TSTP Solution File: SEV214^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV214^5 : 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 : n026.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 04:12:25 EDT 2024

% Result   : Theorem 0.14s 0.42s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   76 (   4 unt;  14 typ;   0 def)
%            Number of atoms       :  421 ( 270 equ;   6 cnn)
%            Maximal formula atoms :   11 (   6 avg)
%            Number of connectives :  605 (  60   ~; 122   |;  52   &; 316   @)
%                                         (   6 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  18 usr;  17 con; 0-2 aty)
%                                         (   0  !!;  32  ??;   0 @@+;   0 @@-)
%            Number of variables   :  187 (  96   ^  75   !;  14   ?; 187   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    c0: iS ).

thf(func_def_2,type,
    cP: iS > iS > iS ).

thf(func_def_4,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_13,type,
    sK0: ( iS > $o ) > iS ).

thf(func_def_14,type,
    sK1: ( iS > $o ) > iS ).

thf(func_def_16,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_17,type,
    sK4: iS ).

thf(func_def_18,type,
    sK5: iS ).

thf(func_def_19,type,
    sK6: iS ).

thf(func_def_20,type,
    sK7: iS ).

thf(func_def_21,type,
    sK8: iS ).

thf(func_def_22,type,
    sK9: iS ).

thf(f160,plain,
    $false,
    inference(avatar_sat_refutation,[],[f27,f57,f58,f101,f102,f109,f159]) ).

thf(f159,plain,
    ~ spl2_4,
    inference(avatar_contradiction_clause,[],[f158]) ).

thf(f158,plain,
    ( $false
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f157]) ).

thf(f157,plain,
    ( ( c0 != c0 )
    | ~ spl2_4 ),
    inference(superposition,[],[f17,f56]) ).

thf(f56,plain,
    ( ( c0
      = ( cP @ sK5 @ sK4 ) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f54]) ).

thf(f54,plain,
    ( spl2_4
  <=> ( c0
      = ( cP @ sK5 @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f17,plain,
    ! [X0: iS,X1: iS] :
      ( ( cP @ X0 @ X1 )
     != c0 ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ! [X0: iS,X1: iS] :
        ( ( cP @ X0 @ X1 )
       != c0 )
    & ! [X2: iS > $o] :
        ( ( ( $true
            = ( X2 @ ( sK1 @ X2 ) ) )
          & ( ( X2 @ ( cP @ ( sK0 @ X2 ) @ ( sK1 @ X2 ) ) )
           != $true )
          & ( $true
            = ( X2 @ ( sK0 @ X2 ) ) ) )
        | ! [X5: iS] :
            ( $true
            = ( X2 @ X5 ) )
        | ( $true
         != ( X2 @ c0 ) ) )
    & ! [X6: iS,X7: iS,X8: iS,X9: iS] :
        ( ( ( cP @ X7 @ X6 )
         != ( cP @ X8 @ X9 ) )
        | ( ( X7 = X8 )
          & ( X6 = X9 ) ) )
    & ( ( ( ^ [Y0: iS] :
              ( ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y1 @ Y0 ) ) )
              | ( c0 = Y0 ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) )
      | ( ( ^ [Y0: iS] :
              ( ( c0 = Y0 )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y0 @ Y1 ) ) ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).

thf(f9,plain,
    ! [X2: iS > $o] :
      ( ? [X3: iS,X4: iS] :
          ( ( $true
            = ( X2 @ X4 ) )
          & ( ( X2 @ ( cP @ X3 @ X4 ) )
           != $true )
          & ( $true
            = ( X2 @ X3 ) ) )
     => ( ( $true
          = ( X2 @ ( sK1 @ X2 ) ) )
        & ( ( X2 @ ( cP @ ( sK0 @ X2 ) @ ( sK1 @ X2 ) ) )
         != $true )
        & ( $true
          = ( X2 @ ( sK0 @ X2 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ! [X0: iS,X1: iS] :
        ( ( cP @ X0 @ X1 )
       != c0 )
    & ! [X2: iS > $o] :
        ( ? [X3: iS,X4: iS] :
            ( ( $true
              = ( X2 @ X4 ) )
            & ( ( X2 @ ( cP @ X3 @ X4 ) )
             != $true )
            & ( $true
              = ( X2 @ X3 ) ) )
        | ! [X5: iS] :
            ( $true
            = ( X2 @ X5 ) )
        | ( $true
         != ( X2 @ c0 ) ) )
    & ! [X6: iS,X7: iS,X8: iS,X9: iS] :
        ( ( ( cP @ X7 @ X6 )
         != ( cP @ X8 @ X9 ) )
        | ( ( X7 = X8 )
          & ( X6 = X9 ) ) )
    & ( ( ( ^ [Y0: iS] :
              ( ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y1 @ Y0 ) ) )
              | ( c0 = Y0 ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) )
      | ( ( ^ [Y0: iS] :
              ( ( c0 = Y0 )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y0 @ Y1 ) ) ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ! [X8: iS,X9: iS] :
        ( c0
       != ( cP @ X8 @ X9 ) )
    & ! [X4: iS > $o] :
        ( ? [X5: iS,X6: iS] :
            ( ( $true
              = ( X4 @ X6 ) )
            & ( $true
             != ( X4 @ ( cP @ X5 @ X6 ) ) )
            & ( $true
              = ( X4 @ X5 ) ) )
        | ! [X7: iS] :
            ( $true
            = ( X4 @ X7 ) )
        | ( ( X4 @ c0 )
         != $true ) )
    & ! [X0: iS,X1: iS,X2: iS,X3: iS] :
        ( ( ( cP @ X2 @ X3 )
         != ( cP @ X1 @ X0 ) )
        | ( ( X1 = X2 )
          & ( X0 = X3 ) ) )
    & ( ( ( ^ [Y0: iS] :
              ( ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y1 @ Y0 ) ) )
              | ( c0 = Y0 ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) )
      | ( ( ^ [Y0: iS] :
              ( ( c0 = Y0 )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y0 @ Y1 ) ) ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( ( ( ( ^ [Y0: iS] :
              ( ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y1 @ Y0 ) ) )
              | ( c0 = Y0 ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) )
      | ( ( ^ [Y0: iS] :
              ( ( c0 = Y0 )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y0 @ Y1 ) ) ) ) )
       != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
          @ c0 ) ) )
    & ! [X0: iS,X1: iS,X2: iS,X3: iS] :
        ( ( ( cP @ X2 @ X3 )
         != ( cP @ X1 @ X0 ) )
        | ( ( X1 = X2 )
          & ( X0 = X3 ) ) )
    & ! [X4: iS > $o] :
        ( ! [X7: iS] :
            ( $true
            = ( X4 @ X7 ) )
        | ( ( X4 @ c0 )
         != $true )
        | ? [X5: iS,X6: iS] :
            ( ( $true
             != ( X4 @ ( cP @ X5 @ X6 ) ) )
            & ( $true
              = ( X4 @ X5 ) )
            & ( $true
              = ( X4 @ X6 ) ) ) )
    & ! [X8: iS,X9: iS] :
        ( c0
       != ( cP @ X8 @ X9 ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
            ( ( ( cP @ X2 @ X3 )
              = ( cP @ X1 @ X0 ) )
           => ( ( X1 = X2 )
              & ( X0 = X3 ) ) )
        & ! [X4: iS > $o] :
            ( ( ( ( X4 @ c0 )
                = $true )
              & ! [X5: iS,X6: iS] :
                  ( ( ( $true
                      = ( X4 @ X5 ) )
                    & ( $true
                      = ( X4 @ X6 ) ) )
                 => ( $true
                    = ( X4 @ ( cP @ X5 @ X6 ) ) ) ) )
           => ! [X7: iS] :
                ( $true
                = ( X4 @ X7 ) ) )
        & ! [X8: iS,X9: iS] :
            ( c0
           != ( cP @ X8 @ X9 ) ) )
     => ( ( ( ^ [Y0: iS] :
                ( ( c0 = Y0 )
                | ( ?? @ iS
                  @ ^ [Y1: iS] :
                      ( c0
                      = ( cP @ Y0 @ Y1 ) ) ) ) )
          = ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
            @ c0 ) )
        & ( ( ^ [Y0: iS] :
                ( ( ?? @ iS
                  @ ^ [Y1: iS] :
                      ( c0
                      = ( cP @ Y1 @ Y0 ) ) )
                | ( c0 = Y0 ) ) )
          = ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
            @ c0 ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
            ( ( ( cP @ X2 @ X3 )
              = ( cP @ X1 @ X0 ) )
           => ( ( X0 = X3 )
              & ( X1 = X2 ) ) )
        & ! [X4: iS > $o] :
            ( ( ! [X5: iS,X6: iS] :
                  ( ( ( X4 @ X6 )
                    & ( X4 @ X5 ) )
                 => ( X4 @ ( cP @ X5 @ X6 ) ) )
              & ( X4 @ c0 ) )
           => ! [X7: iS] : ( X4 @ X7 ) )
        & ! [X8: iS,X9: iS] :
            ( c0
           != ( cP @ X8 @ X9 ) ) )
     => ( ( ( ^ [X10: iS,X11: iS] : ( X10 = X11 )
            @ c0 )
          = ( ^ [X12: iS] :
                ( ? [X13: iS] :
                    ( c0
                    = ( cP @ X12 @ X13 ) )
                | ( c0 = X12 ) ) ) )
        & ( ( ^ [X14: iS,X15: iS] : ( X14 = X15 )
            @ c0 )
          = ( ^ [X16: iS] :
                ( ( c0 = X16 )
                | ? [X17: iS] :
                    ( c0
                    = ( cP @ X17 @ X16 ) ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ! [X2: iS,X0: iS,X1: iS,X3: iS] :
            ( ( ( cP @ X0 @ X2 )
              = ( cP @ X1 @ X3 ) )
           => ( ( X2 = X3 )
              & ( X0 = X1 ) ) )
        & ! [X4: iS > $o] :
            ( ( ! [X0: iS,X1: iS] :
                  ( ( ( X4 @ X1 )
                    & ( X4 @ X0 ) )
                 => ( X4 @ ( cP @ X0 @ X1 ) ) )
              & ( X4 @ c0 ) )
           => ! [X0: iS] : ( X4 @ X0 ) )
        & ! [X0: iS,X1: iS] :
            ( ( cP @ X0 @ X1 )
           != c0 ) )
     => ( ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
            @ c0 )
          = ( ^ [X0: iS] :
                ( ? [X1: iS] :
                    ( ( cP @ X0 @ X1 )
                    = c0 )
                | ( c0 = X0 ) ) ) )
        & ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
            @ c0 )
          = ( ^ [X1: iS] :
                ( ( c0 = X1 )
                | ? [X0: iS] :
                    ( ( cP @ X0 @ X1 )
                    = c0 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ! [X2: iS,X0: iS,X1: iS,X3: iS] :
          ( ( ( cP @ X0 @ X2 )
            = ( cP @ X1 @ X3 ) )
         => ( ( X2 = X3 )
            & ( X0 = X1 ) ) )
      & ! [X4: iS > $o] :
          ( ( ! [X0: iS,X1: iS] :
                ( ( ( X4 @ X1 )
                  & ( X4 @ X0 ) )
               => ( X4 @ ( cP @ X0 @ X1 ) ) )
            & ( X4 @ c0 ) )
         => ! [X0: iS] : ( X4 @ X0 ) )
      & ! [X0: iS,X1: iS] :
          ( ( cP @ X0 @ X1 )
         != c0 ) )
   => ( ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
          @ c0 )
        = ( ^ [X0: iS] :
              ( ? [X1: iS] :
                  ( ( cP @ X0 @ X1 )
                  = c0 )
              | ( c0 = X0 ) ) ) )
      & ( ( ^ [X0: iS,X1: iS] : ( X0 = X1 )
          @ c0 )
        = ( ^ [X1: iS] :
              ( ( c0 = X1 )
              | ? [X0: iS] :
                  ( ( cP @ X0 @ X1 )
                  = c0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_T_LR_LEM2_pme) ).

thf(f109,plain,
    ~ spl2_6,
    inference(avatar_contradiction_clause,[],[f108]) ).

thf(f108,plain,
    ( $false
    | ~ spl2_6 ),
    inference(trivial_inequality_removal,[],[f107]) ).

thf(f107,plain,
    ( ( c0 != c0 )
    | ~ spl2_6 ),
    inference(superposition,[],[f17,f100]) ).

thf(f100,plain,
    ( ( c0
      = ( cP @ sK6 @ sK7 ) )
    | ~ spl2_6 ),
    inference(avatar_component_clause,[],[f98]) ).

thf(f98,plain,
    ( spl2_6
  <=> ( c0
      = ( cP @ sK6 @ sK7 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

thf(f102,plain,
    ( ~ spl2_5
    | spl2_2 ),
    inference(avatar_split_clause,[],[f81,f24,f94]) ).

thf(f94,plain,
    ( spl2_5
  <=> ( c0 = sK6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

thf(f24,plain,
    ( spl2_2
  <=> ( ( (=) @ c0 )
      = ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f81,plain,
    ( ( c0 != sK6 )
    | spl2_2 ),
    inference(equality_proxy_clausification,[],[f80]) ).

thf(f80,plain,
    ( ( ( c0 = sK6 )
      = $false )
    | spl2_2 ),
    inference(duplicate_literal_removal,[],[f79]) ).

thf(f79,plain,
    ( ( ( c0 = sK6 )
      = $false )
    | ( ( c0 = sK6 )
      = $false )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f77]) ).

thf(f77,plain,
    ( ( ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) )
      = $false )
    | ( ( c0 = sK6 )
      = $false )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f75]) ).

thf(f75,plain,
    ( ( ( c0 = sK6 )
     != ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) ) )
    | spl2_2 ),
    inference(beta_eta_normalization,[],[f74]) ).

thf(f74,plain,
    ( ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) )
        @ sK6 )
     != ( c0 = sK6 ) )
    | spl2_2 ),
    inference(negative_extensionality,[],[f26]) ).

thf(f26,plain,
    ( ( ( (=) @ c0 )
     != ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) ) ) )
    | spl2_2 ),
    inference(avatar_component_clause,[],[f24]) ).

thf(f101,plain,
    ( spl2_5
    | spl2_6
    | spl2_2 ),
    inference(avatar_split_clause,[],[f92,f24,f98,f94]) ).

thf(f92,plain,
    ( ( c0 = sK6 )
    | ( c0
      = ( cP @ sK6 @ sK7 ) )
    | spl2_2 ),
    inference(duplicate_literal_removal,[],[f91]) ).

thf(f91,plain,
    ( ( c0 = sK6 )
    | ( c0 = sK6 )
    | ( c0
      = ( cP @ sK6 @ sK7 ) )
    | spl2_2 ),
    inference(equality_proxy_clausification,[],[f90]) ).

thf(f90,plain,
    ( ( c0 = sK6 )
    | ( c0
      = ( cP @ sK6 @ sK7 ) )
    | ( $true
      = ( c0 = sK6 ) )
    | spl2_2 ),
    inference(equality_proxy_clausification,[],[f89]) ).

thf(f89,plain,
    ( ( c0 = sK6 )
    | ( ( c0
        = ( cP @ sK6 @ sK7 ) )
      = $true )
    | ( $true
      = ( c0 = sK6 ) )
    | spl2_2 ),
    inference(beta_eta_normalization,[],[f88]) ).

thf(f88,plain,
    ( ( c0 = sK6 )
    | ( $true
      = ( ^ [Y0: iS] :
            ( c0
            = ( cP @ sK6 @ Y0 ) )
        @ sK7 ) )
    | ( $true
      = ( c0 = sK6 ) )
    | spl2_2 ),
    inference(sigma_clausification,[],[f87]) ).

thf(f87,plain,
    ( ( $true
      = ( ?? @ iS
        @ ^ [Y0: iS] :
            ( c0
            = ( cP @ sK6 @ Y0 ) ) ) )
    | ( $true
      = ( c0 = sK6 ) )
    | ( c0 = sK6 )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f86]) ).

thf(f86,plain,
    ( ( $true
      = ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) ) )
    | ( c0 = sK6 )
    | spl2_2 ),
    inference(equality_proxy_clausification,[],[f76]) ).

thf(f76,plain,
    ( ( $true
      = ( c0 = sK6 ) )
    | ( $true
      = ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) ) )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f75]) ).

thf(f58,plain,
    ( ~ spl2_3
    | spl2_1 ),
    inference(avatar_split_clause,[],[f41,f20,f50]) ).

thf(f50,plain,
    ( spl2_3
  <=> ( c0 = sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f20,plain,
    ( spl2_1
  <=> ( ( (=) @ c0 )
      = ( ^ [Y0: iS] :
            ( ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) )
            | ( c0 = Y0 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f41,plain,
    ( ( c0 != sK4 )
    | spl2_1 ),
    inference(equality_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ( ( ( c0 = sK4 )
      = $false )
    | spl2_1 ),
    inference(duplicate_literal_removal,[],[f34]) ).

thf(f34,plain,
    ( ( ( c0 = sK4 )
      = $false )
    | ( ( c0 = sK4 )
      = $false )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ( ( ( ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ Y0 @ sK4 ) ) )
        | ( c0 = sK4 ) )
      = $false )
    | ( ( c0 = sK4 )
      = $false )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f31]) ).

thf(f31,plain,
    ( ( ( c0 = sK4 )
     != ( ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ Y0 @ sK4 ) ) )
        | ( c0 = sK4 ) ) )
    | spl2_1 ),
    inference(beta_eta_normalization,[],[f30]) ).

thf(f30,plain,
    ( ( ( c0 = sK4 )
     != ( ^ [Y0: iS] :
            ( ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) )
            | ( c0 = Y0 ) )
        @ sK4 ) )
    | spl2_1 ),
    inference(negative_extensionality,[],[f22]) ).

thf(f22,plain,
    ( ( ( (=) @ c0 )
     != ( ^ [Y0: iS] :
            ( ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) )
            | ( c0 = Y0 ) ) ) )
    | spl2_1 ),
    inference(avatar_component_clause,[],[f20]) ).

thf(f57,plain,
    ( spl2_3
    | spl2_4
    | spl2_1 ),
    inference(avatar_split_clause,[],[f48,f20,f54,f50]) ).

thf(f48,plain,
    ( ( c0
      = ( cP @ sK5 @ sK4 ) )
    | ( c0 = sK4 )
    | spl2_1 ),
    inference(equality_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ( ( c0 = sK4 )
    | ( $true
      = ( c0
        = ( cP @ sK5 @ sK4 ) ) )
    | spl2_1 ),
    inference(beta_eta_normalization,[],[f46]) ).

thf(f46,plain,
    ( ( $true
      = ( ^ [Y0: iS] :
            ( c0
            = ( cP @ Y0 @ sK4 ) )
        @ sK5 ) )
    | ( c0 = sK4 )
    | spl2_1 ),
    inference(sigma_clausification,[],[f45]) ).

thf(f45,plain,
    ( ( $true
      = ( ?? @ iS
        @ ^ [Y0: iS] :
            ( c0
            = ( cP @ Y0 @ sK4 ) ) ) )
    | ( c0 = sK4 )
    | spl2_1 ),
    inference(duplicate_literal_removal,[],[f44]) ).

thf(f44,plain,
    ( ( $true
      = ( ?? @ iS
        @ ^ [Y0: iS] :
            ( c0
            = ( cP @ Y0 @ sK4 ) ) ) )
    | ( c0 = sK4 )
    | ( c0 = sK4 )
    | spl2_1 ),
    inference(equality_proxy_clausification,[],[f43]) ).

thf(f43,plain,
    ( ( c0 = sK4 )
    | ( $true
      = ( c0 = sK4 ) )
    | ( $true
      = ( ?? @ iS
        @ ^ [Y0: iS] :
            ( c0
            = ( cP @ Y0 @ sK4 ) ) ) )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f42]) ).

thf(f42,plain,
    ( ( c0 = sK4 )
    | ( $true
      = ( ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ Y0 @ sK4 ) ) )
        | ( c0 = sK4 ) ) )
    | spl2_1 ),
    inference(equality_proxy_clausification,[],[f32]) ).

thf(f32,plain,
    ( ( $true
      = ( c0 = sK4 ) )
    | ( $true
      = ( ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ Y0 @ sK4 ) ) )
        | ( c0 = sK4 ) ) )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f31]) ).

thf(f27,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f18,f24,f20]) ).

thf(f18,plain,
    ( ( ( (=) @ c0 )
     != ( ^ [Y0: iS] :
            ( ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) )
            | ( c0 = Y0 ) ) ) )
    | ( ( (=) @ c0 )
     != ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f11]) ).

thf(f11,plain,
    ( ( ( ^ [Y0: iS] :
            ( ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) )
            | ( c0 = Y0 ) ) )
     != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
        @ c0 ) )
    | ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) ) )
     != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
        @ c0 ) ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEV214^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % 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
% 0.14/0.39  % Computer : n026.cluster.edu
% 0.14/0.39  % Model    : x86_64 x86_64
% 0.14/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39  % Memory   : 8042.1875MB
% 0.14/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.39  % CPULimit   : 300
% 0.14/0.39  % WCLimit    : 300
% 0.14/0.39  % DateTime   : Sun May 19 19:17:53 EDT 2024
% 0.14/0.39  % CPUTime    : 
% 0.14/0.39  This is a TH0_THM_EQU_NAR problem
% 0.14/0.40  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
% 0.14/0.41  % (20184)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.41  % (20187)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)
% 0.14/0.41  % (20186)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.41  % (20189)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.41  % (20185)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.41  % (20182)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.41  % (20183)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 (2999ds/4Mi)
% 0.14/0.42  % (20188)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.42  % (20185)Instruction limit reached!
% 0.14/0.42  % (20185)------------------------------
% 0.14/0.42  % (20185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42  % (20185)Termination reason: Unknown
% 0.14/0.42  % (20185)Termination phase: Saturation
% 0.14/0.42  
% 0.14/0.42  % (20185)Memory used [KB]: 5500
% 0.14/0.42  % (20186)Instruction limit reached!
% 0.14/0.42  % (20186)------------------------------
% 0.14/0.42  % (20186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42  % (20186)Termination reason: Unknown
% 0.14/0.42  % (20186)Termination phase: Saturation
% 0.14/0.42  
% 0.14/0.42  % (20186)Memory used [KB]: 1023
% 0.14/0.42  % (20186)Time elapsed: 0.004 s
% 0.14/0.42  % (20186)Instructions burned: 3 (million)
% 0.14/0.42  % (20186)------------------------------
% 0.14/0.42  % (20186)------------------------------
% 0.14/0.42  % (20185)Time elapsed: 0.004 s
% 0.14/0.42  % (20185)Instructions burned: 2 (million)
% 0.14/0.42  % (20185)------------------------------
% 0.14/0.42  % (20185)------------------------------
% 0.14/0.42  % (20189)Instruction limit reached!
% 0.14/0.42  % (20189)------------------------------
% 0.14/0.42  % (20189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42  % (20189)Termination reason: Unknown
% 0.14/0.42  % (20189)Termination phase: Saturation
% 0.14/0.42  
% 0.14/0.42  % (20189)Memory used [KB]: 5500
% 0.14/0.42  % (20189)Time elapsed: 0.004 s
% 0.14/0.42  % (20189)Instructions burned: 3 (million)
% 0.14/0.42  % (20189)------------------------------
% 0.14/0.42  % (20189)------------------------------
% 0.14/0.42  % (20183)Instruction limit reached!
% 0.14/0.42  % (20183)------------------------------
% 0.14/0.42  % (20183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42  % (20183)Termination reason: Unknown
% 0.14/0.42  % (20183)Termination phase: Saturation
% 0.14/0.42  
% 0.14/0.42  % (20183)Memory used [KB]: 5500
% 0.14/0.42  % (20183)Time elapsed: 0.005 s
% 0.14/0.42  % (20183)Instructions burned: 5 (million)
% 0.14/0.42  % (20183)------------------------------
% 0.14/0.42  % (20183)------------------------------
% 0.14/0.42  % (20184)First to succeed.
% 0.14/0.42  % (20187)Also succeeded, but the first one will report.
% 0.14/0.42  % (20184)Refutation found. Thanks to Tanya!
% 0.14/0.42  % SZS status Theorem for theBenchmark
% 0.14/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.42  % (20184)------------------------------
% 0.14/0.42  % (20184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42  % (20184)Termination reason: Refutation
% 0.14/0.42  
% 0.14/0.42  % (20184)Memory used [KB]: 5628
% 0.14/0.42  % (20184)Time elapsed: 0.011 s
% 0.14/0.42  % (20184)Instructions burned: 8 (million)
% 0.14/0.42  % (20184)------------------------------
% 0.14/0.42  % (20184)------------------------------
% 0.14/0.42  % (20181)Success in time 0.02 s
% 0.14/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------