TSTP Solution File: SET108+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n022.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 03:45:06 EDT 2024

% Result   : Theorem 0.63s 0.81s
% Output   : Refutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   28 (   8 unt;   1 typ;   0 def)
%            Number of atoms       :  260 (  50 equ)
%            Maximal formula atoms :   16 (   9 avg)
%            Number of connectives :  122 (  48   ~;  37   |;  34   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  159 ( 159 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   58 (  35   !;  22   ?;  23   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_6,type,
    sQ4_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f97,plain,
    $false,
    inference(subsumption_resolution,[],[f96,f86]) ).

tff(f86,plain,
    member(sK1,universal_class),
    inference(equality_resolution,[],[f85]) ).

tff(f85,plain,
    ! [X1: $i] :
      ( ( sK0 != X1 )
      | member(sK1,universal_class) ),
    inference(equality_resolution,[],[f62]) ).

tff(f62,plain,
    ! [X2: $i,X1: $i] :
      ( ( sK0 != X2 )
      | ( sK0 != X1 )
      | member(sK1,universal_class) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X1,X2] :
      ( ( ( sK0 != X2 )
        | ( sK0 != X1 )
        | ( ( sK0 = ordered_pair(sK1,sK2) )
          & member(sK2,universal_class)
          & member(sK1,universal_class) ) )
      & ( ( ordered_pair(X1,X2) != sK0 )
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f48,f51,f50]) ).

tff(f50,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ( ( X0 != X2 )
          | ( X0 != X1 )
          | ? [X3,X4] :
              ( ( ordered_pair(X3,X4) = X0 )
              & member(X4,universal_class)
              & member(X3,universal_class) ) )
        & ( ( ordered_pair(X1,X2) != X0 )
          | ~ member(X2,universal_class)
          | ~ member(X1,universal_class) ) )
   => ! [X2,X1] :
        ( ( ( sK0 != X2 )
          | ( sK0 != X1 )
          | ? [X4,X3] :
              ( ( ordered_pair(X3,X4) = sK0 )
              & member(X4,universal_class)
              & member(X3,universal_class) ) )
        & ( ( ordered_pair(X1,X2) != sK0 )
          | ~ member(X2,universal_class)
          | ~ member(X1,universal_class) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f51,plain,
    ( ? [X4,X3] :
        ( ( ordered_pair(X3,X4) = sK0 )
        & member(X4,universal_class)
        & member(X3,universal_class) )
   => ( ( sK0 = ordered_pair(sK1,sK2) )
      & member(sK2,universal_class)
      & member(sK1,universal_class) ) ),
    introduced(choice_axiom,[]) ).

tff(f48,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ( ( X0 != X2 )
        | ( X0 != X1 )
        | ? [X3,X4] :
            ( ( ordered_pair(X3,X4) = X0 )
            & member(X4,universal_class)
            & member(X3,universal_class) ) )
      & ( ( ordered_pair(X1,X2) != X0 )
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) ) ),
    inference(ennf_transformation,[],[f46]) ).

tff(f46,plain,
    ~ ! [X0] :
      ? [X1,X2] :
        ( ( ( X0 = X2 )
          & ( X0 = X1 )
          & ~ ? [X3,X4] :
                ( ( ordered_pair(X3,X4) = X0 )
                & member(X4,universal_class)
                & member(X3,universal_class) ) )
        | ( ( ordered_pair(X1,X2) = X0 )
          & member(X2,universal_class)
          & member(X1,universal_class) ) ),
    inference(rectify,[],[f45]) ).

tff(f45,negated_conjecture,
    ~ ! [X0] :
      ? [X2,X3] :
        ( ( ( X0 = X3 )
          & ( X0 = X2 )
          & ~ ? [X1,X4] :
                ( ( ordered_pair(X1,X4) = X0 )
                & member(X4,universal_class)
                & member(X1,universal_class) ) )
        | ( ( ordered_pair(X2,X3) = X0 )
          & member(X3,universal_class)
          & member(X2,universal_class) ) ),
    inference(negated_conjecture,[],[f44]) ).

tff(f44,conjecture,
    ! [X0] :
    ? [X2,X3] :
      ( ( ( X0 = X3 )
        & ( X0 = X2 )
        & ~ ? [X1,X4] :
              ( ( ordered_pair(X1,X4) = X0 )
              & member(X4,universal_class)
              & member(X1,universal_class) ) )
      | ( ( ordered_pair(X2,X3) = X0 )
        & member(X3,universal_class)
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcSj8LW86o/Vampire---4.8_29990',existence_of_first_and_second) ).

tff(f96,plain,
    ~ member(sK1,universal_class),
    inference(subsumption_resolution,[],[f95,f84]) ).

tff(f84,plain,
    member(sK2,universal_class),
    inference(equality_resolution,[],[f83]) ).

tff(f83,plain,
    ! [X1: $i] :
      ( ( sK0 != X1 )
      | member(sK2,universal_class) ),
    inference(equality_resolution,[],[f63]) ).

tff(f63,plain,
    ! [X2: $i,X1: $i] :
      ( ( sK0 != X2 )
      | ( sK0 != X1 )
      | member(sK2,universal_class) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f95,plain,
    ( ~ member(sK2,universal_class)
    | ~ member(sK1,universal_class) ),
    inference(resolution,[],[f91,f90]) ).

tff(f90,plain,
    sQ4_eqProxy($i,sK0,unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK2)))),
    inference(equality_proxy_replacement,[],[f82,f89]) ).

tff(f89,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ4_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

tff(f82,plain,
    sK0 = unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK2))),
    inference(equality_resolution,[],[f81]) ).

tff(f81,plain,
    ! [X1: $i] :
      ( ( sK0 != X1 )
      | ( sK0 = unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK2))) ) ),
    inference(equality_resolution,[],[f76]) ).

tff(f76,plain,
    ! [X2: $i,X1: $i] :
      ( ( sK0 != X2 )
      | ( sK0 != X1 )
      | ( sK0 = unordered_pair(singleton(sK1),unordered_pair(sK1,singleton(sK2))) ) ),
    inference(definition_unfolding,[],[f64,f75]) ).

tff(f75,plain,
    ! [X0: $i,X1: $i] : ( ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) ),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ! [X0,X1] : ( ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcSj8LW86o/Vampire---4.8_29990',ordered_pair_defn) ).

tff(f64,plain,
    ! [X2: $i,X1: $i] :
      ( ( sK0 != X2 )
      | ( sK0 != X1 )
      | ( sK0 = ordered_pair(sK1,sK2) ) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f91,plain,
    ! [X2: $i,X1: $i] :
      ( ~ sQ4_eqProxy($i,sK0,unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))))
      | ~ member(X2,universal_class)
      | ~ member(X1,universal_class) ),
    inference(equality_proxy_replacement,[],[f77,f89]) ).

tff(f77,plain,
    ! [X2: $i,X1: $i] :
      ( ( sK0 != unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) )
      | ~ member(X2,universal_class)
      | ~ member(X1,universal_class) ),
    inference(definition_unfolding,[],[f61,f75]) ).

tff(f61,plain,
    ! [X2: $i,X1: $i] :
      ( ( ordered_pair(X1,X2) != sK0 )
      | ~ member(X2,universal_class)
      | ~ member(X1,universal_class) ),
    inference(cnf_transformation,[],[f52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n022.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   : Tue Apr 30 17:16:58 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.KcSj8LW86o/Vampire---4.8_29990
% 0.63/0.81  % (30216)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)
% 0.63/0.81  % (30219)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)
% 0.63/0.81  % (30219)Refutation not found, incomplete strategy% (30219)------------------------------
% 0.63/0.81  % (30219)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.81  % (30219)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.81  
% 0.63/0.81  % (30219)Memory used [KB]: 1040
% 0.63/0.81  % (30219)Time elapsed: 0.002 s
% 0.63/0.81  % (30219)Instructions burned: 2 (million)
% 0.63/0.81  % (30219)------------------------------
% 0.63/0.81  % (30219)------------------------------
% 0.63/0.81  % (30211)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)
% 0.63/0.81  % (30213)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.63/0.81  % (30212)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)
% 0.63/0.81  % (30215)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)
% 0.63/0.81  % (30217)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)
% 0.63/0.81  % (30218)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)
% 0.63/0.81  % (30211)First to succeed.
% 0.63/0.81  % (30215)Also succeeded, but the first one will report.
% 0.63/0.81  % (30213)Also succeeded, but the first one will report.
% 0.63/0.81  % (30211)Refutation found. Thanks to Tanya!
% 0.63/0.81  % SZS status Theorem for Vampire---4
% 0.63/0.81  % SZS output start Proof for Vampire---4
% See solution above
% 0.63/0.81  % (30211)------------------------------
% 0.63/0.81  % (30211)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.81  % (30211)Termination reason: Refutation
% 0.63/0.81  
% 0.63/0.81  % (30211)Memory used [KB]: 1052
% 0.63/0.81  % (30211)Time elapsed: 0.004 s
% 0.63/0.81  % (30211)Instructions burned: 4 (million)
% 0.63/0.81  % (30211)------------------------------
% 0.63/0.81  % (30211)------------------------------
% 0.63/0.81  % (30157)Success in time 0.437 s
% 0.63/0.81  % Vampire---4.8 exiting
%------------------------------------------------------------------------------