TSTP Solution File: SET617^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET617^5 : 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 : n017.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 03:12:28 EDT 2024

% Result   : Theorem 0.15s 0.32s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (   5 unt;   3 typ;   0 def)
%            Number of atoms       :  151 (  36 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  232 (  80   ~;  39   |;  55   &;  57   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1 usr;   2 con; 0-2 aty)
%            Number of variables   :   40 (  34   ^   4   !;   2   ?;  40   :)

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

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

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

thf(f21,plain,
    $false,
    inference(trivial_inequality_removal,[],[f20]) ).

thf(f20,plain,
    sK0 != sK0,
    inference(beta_eta_normalization,[],[f19]) ).

thf(f19,plain,
    ( sK0
   != ( ^ [Y0: a] : ( sK0 @ Y0 ) ) ),
    inference(boolean_simplification,[],[f18]) ).

thf(f18,plain,
    ( ( ^ [Y0: a] :
          ( $true
          & ( sK0 @ Y0 ) ) )
   != sK0 ),
    inference(boolean_simplification,[],[f17]) ).

thf(f17,plain,
    ( ( ^ [Y0: a] :
          ( ~ $false
          & ( sK0 @ Y0 ) ) )
   != sK0 ),
    inference(trivial_inequality_removal,[],[f16]) ).

thf(f16,plain,
    ( ( ( ^ [Y0: a] :
            ( ~ $false
            & ( sK0 @ Y0 ) ) )
     != sK0 )
    | ( sK0 != sK0 ) ),
    inference(beta_eta_normalization,[],[f15]) ).

thf(f15,plain,
    ( ( ( ^ [Y0: a] :
            ( ~ $false
            & ( sK0 @ Y0 ) ) )
     != sK0 )
    | ( sK0
     != ( ^ [Y0: a] : ( sK0 @ Y0 ) ) ) ),
    inference(boolean_simplification,[],[f14]) ).

thf(f14,plain,
    ( ( ( ^ [Y0: a] :
            ( $false
            | ( sK0 @ Y0 ) ) )
     != sK0 )
    | ( ( ^ [Y0: a] :
            ( ~ $false
            & ( sK0 @ Y0 ) ) )
     != sK0 ) ),
    inference(boolean_simplification,[],[f13]) ).

thf(f13,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ~ $false
              & ( sK0 @ Y0 ) )
            | $false ) )
     != sK0 )
    | ( ( ^ [Y0: a] :
            ( $false
            | ( sK0 @ Y0 ) ) )
     != sK0 ) ),
    inference(boolean_simplification,[],[f12]) ).

thf(f12,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ~ ( sK0 @ Y0 )
              & $false )
            | ( sK0 @ Y0 ) ) )
     != sK0 )
    | ( ( ^ [Y0: a] :
            ( ( ~ $false
              & ( sK0 @ Y0 ) )
            | $false ) )
     != sK0 ) ),
    inference(boolean_simplification,[],[f11]) ).

thf(f11,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ~ $false
              & ( sK0 @ Y0 ) )
            | ( $false
              & ~ ( sK0 @ Y0 ) ) ) )
     != sK0 )
    | ( ( ^ [Y0: a] :
            ( ( ~ ( sK0 @ Y0 )
              & $false )
            | ( sK0 @ Y0 ) ) )
     != sK0 ) ),
    inference(boolean_simplification,[],[f10]) ).

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

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

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

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

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

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

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

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

thf(f1,conjecture,
    ! [X0: a > $o] :
      ( ( X0
        = ( ^ [X1: a] :
              ( ( ~ $false
                & ( X0 @ X1 ) )
              | ( $false
                & ~ ( X0 @ X1 ) ) ) ) )
      & ( X0
        = ( ^ [X1: a] :
              ( ( ~ ( X0 @ X1 )
                & $false )
              | ( ( X0 @ X1 )
                & ~ $false ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_92_pme) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SET617^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.11  % 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
% 0.11/0.30  % Computer : n017.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Mon May 20 12:55:52 EDT 2024
% 0.11/0.30  % CPUTime    : 
% 0.11/0.30  This is a TH0_THM_EQU_NAR problem
% 0.11/0.30  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
% 0.15/0.32  % (30597)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)
% 0.15/0.32  % (30597)First to succeed.
% 0.15/0.32  % (30597)Refutation found. Thanks to Tanya!
% 0.15/0.32  % SZS status Theorem for theBenchmark
% 0.15/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.32  % (30597)------------------------------
% 0.15/0.32  % (30597)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32  % (30597)Termination reason: Refutation
% 0.15/0.32  
% 0.15/0.32  % (30597)Memory used [KB]: 5500
% 0.15/0.32  % (30597)Time elapsed: 0.002 s
% 0.15/0.32  % (30597)------------------------------
% 0.15/0.32  % (30597)------------------------------
% 0.15/0.32  % (30589)Success in time 0.001 s
% 0.15/0.32  % Vampire---4.8 exiting
%------------------------------------------------------------------------------