TSTP Solution File: SWW520_5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWW520_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 : n021.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 04:19:46 EDT 2024

% Result   : Theorem 0.61s 0.83s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   45
% Syntax   : Number of formulae    :   57 (   3 unt;  40 typ;   0 def)
%            Number of atoms       :   55 (   9 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   64 (  26   ~;  14   |;  16   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   39 (  24   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-6 aty)
%            Number of functors    :   24 (  24 usr;   5 con; 0-4 aty)
%            Number of variables   :   76 (  30   !;  14   ?;  76   :)
%                                         (  32  !>;   0  ?*;   0  @-;   0  @+)

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

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

tff(type_def_7,type,
    hoare_28830079triple: $tType > $tType ).

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

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

tff(type_def_10,type,
    fun: ( $tType * $tType ) > $tType ).

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

tff(func_def_1,type,
    complete_Sup_Sup: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_2,type,
    suc: nat > nat ).

tff(func_def_3,type,
    semiri532925092at_aux: 
      !>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).

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

tff(func_def_5,type,
    powp: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(fun(X0,bool),bool) ) ).

tff(func_def_6,type,
    pred1: 
      !>[X0: $tType] : ( fun(X0,bool) > pred(X0) ) ).

tff(func_def_7,type,
    pred_case: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,bool),X1) * pred(X0) ) > X1 ) ).

tff(func_def_8,type,
    pred_rec: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,bool),X1) * pred(X0) ) > X1 ) ).

tff(func_def_9,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

tff(func_def_10,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_11,type,
    fFalse: bool ).

tff(func_def_12,type,
    fTrue: bool ).

tff(func_def_13,type,
    ga: fun(hoare_28830079triple(a),bool) ).

tff(func_def_14,type,
    sK0: nat ).

tff(func_def_15,type,
    sK1: hoare_28830079triple(a) ).

tff(func_def_16,type,
    sK2: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_17,type,
    sK3: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_18,type,
    sK4: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_19,type,
    sK5: 
      !>[X0: $tType] : ( ( nat * fun(hoare_28830079triple(X0),bool) ) > hoare_28830079triple(X0) ) ).

tff(func_def_20,type,
    sK6: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

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

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

tff(pred_def_3,type,
    order: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

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

tff(pred_def_6,type,
    preorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    comple187826305attice: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    hoare_592965047valids: 
      !>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).

tff(pred_def_9,type,
    hoare_1633586161_valid: 
      !>[X0: $tType] : ( ( nat * hoare_28830079triple(X0) ) > $o ) ).

tff(pred_def_10,type,
    ord_less_eq: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_11,type,
    inv_imagep: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).

tff(pred_def_12,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_13,type,
    pp: bool > $o ).

tff(f212,plain,
    $false,
    inference(resolution,[],[f182,f207]) ).

tff(f207,plain,
    ! [X0: $tType,X3: X0] : ~ member(X0,X3,bot_bot(fun(X0,bool))),
    inference(equality_resolution,[],[f188]) ).

tff(f188,plain,
    ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
      ( ( bot_bot(fun(X0,bool)) != X1 )
      | ~ member(X0,X3,X1) ),
    inference(cnf_transformation,[],[f171]) ).

tff(f171,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( member(X0,sK3(X0,X1),X1)
        | ( bot_bot(fun(X0,bool)) = X1 ) )
      & ( ( bot_bot(fun(X0,bool)) != X1 )
        | ! [X3: X0] : ~ member(X0,X3,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f169,f170]) ).

tff(f170,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ? [X2: X0] : member(X0,X2,X1)
     => member(X0,sK3(X0,X1),X1) ),
    introduced(choice_axiom,[]) ).

tff(f169,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ? [X2: X0] : member(X0,X2,X1)
        | ( bot_bot(fun(X0,bool)) = X1 ) )
      & ( ( bot_bot(fun(X0,bool)) != X1 )
        | ! [X3: X0] : ~ member(X0,X3,X1) ) ),
    inference(rectify,[],[f168]) ).

tff(f168,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ( ? [X2: X0] : member(X0,X2,X1)
        | ( bot_bot(fun(X0,bool)) = X1 ) )
      & ( ( bot_bot(fun(X0,bool)) != X1 )
        | ! [X2: X0] : ~ member(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f132]) ).

tff(f132,plain,
    ! [X0: $tType,X1: fun(X0,bool)] :
      ( ? [X2: X0] : member(X0,X2,X1)
    <=> ( bot_bot(fun(X0,bool)) != X1 ) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X1: $tType,X5: fun(X1,bool)] :
      ( ? [X6: X1] : member(X1,X6,X5)
    <=> ( bot_bot(fun(X1,bool)) != X5 ) ),
    file('/export/starexec/sandbox/tmp/tmp.NU1RPHdG8k/Vampire---4.8_32361',fact_12_ex__in__conv) ).

tff(f182,plain,
    member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool))),
    inference(cnf_transformation,[],[f164]) ).

tff(f164,plain,
    ( ~ hoare_1633586161_valid(a,sK0,sK1)
    & member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool)))
    & ! [X2: hoare_28830079triple(a)] :
        ( hoare_1633586161_valid(a,sK0,X2)
        | ~ member(hoare_28830079triple(a),X2,ga) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f146,f163,f162]) ).

tff(f162,plain,
    ( ? [X0: nat] :
        ( ? [X1: hoare_28830079triple(a)] :
            ( ~ hoare_1633586161_valid(a,X0,X1)
            & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
        & ! [X2: hoare_28830079triple(a)] :
            ( hoare_1633586161_valid(a,X0,X2)
            | ~ member(hoare_28830079triple(a),X2,ga) ) )
   => ( ? [X1: hoare_28830079triple(a)] :
          ( ~ hoare_1633586161_valid(a,sK0,X1)
          & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
      & ! [X2: hoare_28830079triple(a)] :
          ( hoare_1633586161_valid(a,sK0,X2)
          | ~ member(hoare_28830079triple(a),X2,ga) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f163,plain,
    ( ? [X1: hoare_28830079triple(a)] :
        ( ~ hoare_1633586161_valid(a,sK0,X1)
        & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
   => ( ~ hoare_1633586161_valid(a,sK0,sK1)
      & member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool))) ) ),
    introduced(choice_axiom,[]) ).

tff(f146,plain,
    ? [X0: nat] :
      ( ? [X1: hoare_28830079triple(a)] :
          ( ~ hoare_1633586161_valid(a,X0,X1)
          & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
      & ! [X2: hoare_28830079triple(a)] :
          ( hoare_1633586161_valid(a,X0,X2)
          | ~ member(hoare_28830079triple(a),X2,ga) ) ),
    inference(ennf_transformation,[],[f128]) ).

tff(f128,plain,
    ~ ! [X0: nat] :
        ( ! [X1: hoare_28830079triple(a)] :
            ( member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool)))
           => hoare_1633586161_valid(a,X0,X1) )
        | ? [X2: hoare_28830079triple(a)] :
            ( ~ hoare_1633586161_valid(a,X0,X2)
            & member(hoare_28830079triple(a),X2,ga) ) ),
    inference(rectify,[],[f127]) ).

tff(f127,negated_conjecture,
    ~ ! [X51: nat] :
        ( ! [X19: hoare_28830079triple(a)] :
            ( member(hoare_28830079triple(a),X19,bot_bot(fun(hoare_28830079triple(a),bool)))
           => hoare_1633586161_valid(a,X51,X19) )
        | ? [X4: hoare_28830079triple(a)] :
            ( ~ hoare_1633586161_valid(a,X51,X4)
            & member(hoare_28830079triple(a),X4,ga) ) ),
    inference(negated_conjecture,[],[f126]) ).

tff(f126,conjecture,
    ! [X51: nat] :
      ( ! [X19: hoare_28830079triple(a)] :
          ( member(hoare_28830079triple(a),X19,bot_bot(fun(hoare_28830079triple(a),bool)))
         => hoare_1633586161_valid(a,X51,X19) )
      | ? [X4: hoare_28830079triple(a)] :
          ( ~ hoare_1633586161_valid(a,X51,X4)
          & member(hoare_28830079triple(a),X4,ga) ) ),
    file('/export/starexec/sandbox/tmp/tmp.NU1RPHdG8k/Vampire---4.8_32361',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : SWW520_5 : TPTP v8.1.2. Released v6.0.0.
% 0.09/0.13  % 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
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Apr 30 18:04:41 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  This is a TF1_THM_EQU_NAR problem
% 0.13/0.34  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.NU1RPHdG8k/Vampire---4.8_32361
% 0.61/0.83  % (32481)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.61/0.83  % (32485)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 (2995ds/83Mi)
% 0.61/0.83  % (32479)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 (2995ds/34Mi)
% 0.61/0.83  % (32483)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 (2995ds/34Mi)
% 0.61/0.83  % (32484)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.61/0.83  % (32482)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.61/0.83  % (32486)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 (2995ds/56Mi)
% 0.61/0.83  % (32485)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.61/0.83  % (32480)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 (2995ds/51Mi)
% 0.61/0.83  % (32485)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.61/0.83  % (32482)First to succeed.
% 0.61/0.83  % (32479)Also succeeded, but the first one will report.
% 0.61/0.83  % (32486)Also succeeded, but the first one will report.
% 0.61/0.83  % (32482)Refutation found. Thanks to Tanya!
% 0.61/0.83  % SZS status Theorem for Vampire---4
% 0.61/0.83  % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.83  % (32482)------------------------------
% 0.61/0.83  % (32482)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.83  % (32482)Termination reason: Refutation
% 0.61/0.83  
% 0.61/0.83  % (32482)Memory used [KB]: 1094
% 0.61/0.83  % (32482)Time elapsed: 0.005 s
% 0.61/0.83  % (32482)Instructions burned: 5 (million)
% 0.61/0.83  % (32482)------------------------------
% 0.61/0.83  % (32482)------------------------------
% 0.61/0.83  % (32475)Success in time 0.485 s
% 0.61/0.83  % Vampire---4.8 exiting
%------------------------------------------------------------------------------