TSTP Solution File: SET605^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET605^5 : 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 : n009.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 03:12:21 EDT 2024

% Result   : Theorem 0.13s 0.35s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   22 (  15 unt;   6 typ;   0 def)
%            Number of atoms       :   55 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   88 (  22   ~;  13   |;  11   &;  41   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   33 (  20   ^   8   !;   4   ?;  33   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_9,type,
    sK0: a > $o ).

thf(func_def_10,type,
    sK1: a > $o ).

thf(func_def_12,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_13,type,
    sK4: a ).

thf(f18,plain,
    $false,
    inference(trivial_inequality_removal,[],[f17]) ).

thf(f17,plain,
    $false = $true,
    inference(forward_demodulation,[],[f13,f16]) ).

thf(f16,plain,
    ( $false
    = ( sK0 @ sK4 ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ( $false
    = ( ( sK0 @ sK4 )
      | ( sK1 @ sK4 ) ) ),
    inference(not_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( $true
    = ( ~ ( ( sK0 @ sK4 )
          | ( sK1 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( $false
   != ( ( sK0 @ sK4 )
      & ~ ( ( sK0 @ sK4 )
          | ( sK1 @ sK4 ) ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( ^ [Y0: a] : $false
      @ sK4 )
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          & ~ ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f9]) ).

thf(f9,plain,
    ( ( ^ [Y0: a] : $false )
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          & ~ ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ^ [Y0: a] : $false )
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          & ~ ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: a > $o,X1: a > $o] :
        ( ( ^ [Y0: a] : $false )
       != ( ^ [Y0: a] :
              ( ( X0 @ Y0 )
              & ~ ( ( X0 @ Y0 )
                  | ( X1 @ Y0 ) ) ) ) )
   => ( ( ^ [Y0: a] : $false )
     != ( ^ [Y0: a] :
            ( ( sK0 @ Y0 )
            & ~ ( ( sK0 @ Y0 )
                | ( sK1 @ Y0 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: a > $o,X1: a > $o] :
      ( ( ^ [Y0: a] : $false )
     != ( ^ [Y0: a] :
            ( ( X0 @ Y0 )
            & ~ ( ( X0 @ Y0 )
                | ( X1 @ Y0 ) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ( ^ [Y0: a] : $false )
        = ( ^ [Y0: a] :
              ( ( X0 @ Y0 )
              & ~ ( ( X0 @ Y0 )
                  | ( X1 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o] :
      ( ( ^ [X2: a] :
            ( ~ ( ( X1 @ X2 )
                | ( X0 @ X2 ) )
            & ( X0 @ X2 ) ) )
      = ( ^ [X2: a] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_76_pme) ).

thf(f13,plain,
    ( ( sK0 @ sK4 )
    = $true ),
    inference(binary_proxy_clausification,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SET605^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12  % 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
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon May 20 11:32:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  This is a TH0_THM_EQU_NAR problem
% 0.13/0.34  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
% 0.13/0.35  % (12869)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.13/0.35  % (12869)First to succeed.
% 0.13/0.35  % (12869)Refutation found. Thanks to Tanya!
% 0.13/0.35  % SZS status Theorem for theBenchmark
% 0.13/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.35  % (12869)------------------------------
% 0.13/0.35  % (12869)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35  % (12869)Termination reason: Refutation
% 0.13/0.35  
% 0.13/0.35  % (12869)Memory used [KB]: 5500
% 0.13/0.35  % (12869)Time elapsed: 0.003 s
% 0.13/0.35  % (12869)Instructions burned: 1 (million)
% 0.13/0.35  % (12869)------------------------------
% 0.13/0.35  % (12869)------------------------------
% 0.13/0.35  % (12865)Success in time 0.002 s
% 0.13/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------