TSTP Solution File: SEV241^5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV241^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n027.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 : Mon Jun 24 16:02:25 EDT 2024

% Result   : Theorem 0.12s 0.37s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   33 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :  200 (  65 equ;   0 cnn)
%            Maximal formula atoms :   10 (   6 avg)
%            Number of connectives :  137 (  29   ~;  31   |;  21   &;  44   @)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   20 (   0   ^  12   !;   8   ?;  20   :)

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

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

thf(func_def_1,type,
    cW: a > $o ).

thf(func_def_2,type,
    cU: a > $o ).

thf(func_def_6,type,
    sK0: a ).

thf(func_def_7,type,
    sK1: a > $o ).

thf(func_def_9,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_10,type,
    sK4: a ).

thf(func_def_11,type,
    sK5: a ).

thf(f101,plain,
    $false,
    inference(avatar_sat_refutation,[],[f23,f38,f100]) ).

thf(f100,plain,
    ~ spl2_1,
    inference(avatar_contradiction_clause,[],[f99]) ).

thf(f99,plain,
    ( $false
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f93]) ).

thf(f93,plain,
    ( ( $false = $true )
    | ~ spl2_1 ),
    inference(superposition,[],[f14,f89]) ).

thf(f89,plain,
    ( ( $false
      = ( cW @ sK0 ) )
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f86]) ).

thf(f86,plain,
    ( ( $false
      = ( cW @ sK0 ) )
    | ( $true != $true )
    | ~ spl2_1 ),
    inference(superposition,[],[f13,f41]) ).

thf(f41,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK1 @ X1 ) )
        | ( $false
          = ( cW @ X1 ) ) )
    | ~ spl2_1 ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ( ! [X1: a] :
        ( ( cW @ X1 )
        = ( sK1 @ X1 ) )
    | ~ spl2_1 ),
    inference(argument_congruence,[],[f18]) ).

thf(f18,plain,
    ( ( cW = sK1 )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f16]) ).

thf(f16,plain,
    ( spl2_1
  <=> ( cW = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f13,plain,
    ( $true
   != ( sK1 @ sK0 ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( $true
      = ( cW @ sK0 ) )
    & ( $true
     != ( sK1 @ sK0 ) )
    & ( ( cW = sK1 )
      | ( cU = sK1 ) )
    & ( $true
      = ( cU @ sK0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).

thf(f8,plain,
    ( ? [X0: a] :
        ( ( ( cW @ X0 )
          = $true )
        & ? [X1: a > $o] :
            ( ( ( X1 @ X0 )
             != $true )
            & ( ( cW = X1 )
              | ( cU = X1 ) ) )
        & ( ( cU @ X0 )
          = $true ) )
   => ( ( $true
        = ( cW @ sK0 ) )
      & ? [X1: a > $o] :
          ( ( $true
           != ( X1 @ sK0 ) )
          & ( ( cW = X1 )
            | ( cU = X1 ) ) )
      & ( $true
        = ( cU @ sK0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ( ? [X1: a > $o] :
        ( ( $true
         != ( X1 @ sK0 ) )
        & ( ( cW = X1 )
          | ( cU = X1 ) ) )
   => ( ( $true
       != ( sK1 @ sK0 ) )
      & ( ( cW = sK1 )
        | ( cU = sK1 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f7,plain,
    ? [X0: a] :
      ( ( ( cW @ X0 )
        = $true )
      & ? [X1: a > $o] :
          ( ( ( X1 @ X0 )
           != $true )
          & ( ( cW = X1 )
            | ( cU = X1 ) ) )
      & ( ( cU @ X0 )
        = $true ) ),
    inference(flattening,[],[f6]) ).

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

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

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

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

thf(f1,conjecture,
    ! [X0: a] :
      ( ( ( cU @ X0 )
        & ( cW @ X0 ) )
     => ! [X1: a > $o] :
          ( ( ( cW = X1 )
            | ( cU = X1 ) )
         => ( X1 @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5201A_pme) ).

thf(f14,plain,
    ( $true
    = ( cW @ sK0 ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f38,plain,
    ~ spl2_2,
    inference(avatar_contradiction_clause,[],[f37]) ).

thf(f37,plain,
    ( $false
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f31]) ).

thf(f31,plain,
    ( ( $false = $true )
    | ~ spl2_2 ),
    inference(superposition,[],[f11,f28]) ).

thf(f28,plain,
    ( ( $false
      = ( cU @ sK0 ) )
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f27]) ).

thf(f27,plain,
    ( ( $false
      = ( cU @ sK0 ) )
    | ( $true != $true )
    | ~ spl2_2 ),
    inference(superposition,[],[f13,f26]) ).

thf(f26,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK1 @ X1 ) )
        | ( $false
          = ( cU @ X1 ) ) )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f24]) ).

thf(f24,plain,
    ( ! [X1: a] :
        ( ( cU @ X1 )
        = ( sK1 @ X1 ) )
    | ~ spl2_2 ),
    inference(argument_congruence,[],[f22]) ).

thf(f22,plain,
    ( ( cU = sK1 )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f20]) ).

thf(f20,plain,
    ( spl2_2
  <=> ( cU = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f11,plain,
    ( $true
    = ( cU @ sK0 ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f23,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f12,f20,f16]) ).

thf(f12,plain,
    ( ( cU = sK1 )
    | ( cW = sK1 ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV241^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 21 19:04:39 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a TH0_THM_EQU_NAR problem
% 0.12/0.35  Running higher-order theorem proving
% 0.12/0.35  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.37  % (20866)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.12/0.37  % (20866)First to succeed.
% 0.12/0.37  % (20866)Refutation found. Thanks to Tanya!
% 0.12/0.37  % SZS status Theorem for theBenchmark
% 0.12/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37  % (20866)------------------------------
% 0.12/0.37  % (20866)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37  % (20866)Termination reason: Refutation
% 0.12/0.37  
% 0.12/0.37  % (20866)Memory used [KB]: 5500
% 0.12/0.37  % (20866)Time elapsed: 0.005 s
% 0.12/0.37  % (20866)Instructions burned: 3 (million)
% 0.12/0.37  % (20866)------------------------------
% 0.12/0.37  % (20866)------------------------------
% 0.12/0.37  % (20857)Success in time 0.013 s
%------------------------------------------------------------------------------