TSTP Solution File: SET790+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% 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 : n029.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 : Sun May  5 09:08:30 EDT 2024

% Result   : Theorem 0.55s 0.75s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   48 (  10 unt;   1 typ;   0 def)
%            Number of atoms       :  290 (  18 equ)
%            Maximal formula atoms :   14 (   6 avg)
%            Number of connectives :  239 (  87   ~;  68   |;  49   &)
%                                         (   7 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   91 (  91 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   7 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  111 (  96   !;  14   ?;  28   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_13,type,
    sQ4_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f83,plain,
    $false,
    inference(avatar_sat_refutation,[],[f56,f74,f82]) ).

tff(f82,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f81]) ).

tff(f81,plain,
    ( $false
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f80,f40]) ).

tff(f40,plain,
    member(sK2,sK1),
    inference(resolution,[],[f33,f27]) ).

tff(f27,plain,
    least(sK2,sK0,sK1),
    inference(cnf_transformation,[],[f25]) ).

tff(f25,plain,
    ( ( sK2 != sK3 )
    & least(sK3,sK0,sK1)
    & least(sK2,sK0,sK1)
    & order(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f24,f23]) ).

tff(f23,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3] :
            ( ( X2 != X3 )
            & least(X3,X0,X1) )
        & least(X2,X0,X1)
        & order(X0,X1) )
   => ( ? [X3] :
          ( ( sK2 != X3 )
          & least(X3,sK0,sK1) )
      & least(sK2,sK0,sK1)
      & order(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ( ? [X3] :
        ( ( sK2 != X3 )
        & least(X3,sK0,sK1) )
   => ( ( sK2 != sK3 )
      & least(sK3,sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ? [X0,X1,X2] :
      ( ? [X3] :
          ( ( X2 != X3 )
          & least(X3,X0,X1) )
      & least(X2,X0,X1)
      & order(X0,X1) ),
    inference(flattening,[],[f18]) ).

tff(f18,plain,
    ? [X0,X1,X2] :
      ( ? [X3] :
          ( ( X2 != X3 )
          & least(X3,X0,X1) )
      & least(X2,X0,X1)
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

tff(f13,plain,
    ~ ! [X0,X1,X2] :
        ( ( least(X2,X0,X1)
          & order(X0,X1) )
       => ! [X3] :
            ( least(X3,X0,X1)
           => ( X2 = X3 ) ) ),
    inference(rectify,[],[f12]) ).

tff(f12,negated_conjecture,
    ~ ! [X0,X1,X5] :
        ( ( least(X5,X0,X1)
          & order(X0,X1) )
       => ! [X2] :
            ( least(X2,X0,X1)
           => ( X2 = X5 ) ) ),
    inference(negated_conjecture,[],[f11]) ).

tff(f11,conjecture,
    ! [X0,X1,X5] :
      ( ( least(X5,X0,X1)
        & order(X0,X1) )
     => ! [X2] :
          ( least(X2,X0,X1)
         => ( X2 = X5 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Mtn525P960/Vampire---4.8_31623',thIV2) ).

tff(f33,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ least(X2,X0,X1)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( apply(X0,X2,X3)
            | ~ member(X3,X1) )
        & member(X2,X1) )
      | ~ least(X2,X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ! [X0,X1,X2] :
      ( least(X2,X0,X1)
     => ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X2,X3) )
        & member(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

tff(f15,plain,
    ! [X0,X1,X2] :
      ( least(X2,X0,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X2,X3) )
        & member(X2,X1) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0,X1,X5] :
      ( least(X5,X0,X1)
    <=> ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X5,X2) )
        & member(X5,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Mtn525P960/Vampire---4.8_31623',least) ).

tff(f80,plain,
    ( ~ member(sK2,sK1)
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f79,f26]) ).

tff(f26,plain,
    order(sK0,sK1),
    inference(cnf_transformation,[],[f25]) ).

tff(f79,plain,
    ( ~ order(sK0,sK1)
    | ~ member(sK2,sK1)
    | ~ spl5_2 ),
    inference(resolution,[],[f55,f41]) ).

tff(f41,plain,
    member(sK3,sK1),
    inference(resolution,[],[f33,f28]) ).

tff(f28,plain,
    least(sK3,sK0,sK1),
    inference(cnf_transformation,[],[f25]) ).

tff(f55,plain,
    ( ! [X0: $i] :
        ( ~ member(sK3,X0)
        | ~ order(sK0,X0)
        | ~ member(sK2,X0) )
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f54]) ).

tff(f54,plain,
    ( spl5_2
  <=> ! [X0] :
        ( ~ member(sK3,X0)
        | ~ order(sK0,X0)
        | ~ member(sK2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

tff(f74,plain,
    spl5_1,
    inference(avatar_contradiction_clause,[],[f73]) ).

tff(f73,plain,
    ( $false
    | spl5_1 ),
    inference(subsumption_resolution,[],[f72,f41]) ).

tff(f72,plain,
    ( ~ member(sK3,sK1)
    | spl5_1 ),
    inference(resolution,[],[f62,f27]) ).

tff(f62,plain,
    ( ! [X0: $i] :
        ( ~ least(sK2,sK0,X0)
        | ~ member(sK3,X0) )
    | spl5_1 ),
    inference(resolution,[],[f52,f34]) ).

tff(f34,plain,
    ! [X2: $i,X3: $i,X0: $i,X1: $i] :
      ( apply(X0,X2,X3)
      | ~ member(X3,X1)
      | ~ least(X2,X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f52,plain,
    ( ~ apply(sK0,sK2,sK3)
    | spl5_1 ),
    inference(avatar_component_clause,[],[f50]) ).

tff(f50,plain,
    ( spl5_1
  <=> apply(sK0,sK2,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

tff(f56,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f48,f54,f50]) ).

tff(f48,plain,
    ! [X0: $i] :
      ( ~ member(sK3,X0)
      | ~ member(sK2,X0)
      | ~ order(sK0,X0)
      | ~ apply(sK0,sK2,sK3) ),
    inference(subsumption_resolution,[],[f47,f40]) ).

tff(f47,plain,
    ! [X0: $i] :
      ( ~ member(sK3,X0)
      | ~ member(sK2,X0)
      | ~ order(sK0,X0)
      | ~ member(sK2,sK1)
      | ~ apply(sK0,sK2,sK3) ),
    inference(resolution,[],[f46,f28]) ).

tff(f46,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ least(sK3,X0,X2)
      | ~ member(sK3,X1)
      | ~ member(sK2,X1)
      | ~ order(X0,X1)
      | ~ member(sK2,X2)
      | ~ apply(X0,sK2,sK3) ),
    inference(resolution,[],[f44,f34]) ).

tff(f44,plain,
    ! [X0: $i,X1: $i] :
      ( ~ apply(X0,sK3,sK2)
      | ~ apply(X0,sK2,sK3)
      | ~ member(sK3,X1)
      | ~ member(sK2,X1)
      | ~ order(X0,X1) ),
    inference(resolution,[],[f37,f36]) ).

tff(f36,plain,
    ~ sQ4_eqProxy($i,sK2,sK3),
    inference(equality_proxy_replacement,[],[f29,f35]) ).

tff(f35,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ4_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

tff(f29,plain,
    sK2 != sK3,
    inference(cnf_transformation,[],[f25]) ).

tff(f37,plain,
    ! [X0: $i,X1: $i,X6: $i,X5: $i] :
      ( sQ4_eqProxy($i,X5,X6)
      | ~ apply(X0,X6,X5)
      | ~ apply(X0,X5,X6)
      | ~ member(X6,X1)
      | ~ member(X5,X1)
      | ~ order(X0,X1) ),
    inference(equality_proxy_replacement,[],[f31,f35]) ).

tff(f31,plain,
    ! [X0: $i,X1: $i,X6: $i,X5: $i] :
      ( ( X5 = X6 )
      | ~ apply(X0,X6,X5)
      | ~ apply(X0,X5,X6)
      | ~ member(X6,X1)
      | ~ member(X5,X1)
      | ~ order(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( apply(X0,X2,X4)
            | ~ apply(X0,X3,X4)
            | ~ apply(X0,X2,X3)
            | ~ member(X4,X1)
            | ~ member(X3,X1)
            | ~ member(X2,X1) )
        & ! [X5,X6] :
            ( ( X5 = X6 )
            | ~ apply(X0,X6,X5)
            | ~ apply(X0,X5,X6)
            | ~ member(X6,X1)
            | ~ member(X5,X1) )
        & ! [X7] :
            ( apply(X0,X7,X7)
            | ~ member(X7,X1) ) )
      | ~ order(X0,X1) ),
    inference(flattening,[],[f20]) ).

tff(f20,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( apply(X0,X2,X4)
            | ~ apply(X0,X3,X4)
            | ~ apply(X0,X2,X3)
            | ~ member(X4,X1)
            | ~ member(X3,X1)
            | ~ member(X2,X1) )
        & ! [X5,X6] :
            ( ( X5 = X6 )
            | ~ apply(X0,X6,X5)
            | ~ apply(X0,X5,X6)
            | ~ member(X6,X1)
            | ~ member(X5,X1) )
        & ! [X7] :
            ( apply(X0,X7,X7)
            | ~ member(X7,X1) ) )
      | ~ order(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

tff(f17,plain,
    ! [X0,X1] :
      ( order(X0,X1)
     => ( ! [X2,X3,X4] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X1)
              & member(X5,X1) )
           => ( ( apply(X0,X6,X5)
                & apply(X0,X5,X6) )
             => ( X5 = X6 ) ) )
        & ! [X7] :
            ( member(X7,X1)
           => apply(X0,X7,X7) ) ) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

tff(f14,plain,
    ! [X0,X1] :
      ( order(X0,X1)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X1)
              & member(X5,X1) )
           => ( ( apply(X0,X6,X5)
                & apply(X0,X5,X6) )
             => ( X5 = X6 ) ) )
        & ! [X7] :
            ( member(X7,X1)
           => apply(X0,X7,X7) ) ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X0,X1] :
      ( order(X0,X1)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X2,X3] :
            ( ( member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X2)
                & apply(X0,X2,X3) )
             => ( X2 = X3 ) ) )
        & ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Mtn525P960/Vampire---4.8_31623',order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET790+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15  % 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
% 0.16/0.36  % Computer : n029.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 16:36:38 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  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.Mtn525P960/Vampire---4.8_31623
% 0.55/0.75  % (31967)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)
% 0.55/0.75  % (31969)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.75  % (31970)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)
% 0.55/0.75  % (31971)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)
% 0.55/0.75  % (31968)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)
% 0.55/0.75  % (31972)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)
% 0.55/0.75  % (31973)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)
% 0.55/0.75  % (31974)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)
% 0.55/0.75  % (31972)Also succeeded, but the first one will report.
% 0.55/0.75  % (31970)Also succeeded, but the first one will report.
% 0.55/0.75  % (31967)First to succeed.
% 0.55/0.75  % (31974)Also succeeded, but the first one will report.
% 0.55/0.75  % (31968)Also succeeded, but the first one will report.
% 0.55/0.75  % (31971)Also succeeded, but the first one will report.
% 0.55/0.75  % (31973)Also succeeded, but the first one will report.
% 0.55/0.75  % (31967)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31874"
% 0.55/0.75  % (31969)Also succeeded, but the first one will report.
% 0.55/0.75  % (31967)Refutation found. Thanks to Tanya!
% 0.55/0.75  % SZS status Theorem for Vampire---4
% 0.55/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.75  % (31967)------------------------------
% 0.55/0.75  % (31967)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.75  % (31967)Termination reason: Refutation
% 0.55/0.75  
% 0.55/0.75  % (31967)Memory used [KB]: 1083
% 0.55/0.75  % (31967)Time elapsed: 0.004 s
% 0.55/0.75  % (31967)Instructions burned: 6 (million)
% 0.55/0.75  % (31874)Success in time 0.382 s
% 0.55/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------