TSTP Solution File: SET173^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET173^5 : TPTP v8.1.2. 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 : n032.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 09:04:33 EDT 2024

% Result   : Theorem 0.08s 0.29s
% Output   : Refutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   31 (  14 unt;   6 typ;   0 def)
%            Number of atoms       :   99 (  29 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  113 (  14   ~;  25   |;  13   &;  59   @)
%                                         (   1 <=>;   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     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   23 (  10   ^   8   !;   4   ?;  23   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_8,type,
    sK0: a > $o ).

thf(func_def_9,type,
    sK1: a > $o ).

thf(func_def_11,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_12,type,
    sK4: a ).

thf(f43,plain,
    $false,
    inference(avatar_sat_refutation,[],[f33,f42]) ).

thf(f42,plain,
    ~ spl2_2,
    inference(avatar_contradiction_clause,[],[f41]) ).

thf(f41,plain,
    ( $false
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f37]) ).

thf(f37,plain,
    ( ( $true = $false )
    | ~ spl2_2 ),
    inference(superposition,[],[f31,f18]) ).

thf(f18,plain,
    ( ( sK0 @ sK4 )
    = $false ),
    inference(duplicate_literal_removal,[],[f17]) ).

thf(f17,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f14]) ).

thf(f14,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false )
    | ( ( ( sK0 @ sK4 )
        | ( sK1 @ sK4 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( ( sK0 @ sK4 )
        & ( ( sK0 @ sK4 )
          | ( sK1 @ sK4 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

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

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

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

thf(f8,plain,
    ( sK0
   != ( ^ [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] :
              ( ( X0 @ Y0 )
              & ( ( X0 @ Y0 )
                | ( X1 @ Y0 ) ) ) )
       != X0 )
   => ( sK0
     != ( ^ [Y0: a] :
            ( ( sK0 @ Y0 )
            & ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o] :
      ( ( ^ [X2: a] :
            ( ( ( X1 @ X2 )
              | ( X0 @ X2 ) )
            & ( X0 @ X2 ) ) )
      = X0 ),
    file('/export/starexec/sandbox2/tmp/tmp.j1PBVpeDTk/Vampire---4.8_20871',cBOOL_PROP_68_pme) ).

thf(f31,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f29]) ).

thf(f29,plain,
    ( spl2_2
  <=> ( ( sK0 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f33,plain,
    spl2_2,
    inference(avatar_split_clause,[],[f21,f29]) ).

thf(f21,plain,
    ( ( sK0 @ sK4 )
    = $true ),
    inference(duplicate_literal_removal,[],[f20]) ).

thf(f20,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SET173^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09  % 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
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Fri May  3 16:55:07 EDT 2024
% 0.08/0.28  % CPUTime    : 
% 0.08/0.28  This is a TH0_THM_EQU_NAR problem
% 0.08/0.28  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/tmp/tmp.j1PBVpeDTk/Vampire---4.8_20871
% 0.08/0.29  % (21061)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (3000ds/4Mi)
% 0.08/0.29  % (21060)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.08/0.29  % (21061)First to succeed.
% 0.08/0.29  % (21068)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.08/0.29  % (21062)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 Vampire---4 for (3000ds/27Mi)
% 0.08/0.29  % (21060)Also succeeded, but the first one will report.
% 0.08/0.29  % (21068)Refutation not found, incomplete strategy
% 0.08/0.29  % (21068)------------------------------
% 0.08/0.29  % (21068)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.29  % (21068)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.29  
% 0.08/0.29  
% 0.08/0.29  % (21068)Memory used [KB]: 5500
% 0.08/0.29  % (21068)Time elapsed: 0.002 s
% 0.08/0.29  % (21068)------------------------------
% 0.08/0.29  % (21068)------------------------------
% 0.08/0.29  % (21062)Also succeeded, but the first one will report.
% 0.08/0.29  % (21061)Refutation found. Thanks to Tanya!
% 0.08/0.29  % SZS status Theorem for Vampire---4
% 0.08/0.29  % SZS output start Proof for Vampire---4
% See solution above
% 0.08/0.29  % (21061)------------------------------
% 0.08/0.29  % (21061)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.29  % (21061)Termination reason: Refutation
% 0.08/0.29  
% 0.08/0.29  % (21061)Memory used [KB]: 5500
% 0.08/0.29  % (21061)Time elapsed: 0.003 s
% 0.08/0.29  % (21061)Instructions burned: 1 (million)
% 0.08/0.29  % (21061)------------------------------
% 0.08/0.29  % (21061)------------------------------
% 0.08/0.29  % (21059)Success in time 0.01 s
% 0.08/0.29  % Vampire---4.8 exiting
%------------------------------------------------------------------------------