TSTP Solution File: SEU845^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU845^5 : 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 : n021.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 03:51:54 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   46 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :  214 (  64 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :  244 (  61   ~;  36   |;  34   &; 101   @)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   32 (  10   ^  17   !;   4   ?;  32   :)
%                                         (   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(f54,plain,
    $false,
    inference(avatar_sat_refutation,[],[f35,f47,f50,f53]) ).

thf(f53,plain,
    ( ~ spl2_1
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f52]) ).

thf(f52,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f51]) ).

thf(f51,plain,
    ( ( $true = $false )
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f46,f30]) ).

thf(f30,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f28]) ).

thf(f28,plain,
    ( spl2_1
  <=> ( ( sK1 @ sK4 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f46,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f44]) ).

thf(f44,plain,
    ( spl2_3
  <=> ( ( sK1 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f50,plain,
    ~ spl2_2,
    inference(avatar_contradiction_clause,[],[f49]) ).

thf(f49,plain,
    ( $false
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f48]) ).

thf(f48,plain,
    ( ( $true = $false )
    | ~ spl2_2 ),
    inference(backward_demodulation,[],[f38,f34]) ).

thf(f34,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f32]) ).

thf(f32,plain,
    ( spl2_2
  <=> ( ( sK0 @ sK4 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f38,plain,
    ( ( sK0 @ sK4 )
    = $true ),
    inference(subsumption_resolution,[],[f37,f9]) ).

thf(f9,plain,
    ! [X2: a] :
      ( ( $true
       != ( sK1 @ X2 ) )
      | ( $true
        = ( sK0 @ X2 ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( sK1
     != ( ^ [Y0: a] :
            ( ( sK0 @ Y0 )
            & ~ ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) ) ) ) )
    & ! [X2: a] :
        ( ( $true
         != ( sK1 @ X2 ) )
        | ( $true
          = ( sK0 @ X2 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: a > $o,X1: a > $o] :
        ( ( ( ^ [Y0: a] :
                ( ( X0 @ Y0 )
                & ~ ( ~ ( X1 @ Y0 )
                    & ( X0 @ Y0 ) ) ) )
         != X1 )
        & ! [X2: a] :
            ( ( ( X1 @ X2 )
             != $true )
            | ( ( X0 @ X2 )
              = $true ) ) )
   => ( ( sK1
       != ( ^ [Y0: a] :
              ( ( sK0 @ Y0 )
              & ~ ( ~ ( sK1 @ Y0 )
                  & ( sK0 @ Y0 ) ) ) ) )
      & ! [X2: a] :
          ( ( $true
           != ( sK1 @ X2 ) )
          | ( $true
            = ( sK0 @ X2 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: a > $o,X1: a > $o] :
      ( ( ( ^ [Y0: a] :
              ( ( X0 @ Y0 )
              & ~ ( ~ ( X1 @ Y0 )
                  & ( X0 @ Y0 ) ) ) )
       != X1 )
      & ! [X2: a] :
          ( ( ( X1 @ X2 )
           != $true )
          | ( ( X0 @ X2 )
            = $true ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ! [X2: a] :
            ( ( ( X1 @ X2 )
              = $true )
           => ( ( X0 @ X2 )
              = $true ) )
       => ( ( ^ [Y0: a] :
                ( ( X0 @ Y0 )
                & ~ ( ~ ( X1 @ Y0 )
                    & ( X0 @ Y0 ) ) ) )
          = X1 ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X1: a > $o,X0: a > $o] :
      ( ! [X2: a] :
          ( ( X0 @ X2 )
         => ( X1 @ X2 ) )
     => ( X0
        = ( ^ [X2: a] :
              ( ~ ( ( X1 @ X2 )
                  & ~ ( X0 @ X2 ) )
              & ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM12_pme) ).

thf(f37,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( ( ( sK0 @ sK4 )
        & ~ ( ~ ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) ) )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f18]) ).

thf(f18,plain,
    ( ( sK1 @ sK4 )
   != ( ( sK0 @ sK4 )
      & ~ ( ~ ( sK1 @ sK4 )
          & ( sK0 @ sK4 ) ) ) ),
    inference(beta_eta_normalization,[],[f17]) ).

thf(f17,plain,
    ( ( sK1 @ sK4 )
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          & ~ ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f10]) ).

thf(f10,plain,
    ( sK1
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          & ~ ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f47,plain,
    ( spl2_3
    | spl2_2 ),
    inference(avatar_split_clause,[],[f42,f32,f44]) ).

thf(f42,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f41]) ).

thf(f41,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $true )
    | ( ( ~ ( sK1 @ sK4 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ( ( $false
      = ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) ) )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(not_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ( ( ( ~ ( ~ ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) ) )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f19]) ).

thf(f35,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f26,f32,f28]) ).

thf(f26,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f25]) ).

thf(f25,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f24]) ).

thf(f24,plain,
    ( ( ( sK1 @ sK4 )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK4 ) ) )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK4 )
        & ( sK0 @ sK4 ) ) )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f21]) ).

thf(f21,plain,
    ( ( ( ~ ( ~ ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) ) )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

thf(f20,plain,
    ( ( ( ( sK0 @ sK4 )
        & ~ ( ~ ( sK1 @ sK4 )
            & ( sK0 @ sK4 ) ) )
      = $false )
    | ( ( sK1 @ sK4 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : SEU845^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % 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
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 16:44:23 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
% 0.13/0.36  % (23718)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)
% 0.13/0.36  % (23718)Refutation not found, incomplete strategy
% 0.13/0.36  % (23718)------------------------------
% 0.13/0.36  % (23718)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36  % (23718)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.36  
% 0.13/0.36  
% 0.13/0.36  % (23718)Memory used [KB]: 5500
% 0.13/0.36  % (23718)Time elapsed: 0.003 s
% 0.13/0.36  % (23718)Instructions burned: 2 (million)
% 0.13/0.36  % (23718)------------------------------
% 0.13/0.36  % (23718)------------------------------
% 0.13/0.37  % (23712)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 theBenchmark for (3000ds/4Mi)
% 0.13/0.37  % (23712)First to succeed.
% 0.13/0.37  % (23712)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37  % (23712)------------------------------
% 0.13/0.37  % (23712)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (23712)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (23712)Memory used [KB]: 5500
% 0.13/0.37  % (23712)Time elapsed: 0.004 s
% 0.13/0.37  % (23712)Instructions burned: 2 (million)
% 0.13/0.37  % (23712)------------------------------
% 0.13/0.37  % (23712)------------------------------
% 0.13/0.37  % (23710)Success in time 0.024 s
% 0.13/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------