TSTP Solution File: SEV214^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV214^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n001.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 16:02:18 EDT 2024

% Result   : Theorem 0.22s 0.40s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   61 (   4 unt;   0 typ;   0 def)
%            Number of atoms       :  418 ( 267 equ;   6 cnn)
%            Maximal formula atoms :   11 (   6 avg)
%            Number of connectives :  595 (  60   ~; 117   |;  52   &; 312   @)
%                                         (   6 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  19 usr;  17 con; 0-2 aty)
%                                         (   0  !!;  31  ??;   0 @@+;   0 @@-)
%            Number of variables   :  184 (  95   ^  75   !;  14   ?; 184   :)

% 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(func_def_23,type,
    sK10: iS > iS ).

thf(f163,plain,
    $false,
    inference(avatar_sat_refutation,[],[f27,f56,f57,f100,f101,f108,f162]) ).

thf(f162,plain,
    ~ spl2_4,
    inference(avatar_contradiction_clause,[],[f161]) ).

thf(f161,plain,
    ( $false
    | ~ spl2_4 ),
    inference(trivial_inequality_removal,[],[f160]) ).

thf(f160,plain,
    ( ( c0 != c0 )
    | ~ spl2_4 ),
    inference(superposition,[],[f11,f55]) ).

thf(f55,plain,
    ( ( c0
      = ( cP @ sK5 @ sK4 ) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f53]) ).

thf(f53,plain,
    ( spl2_4
  <=> ( c0
      = ( cP @ sK5 @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f11,plain,
    ! [X8: iS,X9: iS] :
      ( c0
     != ( cP @ X8 @ X9 ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ! [X0: iS,X1: iS,X2: iS,X3: iS] :
        ( ( ( cP @ X3 @ X2 )
         != ( cP @ X1 @ X0 ) )
        | ( ( X1 = X3 )
          & ( X0 = X2 ) ) )
    & ( ( ( ^ [Y0: iS] :
              ( ( c0 = Y0 )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( c0
                    = ( cP @ Y1 @ 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 ) ) )
    & ! [X4: iS > $o] :
        ( ( ( X4 @ c0 )
         != $true )
        | ! [X5: iS] :
            ( ( X4 @ X5 )
            = $true )
        | ( ( $true
            = ( X4 @ ( sK0 @ X4 ) ) )
          & ( ( X4 @ ( cP @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) ) )
           != $true )
          & ( ( X4 @ ( sK1 @ X4 ) )
            = $true ) ) )
    & ! [X8: iS,X9: iS] :
        ( c0
       != ( cP @ X8 @ X9 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).

thf(f9,plain,
    ! [X4: iS > $o] :
      ( ? [X6: iS,X7: iS] :
          ( ( ( X4 @ X6 )
            = $true )
          & ( ( X4 @ ( cP @ X7 @ X6 ) )
           != $true )
          & ( $true
            = ( X4 @ X7 ) ) )
     => ( ( $true
          = ( X4 @ ( sK0 @ X4 ) ) )
        & ( ( X4 @ ( cP @ ( sK1 @ X4 ) @ ( sK0 @ X4 ) ) )
         != $true )
        & ( ( X4 @ ( sK1 @ X4 ) )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

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

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

thf(f108,plain,
    ~ spl2_5,
    inference(avatar_contradiction_clause,[],[f107]) ).

thf(f107,plain,
    ( $false
    | ~ spl2_5 ),
    inference(trivial_inequality_removal,[],[f106]) ).

thf(f106,plain,
    ( ( c0 != c0 )
    | ~ spl2_5 ),
    inference(superposition,[],[f11,f95]) ).

thf(f95,plain,
    ( ( c0
      = ( cP @ sK6 @ sK7 ) )
    | ~ spl2_5 ),
    inference(avatar_component_clause,[],[f93]) ).

thf(f93,plain,
    ( spl2_5
  <=> ( c0
      = ( cP @ sK6 @ sK7 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

thf(f101,plain,
    ( ~ spl2_6
    | spl2_2 ),
    inference(avatar_split_clause,[],[f80,f24,f97]) ).

thf(f97,plain,
    ( spl2_6
  <=> ( c0 = sK6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

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

thf(f80,plain,
    ( ( c0 != sK6 )
    | spl2_2 ),
    inference(equality_proxy_clausification,[],[f79]) ).

thf(f79,plain,
    ( ( ( c0 = sK6 )
      = $false )
    | spl2_2 ),
    inference(duplicate_literal_removal,[],[f78]) ).

thf(f78,plain,
    ( ( ( c0 = sK6 )
      = $false )
    | ( ( c0 = sK6 )
      = $false )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f76]) ).

thf(f76,plain,
    ( ( ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) )
      = $false )
    | ( ( c0 = sK6 )
      = $false )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f74]) ).

thf(f74,plain,
    ( ( ( c0 = sK6 )
     != ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) ) )
    | spl2_2 ),
    inference(beta_eta_normalization,[],[f73]) ).

thf(f73,plain,
    ( ( ( c0 = sK6 )
     != ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) )
        @ sK6 ) )
    | spl2_2 ),
    inference(negative_extensionality,[],[f26]) ).

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

thf(f100,plain,
    ( spl2_5
    | spl2_6
    | spl2_2 ),
    inference(avatar_split_clause,[],[f91,f24,f97,f93]) ).

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

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

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

thf(f88,plain,
    ( ( c0 = sK6 )
    | ( ( c0 = sK6 )
      = $true )
    | ( $true
      = ( c0
        = ( cP @ sK6 @ sK7 ) ) )
    | spl2_2 ),
    inference(beta_eta_normalization,[],[f87]) ).

thf(f87,plain,
    ( ( ( c0 = sK6 )
      = $true )
    | ( c0 = sK6 )
    | ( ( ^ [Y0: iS] :
            ( c0
            = ( cP @ sK6 @ Y0 ) )
        @ sK7 )
      = $true )
    | spl2_2 ),
    inference(sigma_clausification,[],[f86]) ).

thf(f86,plain,
    ( ( ( ?? @ iS
        @ ^ [Y0: iS] :
            ( c0
            = ( cP @ sK6 @ Y0 ) ) )
      = $true )
    | ( ( c0 = sK6 )
      = $true )
    | ( c0 = sK6 )
    | spl2_2 ),
    inference(binary_proxy_clausification,[],[f85]) ).

thf(f85,plain,
    ( ( ( ( c0 = sK6 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ sK6 @ Y0 ) ) ) )
      = $true )
    | ( c0 = sK6 )
    | spl2_2 ),
    inference(equality_proxy_clausification,[],[f75]) ).

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

thf(f57,plain,
    ( ~ spl2_3
    | spl2_1 ),
    inference(avatar_split_clause,[],[f37,f20,f49]) ).

thf(f49,plain,
    ( spl2_3
  <=> ( c0 = sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

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

thf(f37,plain,
    ( ( c0 != sK4 )
    | spl2_1 ),
    inference(equality_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ( ( ( c0 = sK4 )
      = $false )
    | spl2_1 ),
    inference(duplicate_literal_removal,[],[f35]) ).

thf(f35,plain,
    ( ( ( c0 = sK4 )
      = $false )
    | ( ( c0 = sK4 )
      = $false )
    | spl2_1 ),
    inference(binary_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ( ( ( ( c0 = sK4 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ Y0 @ 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,
    ( ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) ) )
        @ sK4 )
     != ( c0 = sK4 ) )
    | spl2_1 ),
    inference(negative_extensionality,[],[f22]) ).

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

thf(f56,plain,
    ( spl2_3
    | spl2_4
    | spl2_1 ),
    inference(avatar_split_clause,[],[f47,f20,f53,f49]) ).

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

thf(f46,plain,
    ( ( c0 = sK4 )
    | ( ( c0
        = ( cP @ sK5 @ sK4 ) )
      = $true )
    | spl2_1 ),
    inference(beta_eta_normalization,[],[f45]) ).

thf(f45,plain,
    ( ( $true
      = ( ^ [Y0: iS] :
            ( c0
            = ( cP @ Y0 @ sK4 ) )
        @ sK5 ) )
    | ( c0 = sK4 )
    | spl2_1 ),
    inference(sigma_clausification,[],[f44]) ).

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

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

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

thf(f32,plain,
    ( ( $true
      = ( ( c0 = sK4 )
        | ( ?? @ iS
          @ ^ [Y0: iS] :
              ( c0
              = ( cP @ Y0 @ sK4 ) ) ) ) )
    | ( $true
      = ( 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,
    ( ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) ) )
     != ( (=) @ c0 ) )
    | ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) ) ) )
     != ( (=) @ c0 ) ) ),
    inference(beta_eta_normalization,[],[f15]) ).

thf(f15,plain,
    ( ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y0 @ Y1 ) ) ) ) )
     != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
        @ c0 ) )
    | ( ( ^ [Y0: iS] :
            ( ( c0 = Y0 )
            | ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( c0
                  = ( cP @ Y1 @ Y0 ) ) ) ) )
     != ( ^ [Y0: iS,Y1: iS] : ( Y0 = Y1 )
        @ c0 ) ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEV214^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % Command    : run_vampire %s %d THM
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Jun 21 19:39:09 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  This is a TH0_THM_EQU_NAR problem
% 0.13/0.37  Running higher-order theorem proving
% 0.13/0.37  Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.22/0.39  % (21413)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39  % (21416)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39  % (21414)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)
% 0.22/0.39  % (21415)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)
% 0.22/0.39  % (21418)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)
% 0.22/0.39  % (21419)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39  % (21417)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)
% 0.22/0.39  % (21416)Instruction limit reached!
% 0.22/0.39  % (21416)------------------------------
% 0.22/0.39  % (21416)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39  % (21416)Termination reason: Unknown
% 0.22/0.39  % (21416)Termination phase: Preprocessing 3
% 0.22/0.39  
% 0.22/0.39  % (21416)Memory used [KB]: 895
% 0.22/0.39  % (21416)Time elapsed: 0.003 s
% 0.22/0.39  % (21416)Instructions burned: 2 (million)
% 0.22/0.39  % (21416)------------------------------
% 0.22/0.39  % (21416)------------------------------
% 0.22/0.39  % (21417)Instruction limit reached!
% 0.22/0.39  % (21417)------------------------------
% 0.22/0.39  % (21417)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39  % (21417)Termination reason: Unknown
% 0.22/0.39  % (21417)Termination phase: Property scanning
% 0.22/0.39  
% 0.22/0.39  % (21417)Memory used [KB]: 1023
% 0.22/0.39  % (21417)Time elapsed: 0.004 s
% 0.22/0.39  % (21417)Instructions burned: 2 (million)
% 0.22/0.39  % (21417)------------------------------
% 0.22/0.39  % (21417)------------------------------
% 0.22/0.39  % (21414)Instruction limit reached!
% 0.22/0.39  % (21414)------------------------------
% 0.22/0.39  % (21414)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39  % (21414)Termination reason: Unknown
% 0.22/0.39  % (21414)Termination phase: Saturation
% 0.22/0.39  
% 0.22/0.39  % (21414)Memory used [KB]: 5500
% 0.22/0.39  % (21414)Time elapsed: 0.006 s
% 0.22/0.39  % (21414)Instructions burned: 5 (million)
% 0.22/0.39  % (21414)------------------------------
% 0.22/0.39  % (21414)------------------------------
% 0.22/0.39  % (21415)First to succeed.
% 0.22/0.40  % (21418)Also succeeded, but the first one will report.
% 0.22/0.40  % (21415)Refutation found. Thanks to Tanya!
% 0.22/0.40  % SZS status Theorem for theBenchmark
% 0.22/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40  % (21415)------------------------------
% 0.22/0.40  % (21415)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40  % (21415)Termination reason: Refutation
% 0.22/0.40  
% 0.22/0.40  % (21415)Memory used [KB]: 5628
% 0.22/0.40  % (21415)Time elapsed: 0.011 s
% 0.22/0.40  % (21415)Instructions burned: 7 (million)
% 0.22/0.40  % (21415)------------------------------
% 0.22/0.40  % (21415)------------------------------
% 0.22/0.40  % (21412)Success in time 0.025 s
%------------------------------------------------------------------------------