

tff(f179,plain,
    ( $false
    | ~ spl3_1 ),
    inference(resolution,[],[f172,f154]) ).

tff(f154,plain,
    pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK0)),
    inference(cnf_transformation,[],[f146]) ).

tff(f146,plain,
    ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f139,f145]) ).

tff(f145,plain,
    ( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
   => pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),sK0)) ),
    introduced(choice_axiom,[]) ).

tff(f139,plain,
    ( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
    inference(flattening,[],[f138]) ).

tff(f138,plain,
    ( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4)))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
        | ~ pp(aa(dB,bool,it,X3))
        | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2)) ) ),
    inference(ennf_transformation,[],[f126]) ).

tff(f126,plain,
    ( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
    & ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),b),X2))
       => ( pp(aa(dB,bool,it,X3))
         => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
           => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X3),X4))) ) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ( ? [X8: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X8))
    & ! [X4: fun(nat,type),X5: type,X6: dB,X7: nat] :
        ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X7),t)),b),X5))
       => ( pp(aa(dB,bool,it,X6))
         => ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X6),t))
           => pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,b),X6),X7))) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.OcplWfokU6/Vampire---4.8_15313',fact_2_Cons_I1_J) ).

tff(f172,plain,
    ( ! [X0: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f171]) ).

tff(f171,plain,
    ( spl3_1
  <=> ! [X0: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

tff(f178,plain,
    ~ spl3_2,
    inference(avatar_split_clause,[],[f150,f174]) ).

tff(f174,plain,
    ( spl3_2
  <=> thesis ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

tff(f150,plain,
    ~ thesis,
    inference(cnf_transformation,[],[f123]) ).

tff(f123,plain,
    ~ thesis,
    inference(flattening,[],[f121]) ).

tff(f121,negated_conjecture,
    ~ thesis,
    inference(negated_conjecture,[],[f120]) ).

tff(f120,conjecture,
    thesis,
    file('/export/starexec/sandbox/tmp/tmp.OcplWfokU6/Vampire---4.8_15313',conj_1) ).

tff(f177,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f149,f174,f171]) ).

tff(f149,plain,
    ! [X0: type] :
      ( thesis
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0)) ),
    inference(cnf_transformation,[],[f134]) ).

tff(f134,plain,
    ! [X0: type] :
      ( thesis
      | ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0)) ),
    inference(ennf_transformation,[],[f122]) ).

tff(f122,plain,
    ! [X0: type] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X0))
     => thesis ),
    inference(rectify,[],[f119]) ).

tff(f119,axiom,
    ! [X93: type] :
      ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),b),X93))
     => thesis ),
    file('/export/starexec/sandbox/tmp/tmp.OcplWfokU6/Vampire---4.8_15313',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : LCL807_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 17:00:04 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TF1_THM_EQU_NAR problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.OcplWfokU6/Vampire---4.8_15313
% 0.56/0.73  % (15674)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.56/0.73  % (15667)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.73  % (15669)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.73  % (15670)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.56/0.73  % (15671)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.73  % (15668)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.56/0.73  % (15672)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.56/0.73  % (15673)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.56/0.73  % (15674)First to succeed.
% 0.56/0.74  % (15674)Refutation found. Thanks to Tanya!
% 0.56/0.74  % SZS status Theorem for Vampire---4
% 0.56/0.74  % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.74  % (15674)------------------------------
% 0.56/0.74  % (15674)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.74  % (15674)Termination reason: Refutation
% 0.56/0.74  
% 0.56/0.74  % (15674)Memory used [KB]: 1170
% 0.56/0.74  % (15674)Time elapsed: 0.004 s
% 0.56/0.74  % (15674)Instructions burned: 11 (million)
% 0.56/0.74  % (15674)------------------------------
% 0.56/0.74  % (15674)------------------------------
% 0.56/0.74  % (15569)Success in time 0.366 s
% 0.56/0.74  % Vampire---4.8 exiting
%------------------------------------------------------------------------------