TSTP Solution File: SET200^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET200^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.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 03:17:47 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   48 (   6 unt;  15 typ;   0 def)
%            Number of atoms       :  346 (  88 equ;   0 cnn)
%            Maximal formula atoms :   16 (  10 avg)
%            Number of connectives :  146 (  49   ~;  45   |;  32   &;   0   @)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   54 (  53   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   5 con; 0-6 aty)
%            Number of variables   :   71 (   0   ^  43   !;  22   ?;  71   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

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

thf(func_def_4,type,
    sK0: a > $o ).

thf(func_def_5,type,
    sK1: a > $o ).

thf(func_def_6,type,
    sK2: a > $o ).

thf(func_def_7,type,
    sK3: a > $o ).

thf(func_def_8,type,
    sK4: a ).

thf(func_def_10,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_11,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_12,type,
    vAND: $o > $o > $o ).

thf(func_def_13,type,
    vOR: $o > $o > $o ).

thf(func_def_14,type,
    vIMP: $o > $o > $o ).

thf(func_def_15,type,
    vNOT: $o > $o ).

thf(func_def_16,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f75,plain,
    $false,
    inference(avatar_sat_refutation,[],[f26,f69,f74]) ).

thf(f74,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f73]) ).

thf(f73,plain,
    ( $false
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f72]) ).

thf(f72,plain,
    ( ( $true = $false )
    | ~ spl5_1 ),
    inference(forward_demodulation,[],[f71,f56]) ).

thf(f56,plain,
    $false = vAPP(a,$o,sK1,sK4),
    inference(trivial_inequality_removal,[],[f55]) ).

thf(f55,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,sK1,sK4) ) ),
    inference(superposition,[],[f16,f4]) ).

thf(f4,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f16,plain,
    $true != vAPP(a,$o,sK1,sK4),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ( $true != vAPP(a,$o,sK3,sK4) )
    & ( $true != vAPP(a,$o,sK1,sK4) )
    & ( ( $true = vAPP(a,$o,sK2,sK4) )
      | ( $true = vAPP(a,$o,sK0,sK4) ) )
    & ! [X5: a] :
        ( ( $true = vAPP(a,$o,sK3,X5) )
        | ( $true != vAPP(a,$o,sK2,X5) ) )
    & ! [X6: a] :
        ( ( $true = vAPP(a,$o,sK1,X6) )
        | ( $true != vAPP(a,$o,sK0,X6) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f11,f10]) ).

thf(f10,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ? [X4: a] :
            ( ( vAPP(a,$o,X3,X4) != $true )
            & ( vAPP(a,$o,X1,X4) != $true )
            & ( ( vAPP(a,$o,X2,X4) = $true )
              | ( vAPP(a,$o,X0,X4) = $true ) ) )
        & ! [X5: a] :
            ( ( $true = vAPP(a,$o,X3,X5) )
            | ( $true != vAPP(a,$o,X2,X5) ) )
        & ! [X6: a] :
            ( ( $true = vAPP(a,$o,X1,X6) )
            | ( $true != vAPP(a,$o,X0,X6) ) ) )
   => ( ? [X4: a] :
          ( ( $true != vAPP(a,$o,sK3,X4) )
          & ( $true != vAPP(a,$o,sK1,X4) )
          & ( ( $true = vAPP(a,$o,sK2,X4) )
            | ( $true = vAPP(a,$o,sK0,X4) ) ) )
      & ! [X5: a] :
          ( ( $true = vAPP(a,$o,sK3,X5) )
          | ( $true != vAPP(a,$o,sK2,X5) ) )
      & ! [X6: a] :
          ( ( $true = vAPP(a,$o,sK1,X6) )
          | ( $true != vAPP(a,$o,sK0,X6) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X4: a] :
        ( ( $true != vAPP(a,$o,sK3,X4) )
        & ( $true != vAPP(a,$o,sK1,X4) )
        & ( ( $true = vAPP(a,$o,sK2,X4) )
          | ( $true = vAPP(a,$o,sK0,X4) ) ) )
   => ( ( $true != vAPP(a,$o,sK3,sK4) )
      & ( $true != vAPP(a,$o,sK1,sK4) )
      & ( ( $true = vAPP(a,$o,sK2,sK4) )
        | ( $true = vAPP(a,$o,sK0,sK4) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
      ( ? [X4: a] :
          ( ( vAPP(a,$o,X3,X4) != $true )
          & ( vAPP(a,$o,X1,X4) != $true )
          & ( ( vAPP(a,$o,X2,X4) = $true )
            | ( vAPP(a,$o,X0,X4) = $true ) ) )
      & ! [X5: a] :
          ( ( $true = vAPP(a,$o,X3,X5) )
          | ( $true != vAPP(a,$o,X2,X5) ) )
      & ! [X6: a] :
          ( ( $true = vAPP(a,$o,X1,X6) )
          | ( $true != vAPP(a,$o,X0,X6) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
      ( ? [X6: a] :
          ( ( $true != vAPP(a,$o,X3,X6) )
          & ( $true != vAPP(a,$o,X1,X6) )
          & ( ( $true = vAPP(a,$o,X2,X6) )
            | ( $true = vAPP(a,$o,X0,X6) ) ) )
      & ! [X4: a] :
          ( ( vAPP(a,$o,X3,X4) = $true )
          | ( vAPP(a,$o,X2,X4) != $true ) )
      & ! [X5: a] :
          ( ( $true = vAPP(a,$o,X1,X5) )
          | ( $true != vAPP(a,$o,X0,X5) ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
      ( ? [X6: a] :
          ( ( $true != vAPP(a,$o,X3,X6) )
          & ( $true != vAPP(a,$o,X1,X6) )
          & ( ( $true = vAPP(a,$o,X2,X6) )
            | ( $true = vAPP(a,$o,X0,X6) ) ) )
      & ! [X4: a] :
          ( ( vAPP(a,$o,X3,X4) = $true )
          | ( vAPP(a,$o,X2,X4) != $true ) )
      & ! [X5: a] :
          ( ( $true = vAPP(a,$o,X1,X5) )
          | ( $true != vAPP(a,$o,X0,X5) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ( ! [X4: a] :
              ( ( vAPP(a,$o,X2,X4) = $true )
             => ( vAPP(a,$o,X3,X4) = $true ) )
          & ! [X5: a] :
              ( ( $true = vAPP(a,$o,X0,X5) )
             => ( $true = vAPP(a,$o,X1,X5) ) ) )
       => ! [X6: a] :
            ( ( ( $true = vAPP(a,$o,X2,X6) )
              | ( $true = vAPP(a,$o,X0,X6) ) )
           => ( ( $true = vAPP(a,$o,X3,X6) )
              | ( $true = vAPP(a,$o,X1,X6) ) ) ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ( ! [X4: a] :
              ( vAPP(a,$o,X2,X4)
             => vAPP(a,$o,X3,X4) )
          & ! [X5: a] :
              ( vAPP(a,$o,X0,X5)
             => vAPP(a,$o,X1,X5) ) )
       => ! [X6: a] :
            ( ( vAPP(a,$o,X2,X6)
              | vAPP(a,$o,X0,X6) )
           => ( vAPP(a,$o,X3,X6)
              | vAPP(a,$o,X1,X6) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ( ! [X4: a] :
              ( vAPP(a,$o,X2,X4)
             => vAPP(a,$o,X3,X4) )
          & ! [X4: a] :
              ( vAPP(a,$o,X0,X4)
             => vAPP(a,$o,X1,X4) ) )
       => ! [X4: a] :
            ( ( vAPP(a,$o,X2,X4)
              | vAPP(a,$o,X0,X4) )
           => ( vAPP(a,$o,X3,X4)
              | vAPP(a,$o,X1,X4) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
      ( ( ! [X4: a] :
            ( vAPP(a,$o,X2,X4)
           => vAPP(a,$o,X3,X4) )
        & ! [X4: a] :
            ( vAPP(a,$o,X0,X4)
           => vAPP(a,$o,X1,X4) ) )
     => ! [X4: a] :
          ( ( vAPP(a,$o,X2,X4)
            | vAPP(a,$o,X0,X4) )
         => ( vAPP(a,$o,X3,X4)
            | vAPP(a,$o,X1,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_34_pme) ).

thf(f71,plain,
    ( ( $true = vAPP(a,$o,sK1,sK4) )
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f70]) ).

thf(f70,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,sK1,sK4) )
    | ~ spl5_1 ),
    inference(superposition,[],[f13,f21]) ).

thf(f21,plain,
    ( ( $true = vAPP(a,$o,sK0,sK4) )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f19]) ).

thf(f19,plain,
    ( spl5_1
  <=> ( $true = vAPP(a,$o,sK0,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

thf(f13,plain,
    ! [X6: a] :
      ( ( $true != vAPP(a,$o,sK0,X6) )
      | ( $true = vAPP(a,$o,sK1,X6) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f69,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f68]) ).

thf(f68,plain,
    ( $false
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f67,f17]) ).

thf(f17,plain,
    $true != vAPP(a,$o,sK3,sK4),
    inference(cnf_transformation,[],[f12]) ).

thf(f67,plain,
    ( ( $true = vAPP(a,$o,sK3,sK4) )
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f64]) ).

thf(f64,plain,
    ( ( $true != $true )
    | ( $true = vAPP(a,$o,sK3,sK4) )
    | ~ spl5_2 ),
    inference(superposition,[],[f14,f25]) ).

thf(f25,plain,
    ( ( $true = vAPP(a,$o,sK2,sK4) )
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f23]) ).

thf(f23,plain,
    ( spl5_2
  <=> ( $true = vAPP(a,$o,sK2,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

thf(f14,plain,
    ! [X5: a] :
      ( ( $true != vAPP(a,$o,sK2,X5) )
      | ( $true = vAPP(a,$o,sK3,X5) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f26,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f15,f23,f19]) ).

thf(f15,plain,
    ( ( $true = vAPP(a,$o,sK2,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK4) ) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET200^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 12:14:38 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (19708)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (19709)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.37  % (19710)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37  % (19712)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.37  % (19711)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.37  % (19713)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.37  % (19714)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.37  % (19715)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (19712)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.38  % (19711)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.38  % Exception at run slice level% Exception at run slice level
% 0.15/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  
% 0.15/0.38  User error: % Exception at run slice levelFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  
% 0.15/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  % Exception at run slice level
% 0.15/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  % (19714)First to succeed.
% 0.15/0.38  % (19713)Also succeeded, but the first one will report.
% 0.15/0.38  % (19711)Also succeeded, but the first one will report.
% 0.15/0.38  % (19714)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19708"
% 0.15/0.38  % (19714)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (19714)------------------------------
% 0.15/0.38  % (19714)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (19714)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (19714)Memory used [KB]: 771
% 0.15/0.38  % (19714)Time elapsed: 0.006 s
% 0.15/0.38  % (19714)Instructions burned: 6 (million)
% 0.15/0.38  % (19708)Success in time 0.021 s
%------------------------------------------------------------------------------