TSTP Solution File: SET580^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET580^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% 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 : Sun May  5 09:14:13 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   53 (   2 unt;  13 typ;   0 def)
%            Number of atoms       :  643 ( 173 equ;   0 cnn)
%            Maximal formula atoms :   44 (  16 avg)
%            Number of connectives :  287 ( 109   ~; 106   |;  57   &;   0   @)
%                                         (  13 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   38 (  37   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   5 con; 0-6 aty)
%            Number of variables   :   34 (   0   ^  16   !;  12   ?;  34   :)
%                                         (   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 ).

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

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

thf(func_def_8,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_9,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_10,type,
    vAND: $o > $o > $o ).

thf(func_def_11,type,
    vOR: $o > $o > $o ).

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

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

thf(func_def_14,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f92,plain,
    $false,
    inference(avatar_sat_refutation,[],[f69,f84,f91]) ).

thf(f91,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_contradiction_clause,[],[f90]) ).

thf(f90,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_2 ),
    inference(trivial_inequality_removal,[],[f87]) ).

thf(f87,plain,
    ( ( $true != $true )
    | ~ spl3_1
    | ~ spl3_2 ),
    inference(superposition,[],[f86,f67]) ).

thf(f67,plain,
    ( ( $true = vAPP(a,$o,sK2,sK0) )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f66]) ).

thf(f66,plain,
    ( spl3_2
  <=> ( $true = vAPP(a,$o,sK2,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f86,plain,
    ( ( $true != vAPP(a,$o,sK2,sK0) )
    | ~ spl3_1 ),
    inference(trivial_inequality_removal,[],[f85]) ).

thf(f85,plain,
    ( ( $true != $true )
    | ( $true != vAPP(a,$o,sK2,sK0) )
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f28,f64]) ).

thf(f64,plain,
    ( ( $true = vAPP(a,$o,sK1,sK0) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f62]) ).

thf(f62,plain,
    ( spl3_1
  <=> ( $true = vAPP(a,$o,sK1,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f28,plain,
    ( ( $true != vAPP(a,$o,sK2,sK0) )
    | ( $true != vAPP(a,$o,sK1,sK0) ) ),
    inference(duplicate_literal_removal,[],[f18]) ).

thf(f18,plain,
    ( ( $true != vAPP(a,$o,sK2,sK0) )
    | ( $true != vAPP(a,$o,sK1,sK0) )
    | ( $true != vAPP(a,$o,sK2,sK0) )
    | ( $true != vAPP(a,$o,sK1,sK0) ) ),
    inference(cnf_transformation,[],[f12]) ).

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

thf(f11,plain,
    ( ? [X0: a,X1: a > $o,X2: a > $o] :
        ( ( ( vAPP(a,$o,X2,X0) = $true )
          | ( ( ( vAPP(a,$o,X1,X0) != $true )
              | ( ( ( vAPP(a,$o,X1,X0) = $true )
                  | ( vAPP(a,$o,X2,X0) != $true ) )
                & ( ( vAPP(a,$o,X2,X0) = $true )
                  | ( vAPP(a,$o,X1,X0) != $true ) ) ) )
            & ( ( vAPP(a,$o,X1,X0) = $true )
              | ( ( vAPP(a,$o,X1,X0) != $true )
                & ( vAPP(a,$o,X2,X0) = $true ) )
              | ( ( vAPP(a,$o,X2,X0) != $true )
                & ( vAPP(a,$o,X1,X0) = $true ) ) ) ) )
        & ( ( vAPP(a,$o,X2,X0) != $true )
          | ( ( ( ( vAPP(a,$o,X1,X0) != $true )
                & ( vAPP(a,$o,X2,X0) = $true ) )
              | ( ( vAPP(a,$o,X2,X0) != $true )
                & ( vAPP(a,$o,X1,X0) = $true ) )
              | ( vAPP(a,$o,X1,X0) != $true ) )
            & ( ( vAPP(a,$o,X1,X0) = $true )
              | ( ( ( vAPP(a,$o,X1,X0) = $true )
                  | ( vAPP(a,$o,X2,X0) != $true ) )
                & ( ( vAPP(a,$o,X2,X0) = $true )
                  | ( vAPP(a,$o,X1,X0) != $true ) ) ) ) ) ) )
   => ( ( ( $true = vAPP(a,$o,sK2,sK0) )
        | ( ( ( $true != vAPP(a,$o,sK1,sK0) )
            | ( ( ( $true = vAPP(a,$o,sK1,sK0) )
                | ( $true != vAPP(a,$o,sK2,sK0) ) )
              & ( ( $true = vAPP(a,$o,sK2,sK0) )
                | ( $true != vAPP(a,$o,sK1,sK0) ) ) ) )
          & ( ( $true = vAPP(a,$o,sK1,sK0) )
            | ( ( $true != vAPP(a,$o,sK1,sK0) )
              & ( $true = vAPP(a,$o,sK2,sK0) ) )
            | ( ( $true != vAPP(a,$o,sK2,sK0) )
              & ( $true = vAPP(a,$o,sK1,sK0) ) ) ) ) )
      & ( ( $true != vAPP(a,$o,sK2,sK0) )
        | ( ( ( ( $true != vAPP(a,$o,sK1,sK0) )
              & ( $true = vAPP(a,$o,sK2,sK0) ) )
            | ( ( $true != vAPP(a,$o,sK2,sK0) )
              & ( $true = vAPP(a,$o,sK1,sK0) ) )
            | ( $true != vAPP(a,$o,sK1,sK0) ) )
          & ( ( $true = vAPP(a,$o,sK1,sK0) )
            | ( ( ( $true = vAPP(a,$o,sK1,sK0) )
                | ( $true != vAPP(a,$o,sK2,sK0) ) )
              & ( ( $true = vAPP(a,$o,sK2,sK0) )
                | ( $true != vAPP(a,$o,sK1,sK0) ) ) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ? [X0: a,X1: a > $o,X2: a > $o] :
      ( ( ( vAPP(a,$o,X2,X0) = $true )
        | ( ( ( vAPP(a,$o,X1,X0) != $true )
            | ( ( ( vAPP(a,$o,X1,X0) = $true )
                | ( vAPP(a,$o,X2,X0) != $true ) )
              & ( ( vAPP(a,$o,X2,X0) = $true )
                | ( vAPP(a,$o,X1,X0) != $true ) ) ) )
          & ( ( vAPP(a,$o,X1,X0) = $true )
            | ( ( vAPP(a,$o,X1,X0) != $true )
              & ( vAPP(a,$o,X2,X0) = $true ) )
            | ( ( vAPP(a,$o,X2,X0) != $true )
              & ( vAPP(a,$o,X1,X0) = $true ) ) ) ) )
      & ( ( vAPP(a,$o,X2,X0) != $true )
        | ( ( ( ( vAPP(a,$o,X1,X0) != $true )
              & ( vAPP(a,$o,X2,X0) = $true ) )
            | ( ( vAPP(a,$o,X2,X0) != $true )
              & ( vAPP(a,$o,X1,X0) = $true ) )
            | ( vAPP(a,$o,X1,X0) != $true ) )
          & ( ( vAPP(a,$o,X1,X0) = $true )
            | ( ( ( vAPP(a,$o,X1,X0) = $true )
                | ( vAPP(a,$o,X2,X0) != $true ) )
              & ( ( vAPP(a,$o,X2,X0) = $true )
                | ( vAPP(a,$o,X1,X0) != $true ) ) ) ) ) ) ),
    inference(flattening,[],[f9]) ).

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

thf(f8,plain,
    ? [X0: a,X1: a > $o,X2: a > $o] :
      ( ( ( ( ( vAPP(a,$o,X1,X0) != $true )
            & ( vAPP(a,$o,X2,X0) = $true ) )
          | ( ( vAPP(a,$o,X2,X0) != $true )
            & ( vAPP(a,$o,X1,X0) = $true ) ) )
      <=> ( vAPP(a,$o,X1,X0) = $true ) )
    <~> ( vAPP(a,$o,X2,X0) != $true ) ),
    inference(ennf_transformation,[],[f7]) ).

thf(f7,plain,
    ~ ! [X0: a,X1: a > $o,X2: a > $o] :
        ( ( ( ( ( vAPP(a,$o,X1,X0) != $true )
              & ( vAPP(a,$o,X2,X0) = $true ) )
            | ( ( vAPP(a,$o,X2,X0) != $true )
              & ( vAPP(a,$o,X1,X0) = $true ) ) )
        <=> ( vAPP(a,$o,X1,X0) = $true ) )
      <=> ( vAPP(a,$o,X2,X0) != $true ) ),
    inference(flattening,[],[f6]) ).

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

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

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

thf(f1,conjecture,
    ! [X0: a,X1: a > $o,X2: a > $o] :
      ( ( ( ( ~ vAPP(a,$o,X1,X0)
            & vAPP(a,$o,X2,X0) )
          | ( ~ vAPP(a,$o,X2,X0)
            & vAPP(a,$o,X1,X0) ) )
      <=> vAPP(a,$o,X1,X0) )
    <=> ~ vAPP(a,$o,X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_23_pme) ).

thf(f84,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f83]) ).

thf(f83,plain,
    ( $false
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f80]) ).

thf(f80,plain,
    ( ( $true != $true )
    | spl3_2 ),
    inference(superposition,[],[f79,f77]) ).

thf(f77,plain,
    ( ( $true = vAPP(a,$o,sK1,sK0) )
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f76]) ).

thf(f76,plain,
    ( ( $true = $false )
    | ( $true = vAPP(a,$o,sK1,sK0) )
    | spl3_2 ),
    inference(forward_demodulation,[],[f29,f71]) ).

thf(f71,plain,
    ( ( $false = vAPP(a,$o,sK2,sK0) )
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f70]) ).

thf(f70,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,sK2,sK0) )
    | spl3_2 ),
    inference(superposition,[],[f68,f4]) ).

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

thf(f68,plain,
    ( ( $true != vAPP(a,$o,sK2,sK0) )
    | spl3_2 ),
    inference(avatar_component_clause,[],[f66]) ).

thf(f29,plain,
    ( ( $true = vAPP(a,$o,sK2,sK0) )
    | ( $true = vAPP(a,$o,sK1,sK0) ) ),
    inference(duplicate_literal_removal,[],[f19]) ).

thf(f19,plain,
    ( ( $true = vAPP(a,$o,sK2,sK0) )
    | ( $true = vAPP(a,$o,sK1,sK0) )
    | ( $true = vAPP(a,$o,sK2,sK0) )
    | ( $true = vAPP(a,$o,sK1,sK0) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f79,plain,
    ( ( $true != vAPP(a,$o,sK1,sK0) )
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f78]) ).

thf(f78,plain,
    ( ( $true = $false )
    | ( $true != vAPP(a,$o,sK1,sK0) )
    | spl3_2 ),
    inference(forward_demodulation,[],[f32,f71]) ).

thf(f32,plain,
    ( ( $true = vAPP(a,$o,sK2,sK0) )
    | ( $true != vAPP(a,$o,sK1,sK0) ) ),
    inference(duplicate_literal_removal,[],[f23]) ).

thf(f23,plain,
    ( ( $true = vAPP(a,$o,sK2,sK0) )
    | ( $true != vAPP(a,$o,sK1,sK0) )
    | ( $true = vAPP(a,$o,sK2,sK0) )
    | ( $true != vAPP(a,$o,sK1,sK0) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f69,plain,
    ( spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f25,f66,f62]) ).

thf(f25,plain,
    ( ( $true != vAPP(a,$o,sK2,sK0) )
    | ( $true = vAPP(a,$o,sK1,sK0) ) ),
    inference(duplicate_literal_removal,[],[f14]) ).

thf(f14,plain,
    ( ( $true != vAPP(a,$o,sK2,sK0) )
    | ( $true = vAPP(a,$o,sK1,sK0) )
    | ( $true = vAPP(a,$o,sK1,sK0) )
    | ( $true != vAPP(a,$o,sK2,sK0) ) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : SET580^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 16:52:07 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (26884)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34  % (26886)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34  % (26889)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.34  % (26887)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)
% 0.11/0.34  % (26890)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.34  % (26887)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34  % (26885)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.34  % (26891)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)
% 0.11/0.34  % (26888)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.34  % Exception at run slice level
% 0.11/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34  % (26888)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.11/0.34  % Exception at run slice level
% 0.11/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34  % Exception at run slice level
% 0.11/0.34  % Exception at run slice level
% 0.11/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.35  % (26887)First to succeed.
% 0.11/0.35  % (26887)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26884"
% 0.11/0.35  % (26887)Refutation found. Thanks to Tanya!
% 0.11/0.35  % SZS status Theorem for theBenchmark
% 0.11/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35  % (26887)------------------------------
% 0.11/0.35  % (26887)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35  % (26887)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (26887)Memory used [KB]: 769
% 0.11/0.35  % (26887)Time elapsed: 0.005 s
% 0.11/0.35  % (26887)Instructions burned: 7 (million)
% 0.11/0.35  % (26884)Success in time 0.017 s
%------------------------------------------------------------------------------