TSTP Solution File: SET624^5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET624^5 : 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 : n012.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 03:19:45 EDT 2024

% Result   : Theorem 0.10s 0.31s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  102 (   1 unt;  16 typ;   0 def)
%            Number of atoms       :  945 ( 221 equ;   0 cnn)
%            Maximal formula atoms :   28 (  10 avg)
%            Number of connectives :  441 ( 157   ~; 209   |;  57   &;   0   @)
%                                         (  13 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   48 (  47   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;  14 con; 0-6 aty)
%            Number of variables   :   93 (   0   ^  39   !;  48   ?;  93   :)
%                                         (   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 ).

thf(func_def_8,type,
    sK4: a ).

thf(func_def_9,type,
    sK5: a ).

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

thf(func_def_12,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

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

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

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

thf(func_def_16,type,
    vNOT: $o > $o ).

thf(func_def_17,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(f187,plain,
    $false,
    inference(avatar_sat_refutation,[],[f68,f73,f78,f87,f91,f100,f108,f117,f133,f144,f153,f174,f177,f186]) ).

thf(f186,plain,
    ( spl6_1
    | spl6_2
    | spl6_5 ),
    inference(avatar_split_clause,[],[f179,f75,f61,f57]) ).

thf(f57,plain,
    ( spl6_1
  <=> ( $true = vAPP(a,$o,sK0,sK5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

thf(f61,plain,
    ( spl6_2
  <=> ( $true = vAPP(a,$o,sK0,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

thf(f75,plain,
    ( spl6_5
  <=> ( $true = vAPP(a,$o,sK2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

thf(f179,plain,
    ( ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK5) )
    | spl6_5 ),
    inference(trivial_inequality_removal,[],[f178]) ).

thf(f178,plain,
    ( ( $true = $false )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK5) )
    | spl6_5 ),
    inference(forward_demodulation,[],[f20,f156]) ).

thf(f156,plain,
    ( ( $false = vAPP(a,$o,sK2,sK3) )
    | spl6_5 ),
    inference(trivial_inequality_removal,[],[f155]) ).

thf(f155,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,sK2,sK3) )
    | spl6_5 ),
    inference(superposition,[],[f76,f4]) ).

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

thf(f76,plain,
    ( ( $true != vAPP(a,$o,sK2,sK3) )
    | spl6_5 ),
    inference(avatar_component_clause,[],[f75]) ).

thf(f20,plain,
    ( ( $true = vAPP(a,$o,sK2,sK3) )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ( ( ( ! [X3: a] :
            ( ( $true != vAPP(a,$o,sK2,X3) )
            | ( $true != vAPP(a,$o,sK0,X3) ) )
        & ! [X4: a] :
            ( ( $true != vAPP(a,$o,sK1,X4) )
            | ( $true != vAPP(a,$o,sK0,X4) ) ) )
      | ! [X5: a] :
          ( ( ( $true != vAPP(a,$o,sK2,X5) )
            & ( $true != vAPP(a,$o,sK1,X5) ) )
          | ( $true != vAPP(a,$o,sK0,X5) ) ) )
    & ( ( ( $true = vAPP(a,$o,sK2,sK3) )
        & ( $true = vAPP(a,$o,sK0,sK3) ) )
      | ( ( $true = vAPP(a,$o,sK1,sK4) )
        & ( $true = vAPP(a,$o,sK0,sK4) ) )
      | ( ( ( $true = vAPP(a,$o,sK2,sK5) )
          | ( $true = vAPP(a,$o,sK1,sK5) ) )
        & ( $true = vAPP(a,$o,sK0,sK5) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f10,f14,f13,f12,f11]) ).

thf(f11,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ( ! [X3: a] :
                ( ( vAPP(a,$o,X2,X3) != $true )
                | ( vAPP(a,$o,X0,X3) != $true ) )
            & ! [X4: a] :
                ( ( $true != vAPP(a,$o,X1,X4) )
                | ( $true != vAPP(a,$o,X0,X4) ) ) )
          | ! [X5: a] :
              ( ( ( $true != vAPP(a,$o,X2,X5) )
                & ( $true != vAPP(a,$o,X1,X5) ) )
              | ( $true != vAPP(a,$o,X0,X5) ) ) )
        & ( ? [X6: a] :
              ( ( $true = vAPP(a,$o,X2,X6) )
              & ( $true = vAPP(a,$o,X0,X6) ) )
          | ? [X7: a] :
              ( ( $true = vAPP(a,$o,X1,X7) )
              & ( $true = vAPP(a,$o,X0,X7) ) )
          | ? [X8: a] :
              ( ( ( $true = vAPP(a,$o,X2,X8) )
                | ( $true = vAPP(a,$o,X1,X8) ) )
              & ( $true = vAPP(a,$o,X0,X8) ) ) ) )
   => ( ( ( ! [X3: a] :
              ( ( $true != vAPP(a,$o,sK2,X3) )
              | ( $true != vAPP(a,$o,sK0,X3) ) )
          & ! [X4: a] :
              ( ( $true != vAPP(a,$o,sK1,X4) )
              | ( $true != vAPP(a,$o,sK0,X4) ) ) )
        | ! [X5: a] :
            ( ( ( $true != vAPP(a,$o,sK2,X5) )
              & ( $true != vAPP(a,$o,sK1,X5) ) )
            | ( $true != vAPP(a,$o,sK0,X5) ) ) )
      & ( ? [X6: a] :
            ( ( $true = vAPP(a,$o,sK2,X6) )
            & ( $true = vAPP(a,$o,sK0,X6) ) )
        | ? [X7: a] :
            ( ( $true = vAPP(a,$o,sK1,X7) )
            & ( $true = vAPP(a,$o,sK0,X7) ) )
        | ? [X8: a] :
            ( ( ( $true = vAPP(a,$o,sK2,X8) )
              | ( $true = vAPP(a,$o,sK1,X8) ) )
            & ( $true = vAPP(a,$o,sK0,X8) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X6: a] :
        ( ( $true = vAPP(a,$o,sK2,X6) )
        & ( $true = vAPP(a,$o,sK0,X6) ) )
   => ( ( $true = vAPP(a,$o,sK2,sK3) )
      & ( $true = vAPP(a,$o,sK0,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ( ? [X7: a] :
        ( ( $true = vAPP(a,$o,sK1,X7) )
        & ( $true = vAPP(a,$o,sK0,X7) ) )
   => ( ( $true = vAPP(a,$o,sK1,sK4) )
      & ( $true = vAPP(a,$o,sK0,sK4) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f14,plain,
    ( ? [X8: a] :
        ( ( ( $true = vAPP(a,$o,sK2,X8) )
          | ( $true = vAPP(a,$o,sK1,X8) ) )
        & ( $true = vAPP(a,$o,sK0,X8) ) )
   => ( ( ( $true = vAPP(a,$o,sK2,sK5) )
        | ( $true = vAPP(a,$o,sK1,sK5) ) )
      & ( $true = vAPP(a,$o,sK0,sK5) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ( ! [X3: a] :
              ( ( vAPP(a,$o,X2,X3) != $true )
              | ( vAPP(a,$o,X0,X3) != $true ) )
          & ! [X4: a] :
              ( ( $true != vAPP(a,$o,X1,X4) )
              | ( $true != vAPP(a,$o,X0,X4) ) ) )
        | ! [X5: a] :
            ( ( ( $true != vAPP(a,$o,X2,X5) )
              & ( $true != vAPP(a,$o,X1,X5) ) )
            | ( $true != vAPP(a,$o,X0,X5) ) ) )
      & ( ? [X6: a] :
            ( ( $true = vAPP(a,$o,X2,X6) )
            & ( $true = vAPP(a,$o,X0,X6) ) )
        | ? [X7: a] :
            ( ( $true = vAPP(a,$o,X1,X7) )
            & ( $true = vAPP(a,$o,X0,X7) ) )
        | ? [X8: a] :
            ( ( ( $true = vAPP(a,$o,X2,X8) )
              | ( $true = vAPP(a,$o,X1,X8) ) )
            & ( $true = vAPP(a,$o,X0,X8) ) ) ) ),
    inference(rectify,[],[f9]) ).

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

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

thf(f7,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ? [X3: a] :
          ( ( ( vAPP(a,$o,X2,X3) = $true )
            | ( vAPP(a,$o,X1,X3) = $true ) )
          & ( vAPP(a,$o,X0,X3) = $true ) )
    <~> ( ? [X4: a] :
            ( ( $true = vAPP(a,$o,X2,X4) )
            & ( $true = vAPP(a,$o,X0,X4) ) )
        | ? [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 > $o] :
        ( ? [X3: a] :
            ( ( ( vAPP(a,$o,X2,X3) = $true )
              | ( vAPP(a,$o,X1,X3) = $true ) )
            & ( vAPP(a,$o,X0,X3) = $true ) )
      <=> ( ? [X4: a] :
              ( ( $true = vAPP(a,$o,X2,X4) )
              & ( $true = vAPP(a,$o,X0,X4) ) )
          | ? [X5: a] :
              ( ( $true = vAPP(a,$o,X1,X5) )
              & ( $true = vAPP(a,$o,X0,X5) ) ) ) ),
    inference(fool_elimination,[],[f5]) ).

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

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

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ? [X3: a] :
          ( ( vAPP(a,$o,X2,X3)
            | vAPP(a,$o,X1,X3) )
          & vAPP(a,$o,X0,X3) )
    <=> ( ? [X3: a] :
            ( vAPP(a,$o,X2,X3)
            & vAPP(a,$o,X0,X3) )
        | ? [X3: a] :
            ( vAPP(a,$o,X1,X3)
            & vAPP(a,$o,X0,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_100_pme) ).

thf(f177,plain,
    ( spl6_6
    | spl6_7
    | spl6_2
    | spl6_5 ),
    inference(avatar_split_clause,[],[f176,f75,f61,f84,f80]) ).

thf(f80,plain,
    ( spl6_6
  <=> ( $true = vAPP(a,$o,sK1,sK5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

thf(f84,plain,
    ( spl6_7
  <=> ( $true = vAPP(a,$o,sK2,sK5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

thf(f176,plain,
    ( ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) )
    | spl6_5 ),
    inference(trivial_inequality_removal,[],[f175]) ).

thf(f175,plain,
    ( ( $true = $false )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) )
    | spl6_5 ),
    inference(forward_demodulation,[],[f21,f156]) ).

thf(f21,plain,
    ( ( $true = vAPP(a,$o,sK2,sK3) )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f174,plain,
    ( ~ spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(avatar_contradiction_clause,[],[f173]) ).

thf(f173,plain,
    ( $false
    | ~ spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f170]) ).

thf(f170,plain,
    ( ( $true != $true )
    | ~ spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(superposition,[],[f161,f59]) ).

thf(f59,plain,
    ( ( $true = vAPP(a,$o,sK0,sK5) )
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f57]) ).

thf(f161,plain,
    ( ( $true != vAPP(a,$o,sK0,sK5) )
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f160]) ).

thf(f160,plain,
    ( ( $true != $true )
    | ( $true != vAPP(a,$o,sK0,sK5) )
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(superposition,[],[f107,f86]) ).

thf(f86,plain,
    ( ( $true = vAPP(a,$o,sK2,sK5) )
    | ~ spl6_7 ),
    inference(avatar_component_clause,[],[f84]) ).

thf(f107,plain,
    ( ! [X5: a] :
        ( ( $true != vAPP(a,$o,sK2,X5) )
        | ( $true != vAPP(a,$o,sK0,X5) ) )
    | ~ spl6_9 ),
    inference(avatar_component_clause,[],[f106]) ).

thf(f106,plain,
    ( spl6_9
  <=> ! [X5: a] :
        ( ( $true != vAPP(a,$o,sK2,X5) )
        | ( $true != vAPP(a,$o,sK0,X5) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).

thf(f153,plain,
    ( spl6_6
    | spl6_7
    | spl6_2
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(avatar_split_clause,[],[f146,f106,f75,f61,f84,f80]) ).

thf(f146,plain,
    ( ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f145]) ).

thf(f145,plain,
    ( ( $true = $false )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(forward_demodulation,[],[f17,f115]) ).

thf(f115,plain,
    ( ( $false = vAPP(a,$o,sK0,sK3) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f114]) ).

thf(f114,plain,
    ( ( $true != $true )
    | ( $false = vAPP(a,$o,sK0,sK3) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(superposition,[],[f112,f4]) ).

thf(f112,plain,
    ( ( $true != vAPP(a,$o,sK0,sK3) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f109]) ).

thf(f109,plain,
    ( ( $true != $true )
    | ( $true != vAPP(a,$o,sK0,sK3) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(superposition,[],[f107,f77]) ).

thf(f77,plain,
    ( ( $true = vAPP(a,$o,sK2,sK3) )
    | ~ spl6_5 ),
    inference(avatar_component_clause,[],[f75]) ).

thf(f17,plain,
    ( ( $true = vAPP(a,$o,sK0,sK3) )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f144,plain,
    ( ~ spl6_1
    | ~ spl6_6
    | ~ spl6_8 ),
    inference(avatar_contradiction_clause,[],[f143]) ).

thf(f143,plain,
    ( $false
    | ~ spl6_1
    | ~ spl6_6
    | ~ spl6_8 ),
    inference(trivial_inequality_removal,[],[f140]) ).

thf(f140,plain,
    ( ( $true != $true )
    | ~ spl6_1
    | ~ spl6_6
    | ~ spl6_8 ),
    inference(superposition,[],[f137,f59]) ).

thf(f137,plain,
    ( ( $true != vAPP(a,$o,sK0,sK5) )
    | ~ spl6_6
    | ~ spl6_8 ),
    inference(trivial_inequality_removal,[],[f136]) ).

thf(f136,plain,
    ( ( $true != $true )
    | ( $true != vAPP(a,$o,sK0,sK5) )
    | ~ spl6_6
    | ~ spl6_8 ),
    inference(superposition,[],[f90,f82]) ).

thf(f82,plain,
    ( ( $true = vAPP(a,$o,sK1,sK5) )
    | ~ spl6_6 ),
    inference(avatar_component_clause,[],[f80]) ).

thf(f90,plain,
    ( ! [X5: a] :
        ( ( $true != vAPP(a,$o,sK1,X5) )
        | ( $true != vAPP(a,$o,sK0,X5) ) )
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f89]) ).

thf(f89,plain,
    ( spl6_8
  <=> ! [X5: a] :
        ( ( $true != vAPP(a,$o,sK1,X5) )
        | ( $true != vAPP(a,$o,sK0,X5) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

thf(f133,plain,
    ( spl6_6
    | spl6_7
    | spl6_4
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(avatar_split_clause,[],[f132,f106,f75,f70,f84,f80]) ).

thf(f70,plain,
    ( spl6_4
  <=> ( $true = vAPP(a,$o,sK1,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

thf(f132,plain,
    ( ( $true = vAPP(a,$o,sK1,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f131]) ).

thf(f131,plain,
    ( ( $true = $false )
    | ( $true = vAPP(a,$o,sK1,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) )
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(forward_demodulation,[],[f19,f115]) ).

thf(f19,plain,
    ( ( $true = vAPP(a,$o,sK0,sK3) )
    | ( $true = vAPP(a,$o,sK1,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f117,plain,
    ( ~ spl6_3
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(avatar_contradiction_clause,[],[f116]) ).

thf(f116,plain,
    ( $false
    | ~ spl6_3
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f113]) ).

thf(f113,plain,
    ( ( $true != $true )
    | ~ spl6_3
    | ~ spl6_5
    | ~ spl6_9 ),
    inference(superposition,[],[f112,f67]) ).

thf(f67,plain,
    ( ( $true = vAPP(a,$o,sK0,sK3) )
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f65]) ).

thf(f65,plain,
    ( spl6_3
  <=> ( $true = vAPP(a,$o,sK0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

thf(f108,plain,
    ( spl6_9
    | spl6_9 ),
    inference(avatar_split_clause,[],[f27,f106,f106]) ).

thf(f27,plain,
    ! [X3: a,X5: a] :
      ( ( $true != vAPP(a,$o,sK2,X3) )
      | ( $true != vAPP(a,$o,sK0,X3) )
      | ( $true != vAPP(a,$o,sK2,X5) )
      | ( $true != vAPP(a,$o,sK0,X5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f100,plain,
    ( ~ spl6_2
    | ~ spl6_4
    | ~ spl6_8 ),
    inference(avatar_contradiction_clause,[],[f99]) ).

thf(f99,plain,
    ( $false
    | ~ spl6_2
    | ~ spl6_4
    | ~ spl6_8 ),
    inference(trivial_inequality_removal,[],[f96]) ).

thf(f96,plain,
    ( ( $true != $true )
    | ~ spl6_2
    | ~ spl6_4
    | ~ spl6_8 ),
    inference(superposition,[],[f95,f63]) ).

thf(f63,plain,
    ( ( $true = vAPP(a,$o,sK0,sK4) )
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f61]) ).

thf(f95,plain,
    ( ( $true != vAPP(a,$o,sK0,sK4) )
    | ~ spl6_4
    | ~ spl6_8 ),
    inference(trivial_inequality_removal,[],[f92]) ).

thf(f92,plain,
    ( ( $true != $true )
    | ( $true != vAPP(a,$o,sK0,sK4) )
    | ~ spl6_4
    | ~ spl6_8 ),
    inference(superposition,[],[f90,f72]) ).

thf(f72,plain,
    ( ( $true = vAPP(a,$o,sK1,sK4) )
    | ~ spl6_4 ),
    inference(avatar_component_clause,[],[f70]) ).

thf(f91,plain,
    ( spl6_8
    | spl6_8 ),
    inference(avatar_split_clause,[],[f24,f89,f89]) ).

thf(f24,plain,
    ! [X4: a,X5: a] :
      ( ( $true != vAPP(a,$o,sK1,X4) )
      | ( $true != vAPP(a,$o,sK0,X4) )
      | ( $true != vAPP(a,$o,sK1,X5) )
      | ( $true != vAPP(a,$o,sK0,X5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f87,plain,
    ( spl6_6
    | spl6_7
    | spl6_4
    | spl6_5 ),
    inference(avatar_split_clause,[],[f23,f75,f70,f84,f80]) ).

thf(f23,plain,
    ( ( $true = vAPP(a,$o,sK2,sK3) )
    | ( $true = vAPP(a,$o,sK1,sK4) )
    | ( $true = vAPP(a,$o,sK2,sK5) )
    | ( $true = vAPP(a,$o,sK1,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f78,plain,
    ( spl6_1
    | spl6_4
    | spl6_5 ),
    inference(avatar_split_clause,[],[f22,f75,f70,f57]) ).

thf(f22,plain,
    ( ( $true = vAPP(a,$o,sK2,sK3) )
    | ( $true = vAPP(a,$o,sK1,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f73,plain,
    ( spl6_1
    | spl6_4
    | spl6_3 ),
    inference(avatar_split_clause,[],[f18,f65,f70,f57]) ).

thf(f18,plain,
    ( ( $true = vAPP(a,$o,sK0,sK3) )
    | ( $true = vAPP(a,$o,sK1,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f68,plain,
    ( spl6_1
    | spl6_2
    | spl6_3 ),
    inference(avatar_split_clause,[],[f16,f65,f61,f57]) ).

thf(f16,plain,
    ( ( $true = vAPP(a,$o,sK0,sK3) )
    | ( $true = vAPP(a,$o,sK0,sK4) )
    | ( $true = vAPP(a,$o,sK0,sK5) ) ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SET624^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.29  % Computer : n012.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Mon May 20 11:30:52 EDT 2024
% 0.10/0.29  % CPUTime    : 
% 0.10/0.30  % (25377)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.30  % (25378)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.30  % (25380)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)
% 0.10/0.30  % (25379)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.30  % (25380)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.10/0.31  % Exception at run slice level
% 0.10/0.31  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.10/0.31  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.31  
% 0.10/0.31  % (25380)First to succeed.
% 0.10/0.31  % (25380)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25377"
% 0.10/0.31  % (25380)Refutation found. Thanks to Tanya!
% 0.10/0.31  % SZS status Theorem for theBenchmark
% 0.10/0.31  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.31  % (25380)------------------------------
% 0.14/0.31  % (25380)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.31  % (25380)Termination reason: Refutation
% 0.14/0.31  
% 0.14/0.31  % (25380)Memory used [KB]: 864
% 0.14/0.31  % (25380)Time elapsed: 0.007 s
% 0.14/0.31  % (25380)Instructions burned: 13 (million)
% 0.14/0.31  % (25377)Success in time 0.003 s
%------------------------------------------------------------------------------