TSTP Solution File: SET199^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET199^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n014.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 : Tue May 21 03:09:37 EDT 2024

% Result   : Theorem 0.16s 0.33s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   24 (   5 unt;   7 typ;   0 def)
%            Number of atoms       :  155 (  63 equ;   0 cnn)
%            Maximal formula atoms :   14 (   9 avg)
%            Number of connectives :  185 (  35   ~;  18   |;  32   &;  82   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   56 (   0   ^  37   !;  18   ?;  56   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

thf(func_def_0,type,
    a: $tType ).

thf(func_def_2,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_5,type,
    sK0: a > $o ).

thf(func_def_6,type,
    sK1: a > $o ).

thf(func_def_7,type,
    sK2: a > $o ).

thf(func_def_8,type,
    sK3: a ).

thf(f20,plain,
    $false,
    inference(trivial_inequality_removal,[],[f19]) ).

thf(f19,plain,
    $true != $true,
    inference(superposition,[],[f12,f18]) ).

thf(f18,plain,
    ( $true
    = ( sK0 @ sK3 ) ),
    inference(trivial_inequality_removal,[],[f17]) ).

thf(f17,plain,
    ( ( $true != $true )
    | ( $true
      = ( sK0 @ sK3 ) ) ),
    inference(superposition,[],[f15,f13]) ).

thf(f13,plain,
    ( $true
    = ( sK2 @ sK3 ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f11,plain,
    ( ! [X3: a] :
        ( ( $true
         != ( sK2 @ X3 ) )
        | ( $true
          = ( sK1 @ X3 ) ) )
    & ! [X4: a] :
        ( ( $true
          = ( sK0 @ X4 ) )
        | ( $true
         != ( sK2 @ X4 ) ) )
    & ( $true
     != ( sK1 @ sK3 ) )
    & ( $true
      = ( sK2 @ sK3 ) )
    & ( $true
     != ( sK0 @ sK3 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ! [X3: a] :
            ( ( ( X2 @ X3 )
             != $true )
            | ( ( X1 @ X3 )
              = $true ) )
        & ! [X4: a] :
            ( ( ( X0 @ X4 )
              = $true )
            | ( $true
             != ( X2 @ X4 ) ) )
        & ? [X5: a] :
            ( ( $true
             != ( X1 @ X5 ) )
            & ( $true
              = ( X2 @ X5 ) )
            & ( $true
             != ( X0 @ X5 ) ) ) )
   => ( ! [X3: a] :
          ( ( $true
           != ( sK2 @ X3 ) )
          | ( $true
            = ( sK1 @ X3 ) ) )
      & ! [X4: a] :
          ( ( $true
            = ( sK0 @ X4 ) )
          | ( $true
           != ( sK2 @ X4 ) ) )
      & ? [X5: a] :
          ( ( $true
           != ( sK1 @ X5 ) )
          & ( $true
            = ( sK2 @ X5 ) )
          & ( $true
           != ( sK0 @ X5 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X5: a] :
        ( ( $true
         != ( sK1 @ X5 ) )
        & ( $true
          = ( sK2 @ X5 ) )
        & ( $true
         != ( sK0 @ X5 ) ) )
   => ( ( $true
       != ( sK1 @ sK3 ) )
      & ( $true
        = ( sK2 @ sK3 ) )
      & ( $true
       != ( sK0 @ sK3 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ! [X3: a] :
          ( ( ( X2 @ X3 )
           != $true )
          | ( ( X1 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( ( X0 @ X4 )
            = $true )
          | ( $true
           != ( X2 @ X4 ) ) )
      & ? [X5: a] :
          ( ( $true
           != ( X1 @ X5 ) )
          & ( $true
            = ( X2 @ X5 ) )
          & ( $true
           != ( X0 @ X5 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ? [X2: a > $o,X1: a > $o,X0: a > $o] :
      ( ! [X3: a] :
          ( ( ( X0 @ X3 )
           != $true )
          | ( ( X1 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( $true
            = ( X2 @ X4 ) )
          | ( ( X0 @ X4 )
           != $true ) )
      & ? [X5: a] :
          ( ( $true
           != ( X1 @ X5 ) )
          & ( $true
            = ( X0 @ X5 ) )
          & ( $true
           != ( X2 @ X5 ) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ? [X1: a > $o,X2: a > $o,X0: a > $o] :
      ( ? [X5: a] :
          ( ( $true
           != ( X2 @ X5 ) )
          & ( $true
           != ( X1 @ X5 ) )
          & ( $true
            = ( X0 @ X5 ) ) )
      & ! [X3: a] :
          ( ( ( X0 @ X3 )
           != $true )
          | ( ( X1 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( $true
            = ( X2 @ X4 ) )
          | ( ( X0 @ X4 )
           != $true ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
        ( ( ! [X3: a] :
              ( ( ( X0 @ X3 )
                = $true )
             => ( ( X1 @ X3 )
                = $true ) )
          & ! [X4: a] :
              ( ( ( X0 @ X4 )
                = $true )
             => ( $true
                = ( X2 @ X4 ) ) ) )
       => ! [X5: a] :
            ( ( $true
              = ( X0 @ X5 ) )
           => ( ( $true
                = ( X2 @ X5 ) )
              | ( $true
                = ( X1 @ X5 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ! [X3: a] :
              ( ( X0 @ X3 )
             => ( X1 @ X3 ) )
          & ! [X4: a] :
              ( ( X0 @ X4 )
             => ( X2 @ X4 ) ) )
       => ! [X5: a] :
            ( ( X0 @ X5 )
           => ( ( X1 @ X5 )
              | ( X2 @ X5 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
        ( ( ! [X3: a] :
              ( ( X2 @ X3 )
             => ( X1 @ X3 ) )
          & ! [X3: a] :
              ( ( X2 @ X3 )
             => ( X0 @ X3 ) ) )
       => ! [X3: a] :
            ( ( X2 @ X3 )
           => ( ( X1 @ X3 )
              | ( X0 @ X3 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X2: a > $o,X1: a > $o,X0: a > $o] :
      ( ( ! [X3: a] :
            ( ( X2 @ X3 )
           => ( X1 @ X3 ) )
        & ! [X3: a] :
            ( ( X2 @ X3 )
           => ( X0 @ X3 ) ) )
     => ! [X3: a] :
          ( ( X2 @ X3 )
         => ( ( X1 @ X3 )
            | ( X0 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_39_pme) ).

thf(f15,plain,
    ! [X4: a] :
      ( ( $true
       != ( sK2 @ X4 ) )
      | ( $true
        = ( sK0 @ X4 ) ) ),
    inference(cnf_transformation,[],[f11]) ).

thf(f12,plain,
    ( $true
   != ( sK0 @ sK3 ) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET199^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13  % 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
% 0.12/0.31  % Computer : n014.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit   : 300
% 0.12/0.31  % WCLimit    : 300
% 0.12/0.31  % DateTime   : Mon May 20 11:13:38 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.31  This is a TH0_THM_NEQ_NAR problem
% 0.16/0.32  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.33  % (11905)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.16/0.33  % (11906)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.33  % (11906)Instruction limit reached!
% 0.16/0.33  % (11906)------------------------------
% 0.16/0.33  % (11906)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (11906)Termination reason: Unknown
% 0.16/0.33  % (11906)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (11906)Memory used [KB]: 5373
% 0.16/0.33  % (11906)Time elapsed: 0.002 s
% 0.16/0.33  % (11906)Instructions burned: 2 (million)
% 0.16/0.33  % (11906)------------------------------
% 0.16/0.33  % (11906)------------------------------
% 0.16/0.33  % (11905)First to succeed.
% 0.16/0.33  % (11910)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.16/0.33  % (11905)Refutation found. Thanks to Tanya!
% 0.16/0.33  % SZS status Theorem for theBenchmark
% 0.16/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33  % (11905)------------------------------
% 0.16/0.33  % (11905)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (11905)Termination reason: Refutation
% 0.16/0.33  
% 0.16/0.33  % (11905)Memory used [KB]: 5500
% 0.16/0.33  % (11905)Time elapsed: 0.002 s
% 0.16/0.33  % (11905)Instructions burned: 2 (million)
% 0.16/0.33  % (11905)------------------------------
% 0.16/0.33  % (11905)------------------------------
% 0.16/0.33  % (11902)Success in time 0.008 s
% 0.16/0.33  % Vampire---4.8 exiting
%------------------------------------------------------------------------------