TSTP Solution File: SEU858^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU858^5 : 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 : n007.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 03:51:57 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   15 (   3 unt;   3 typ;   0 def)
%            Number of atoms       :  103 (  40 equ;   0 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives :  108 (  15   ~;  15   |;  15   &;  52   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1 usr;   2 con; 0-2 aty)
%            Number of variables   :   60 (  32   ^  25   !;   3   ?;  60   :)

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

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

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

thf(f14,plain,
    $false,
    inference(subsumption_resolution,[],[f11,f13]) ).

thf(f13,plain,
    ( $true
   != ( sK0
      @ ^ [Y0: a] : $false ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( $true
     != ( sK0
        @ ^ [Y0: a] : $false ) )
    & ! [X1: a,X2: a > $o] :
        ( ( $true
         != ( sK0 @ X2 ) )
        | ( ( sK0
            @ ^ [Y0: a] :
                ( ( X1 = Y0 )
                | ( X2 @ Y0 ) ) )
          = $true ) )
    & ( $true
      = ( sK0
        @ ^ [Y0: a] : $false ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).

thf(f9,plain,
    ( ? [X0: ( a > $o ) > $o] :
        ( ( $true
         != ( X0
            @ ^ [Y0: a] : $false ) )
        & ! [X1: a,X2: a > $o] :
            ( ( ( X0 @ X2 )
             != $true )
            | ( $true
              = ( X0
                @ ^ [Y0: a] :
                    ( ( X1 = Y0 )
                    | ( X2 @ Y0 ) ) ) ) )
        & ( $true
          = ( X0
            @ ^ [Y0: a] : $false ) ) )
   => ( ( $true
       != ( sK0
          @ ^ [Y0: a] : $false ) )
      & ! [X2: a > $o,X1: a] :
          ( ( $true
           != ( sK0 @ X2 ) )
          | ( ( sK0
              @ ^ [Y0: a] :
                  ( ( X1 = Y0 )
                  | ( X2 @ Y0 ) ) )
            = $true ) )
      & ( $true
        = ( sK0
          @ ^ [Y0: a] : $false ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: ( a > $o ) > $o] :
      ( ( $true
       != ( X0
          @ ^ [Y0: a] : $false ) )
      & ! [X1: a,X2: a > $o] :
          ( ( ( X0 @ X2 )
           != $true )
          | ( $true
            = ( X0
              @ ^ [Y0: a] :
                  ( ( X1 = Y0 )
                  | ( X2 @ Y0 ) ) ) ) )
      & ( $true
        = ( X0
          @ ^ [Y0: a] : $false ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ? [X0: ( a > $o ) > $o] :
      ( ( $true
       != ( X0
          @ ^ [Y0: a] : $false ) )
      & ! [X1: a,X2: a > $o] :
          ( ( ( X0 @ X2 )
           != $true )
          | ( $true
            = ( X0
              @ ^ [Y0: a] :
                  ( ( X1 = Y0 )
                  | ( X2 @ Y0 ) ) ) ) )
      & ( $true
        = ( X0
          @ ^ [Y0: a] : $false ) ) ),
    inference(ennf_transformation,[],[f6]) ).

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

thf(f5,plain,
    ~ ! [X0: ( a > $o ) > $o] :
        ( ( ( $true
            = ( X0
              @ ^ [Y0: a] : $false ) )
          & ! [X2: a,X3: a > $o] :
              ( ( $true
                = ( X0 @ X3 ) )
             => ( ( X0
                  @ ^ [Y0: a] :
                      ( ( X2 = Y0 )
                      | ( X3 @ Y0 ) ) )
                = $true ) ) )
       => ( $true
          = ( X0
            @ ^ [Y0: a] : $false ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X0: ( a > $o ) > $o] :
      ( ( ( X0
          @ ^ [X1: a] : $false )
        & ! [X1: a,X2: a > $o] :
            ( ( X0 @ X2 )
           => ( X0
              @ ^ [X3: a] :
                  ( ( X2 @ X3 )
                  | ( X1 = X3 ) ) ) ) )
     => ( X0
        @ ^ [X1: a] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM163_pme) ).

thf(f11,plain,
    ( $true
    = ( sK0
      @ ^ [Y0: a] : $false ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU858^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % 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
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 17:17:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_THM_EQU_NAR problem
% 0.14/0.35  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
% 0.14/0.37  % (12921)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)
% 0.14/0.37  % (12921)First to succeed.
% 0.14/0.37  % (12921)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (12921)------------------------------
% 0.14/0.37  % (12921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (12921)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (12921)Memory used [KB]: 5500
% 0.14/0.37  % (12921)Time elapsed: 0.002 s
% 0.14/0.37  % (12921)Instructions burned: 1 (million)
% 0.14/0.37  % (12921)------------------------------
% 0.14/0.37  % (12921)------------------------------
% 0.14/0.37  % (12919)Success in time 0.001 s
% 0.14/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------