TSTP Solution File: SEV259^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV259^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n021.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 16:02:30 EDT 2024

% Result   : Theorem 0.12s 0.38s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   19 (   4 unt;   0 typ;   0 def)
%            Number of atoms       :  401 ( 192 equ;   0 cnn)
%            Maximal formula atoms :   36 (  21 avg)
%            Number of connectives :  602 ( 109   ~;  64   |; 117   &; 250   @)
%                                         (   0 <=>;  54  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   9 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  177 ( 177   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   6 usr;   4 con; 0-2 aty)
%                                         (   0  !!;   8  ??;   0 @@+;   0 @@-)
%            Number of variables   :  234 (  67   ^ 134   !;  33   ?; 234   :)

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

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

thf(func_def_10,type,
    sK0: ( b > $o ) > $o ).

thf(func_def_11,type,
    sK1: b > $o ).

thf(func_def_12,type,
    sK2: b ).

thf(func_def_13,type,
    sK3: b > $o ).

thf(func_def_14,type,
    sK4: ( ( b > $o ) > $o ) > b > $o ).

thf(func_def_16,type,
    ph6: 
      !>[X0: $tType] : X0 ).

thf(f33,plain,
    $false,
    inference(subsumption_resolution,[],[f32,f17]) ).

thf(f17,plain,
    ( ( sK1 @ sK2 )
    = $true ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ! [X1: b > $o] :
        ( ( ( ^ [Y0: b] : $false )
         != X1 )
        | ( ( sK0 @ X1 )
          = $true ) )
    & ! [X2: b > $o,X3: b > $o,X4: b > $o] :
        ( ( ( sK0 @ X3 )
         != $true )
        | ( ( sK0 @ X2 )
          = $true )
        | ( ( ^ [Y0: b] :
                ( ( X3 @ Y0 )
                & ( X4 @ Y0 ) ) )
         != X2 )
        | ( $true
         != ( sK0 @ X4 ) ) )
    & ! [X5: b > $o] :
        ( ( ( ^ [Y0: b] : ~ $false )
         != X5 )
        | ( $true
          = ( sK0 @ X5 ) ) )
    & ( ( sK3 @ sK2 )
     != $true )
    & ! [X9: b] :
        ( ( ( sK3 @ X9 )
          = $true )
        | ( ( sK1 @ X9 )
         != $true ) )
    & ! [X10: b > $o] :
        ( ( ( ^ [Y0: b] :
                ~ ( sK3 @ Y0 ) )
         != X10 )
        | ( ( sK0 @ X10 )
          = $true ) )
    & ( ( sK1 @ sK2 )
      = $true )
    & ! [X11: ( b > $o ) > $o,X12: b > $o] :
        ( ( ( ^ [Y0: b] :
                ( ?? @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( Y1 @ Y0 )
                    & ( X11 @ Y1 ) ) ) )
         != X12 )
        | ( ( $true
           != ( sK0 @ ( sK4 @ X11 ) ) )
          & ( ( X11 @ ( sK4 @ X11 ) )
            = $true ) )
        | ( ( sK0 @ X12 )
          = $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f13,f12,f11,f10]) ).

thf(f10,plain,
    ( ? [X0: ( b > $o ) > $o] :
        ( ! [X1: b > $o] :
            ( ( ( ^ [Y0: b] : $false )
             != X1 )
            | ( ( X0 @ X1 )
              = $true ) )
        & ! [X2: b > $o,X3: b > $o,X4: b > $o] :
            ( ( ( X0 @ X3 )
             != $true )
            | ( ( X0 @ X2 )
              = $true )
            | ( ( ^ [Y0: b] :
                    ( ( X3 @ Y0 )
                    & ( X4 @ Y0 ) ) )
             != X2 )
            | ( ( X0 @ X4 )
             != $true ) )
        & ! [X5: b > $o] :
            ( ( ( ^ [Y0: b] : ~ $false )
             != X5 )
            | ( ( X0 @ X5 )
              = $true ) )
        & ? [X6: b > $o,X7: b] :
            ( ? [X8: b > $o] :
                ( ( ( X8 @ X7 )
                 != $true )
                & ! [X9: b] :
                    ( ( ( X8 @ X9 )
                      = $true )
                    | ( $true
                     != ( X6 @ X9 ) ) )
                & ! [X10: b > $o] :
                    ( ( ( ^ [Y0: b] :
                            ~ ( X8 @ Y0 ) )
                     != X10 )
                    | ( ( X0 @ X10 )
                      = $true ) ) )
            & ( $true
              = ( X6 @ X7 ) ) )
        & ! [X11: ( b > $o ) > $o,X12: b > $o] :
            ( ( ( ^ [Y0: b] :
                    ( ?? @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( Y1 @ Y0 )
                        & ( X11 @ Y1 ) ) ) )
             != X12 )
            | ? [X13: b > $o] :
                ( ( ( X0 @ X13 )
                 != $true )
                & ( $true
                  = ( X11 @ X13 ) ) )
            | ( $true
              = ( X0 @ X12 ) ) ) )
   => ( ! [X1: b > $o] :
          ( ( ( ^ [Y0: b] : $false )
           != X1 )
          | ( ( sK0 @ X1 )
            = $true ) )
      & ! [X4: b > $o,X3: b > $o,X2: b > $o] :
          ( ( ( sK0 @ X3 )
           != $true )
          | ( ( sK0 @ X2 )
            = $true )
          | ( ( ^ [Y0: b] :
                  ( ( X3 @ Y0 )
                  & ( X4 @ Y0 ) ) )
           != X2 )
          | ( $true
           != ( sK0 @ X4 ) ) )
      & ! [X5: b > $o] :
          ( ( ( ^ [Y0: b] : ~ $false )
           != X5 )
          | ( $true
            = ( sK0 @ X5 ) ) )
      & ? [X7: b,X6: b > $o] :
          ( ? [X8: b > $o] :
              ( ( ( X8 @ X7 )
               != $true )
              & ! [X9: b] :
                  ( ( ( X8 @ X9 )
                    = $true )
                  | ( $true
                   != ( X6 @ X9 ) ) )
              & ! [X10: b > $o] :
                  ( ( ( ^ [Y0: b] :
                          ~ ( X8 @ Y0 ) )
                   != X10 )
                  | ( ( sK0 @ X10 )
                    = $true ) ) )
          & ( $true
            = ( X6 @ X7 ) ) )
      & ! [X12: b > $o,X11: ( b > $o ) > $o] :
          ( ( ( ^ [Y0: b] :
                  ( ?? @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( Y1 @ Y0 )
                      & ( X11 @ Y1 ) ) ) )
           != X12 )
          | ? [X13: b > $o] :
              ( ( ( sK0 @ X13 )
               != $true )
              & ( $true
                = ( X11 @ X13 ) ) )
          | ( ( sK0 @ X12 )
            = $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X7: b,X6: b > $o] :
        ( ? [X8: b > $o] :
            ( ( ( X8 @ X7 )
             != $true )
            & ! [X9: b] :
                ( ( ( X8 @ X9 )
                  = $true )
                | ( $true
                 != ( X6 @ X9 ) ) )
            & ! [X10: b > $o] :
                ( ( ( ^ [Y0: b] :
                        ~ ( X8 @ Y0 ) )
                 != X10 )
                | ( ( sK0 @ X10 )
                  = $true ) ) )
        & ( $true
          = ( X6 @ X7 ) ) )
   => ( ? [X8: b > $o] :
          ( ( ( X8 @ sK2 )
           != $true )
          & ! [X9: b] :
              ( ( ( X8 @ X9 )
                = $true )
              | ( ( sK1 @ X9 )
               != $true ) )
          & ! [X10: b > $o] :
              ( ( ( ^ [Y0: b] :
                      ~ ( X8 @ Y0 ) )
               != X10 )
              | ( ( sK0 @ X10 )
                = $true ) ) )
      & ( ( sK1 @ sK2 )
        = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X8: b > $o] :
        ( ( ( X8 @ sK2 )
         != $true )
        & ! [X9: b] :
            ( ( ( X8 @ X9 )
              = $true )
            | ( ( sK1 @ X9 )
             != $true ) )
        & ! [X10: b > $o] :
            ( ( ( ^ [Y0: b] :
                    ~ ( X8 @ Y0 ) )
             != X10 )
            | ( ( sK0 @ X10 )
              = $true ) ) )
   => ( ( ( sK3 @ sK2 )
       != $true )
      & ! [X9: b] :
          ( ( ( sK3 @ X9 )
            = $true )
          | ( ( sK1 @ X9 )
           != $true ) )
      & ! [X10: b > $o] :
          ( ( ( ^ [Y0: b] :
                  ~ ( sK3 @ Y0 ) )
           != X10 )
          | ( ( sK0 @ X10 )
            = $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ! [X11: ( b > $o ) > $o] :
      ( ? [X13: b > $o] :
          ( ( ( sK0 @ X13 )
           != $true )
          & ( $true
            = ( X11 @ X13 ) ) )
     => ( ( $true
         != ( sK0 @ ( sK4 @ X11 ) ) )
        & ( ( X11 @ ( sK4 @ X11 ) )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ? [X0: ( b > $o ) > $o] :
      ( ! [X1: b > $o] :
          ( ( ( ^ [Y0: b] : $false )
           != X1 )
          | ( ( X0 @ X1 )
            = $true ) )
      & ! [X2: b > $o,X3: b > $o,X4: b > $o] :
          ( ( ( X0 @ X3 )
           != $true )
          | ( ( X0 @ X2 )
            = $true )
          | ( ( ^ [Y0: b] :
                  ( ( X3 @ Y0 )
                  & ( X4 @ Y0 ) ) )
           != X2 )
          | ( ( X0 @ X4 )
           != $true ) )
      & ! [X5: b > $o] :
          ( ( ( ^ [Y0: b] : ~ $false )
           != X5 )
          | ( ( X0 @ X5 )
            = $true ) )
      & ? [X6: b > $o,X7: b] :
          ( ? [X8: b > $o] :
              ( ( ( X8 @ X7 )
               != $true )
              & ! [X9: b] :
                  ( ( ( X8 @ X9 )
                    = $true )
                  | ( $true
                   != ( X6 @ X9 ) ) )
              & ! [X10: b > $o] :
                  ( ( ( ^ [Y0: b] :
                          ~ ( X8 @ Y0 ) )
                   != X10 )
                  | ( ( X0 @ X10 )
                    = $true ) ) )
          & ( $true
            = ( X6 @ X7 ) ) )
      & ! [X11: ( b > $o ) > $o,X12: b > $o] :
          ( ( ( ^ [Y0: b] :
                  ( ?? @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( Y1 @ Y0 )
                      & ( X11 @ Y1 ) ) ) )
           != X12 )
          | ? [X13: b > $o] :
              ( ( ( X0 @ X13 )
               != $true )
              & ( $true
                = ( X11 @ X13 ) ) )
          | ( $true
            = ( X0 @ X12 ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ? [X0: ( b > $o ) > $o] :
      ( ! [X8: b > $o] :
          ( ( ( ^ [Y0: b] : $false )
           != X8 )
          | ( ( X0 @ X8 )
            = $true ) )
      & ! [X5: b > $o,X6: b > $o,X7: b > $o] :
          ( ( ( X0 @ X6 )
           != $true )
          | ( ( X0 @ X5 )
            = $true )
          | ( ( ^ [Y0: b] :
                  ( ( X6 @ Y0 )
                  & ( X7 @ Y0 ) ) )
           != X5 )
          | ( $true
           != ( X0 @ X7 ) ) )
      & ! [X1: b > $o] :
          ( ( ( ^ [Y0: b] : ~ $false )
           != X1 )
          | ( ( X0 @ X1 )
            = $true ) )
      & ? [X9: b > $o,X10: b] :
          ( ? [X11: b > $o] :
              ( ( $true
               != ( X11 @ X10 ) )
              & ! [X12: b] :
                  ( ( $true
                    = ( X11 @ X12 ) )
                  | ( $true
                   != ( X9 @ X12 ) ) )
              & ! [X13: b > $o] :
                  ( ( ( ^ [Y0: b] :
                          ~ ( X11 @ Y0 ) )
                   != X13 )
                  | ( ( X0 @ X13 )
                    = $true ) ) )
          & ( ( X9 @ X10 )
            = $true ) )
      & ! [X2: ( b > $o ) > $o,X3: b > $o] :
          ( ( ( ^ [Y0: b] :
                  ( ?? @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( Y1 @ Y0 )
                      & ( X2 @ Y1 ) ) ) )
           != X3 )
          | ? [X4: b > $o] :
              ( ( ( X0 @ X4 )
               != $true )
              & ( ( X2 @ X4 )
                = $true ) )
          | ( ( X0 @ X3 )
            = $true ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ? [X0: ( b > $o ) > $o] :
      ( ? [X9: b > $o,X10: b] :
          ( ? [X11: b > $o] :
              ( ( $true
               != ( X11 @ X10 ) )
              & ! [X13: b > $o] :
                  ( ( ( ^ [Y0: b] :
                          ~ ( X11 @ Y0 ) )
                   != X13 )
                  | ( ( X0 @ X13 )
                    = $true ) )
              & ! [X12: b] :
                  ( ( $true
                    = ( X11 @ X12 ) )
                  | ( $true
                   != ( X9 @ X12 ) ) ) )
          & ( ( X9 @ X10 )
            = $true ) )
      & ! [X5: b > $o,X6: b > $o,X7: b > $o] :
          ( ( ( X0 @ X5 )
            = $true )
          | ( ( ^ [Y0: b] :
                  ( ( X6 @ Y0 )
                  & ( X7 @ Y0 ) ) )
           != X5 )
          | ( $true
           != ( X0 @ X7 ) )
          | ( ( X0 @ X6 )
           != $true ) )
      & ! [X1: b > $o] :
          ( ( ( ^ [Y0: b] : ~ $false )
           != X1 )
          | ( ( X0 @ X1 )
            = $true ) )
      & ! [X2: ( b > $o ) > $o,X3: b > $o] :
          ( ( ( X0 @ X3 )
            = $true )
          | ( ( ^ [Y0: b] :
                  ( ?? @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( Y1 @ Y0 )
                      & ( X2 @ Y1 ) ) ) )
           != X3 )
          | ? [X4: b > $o] :
              ( ( ( X0 @ X4 )
               != $true )
              & ( ( X2 @ X4 )
                = $true ) ) )
      & ! [X8: b > $o] :
          ( ( ( ^ [Y0: b] : $false )
           != X8 )
          | ( ( X0 @ X8 )
            = $true ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: ( b > $o ) > $o] :
        ( ( ! [X5: b > $o,X6: b > $o,X7: b > $o] :
              ( ( ( ( ^ [Y0: b] :
                        ( ( X6 @ Y0 )
                        & ( X7 @ Y0 ) ) )
                  = X5 )
                & ( $true
                  = ( X0 @ X7 ) )
                & ( ( X0 @ X6 )
                  = $true ) )
             => ( ( X0 @ X5 )
                = $true ) )
          & ! [X1: b > $o] :
              ( ( ( ^ [Y0: b] : ~ $false )
                = X1 )
             => ( ( X0 @ X1 )
                = $true ) )
          & ! [X2: ( b > $o ) > $o,X3: b > $o] :
              ( ( ( ( ^ [Y0: b] :
                        ( ?? @ ( b > $o )
                        @ ^ [Y1: b > $o] :
                            ( ( Y1 @ Y0 )
                            & ( X2 @ Y1 ) ) ) )
                  = X3 )
                & ! [X4: b > $o] :
                    ( ( ( X2 @ X4 )
                      = $true )
                   => ( ( X0 @ X4 )
                      = $true ) ) )
             => ( ( X0 @ X3 )
                = $true ) )
          & ! [X8: b > $o] :
              ( ( ( ^ [Y0: b] : $false )
                = X8 )
             => ( ( X0 @ X8 )
                = $true ) ) )
       => ! [X9: b > $o,X10: b] :
            ( ( ( X9 @ X10 )
              = $true )
           => ! [X11: b > $o] :
                ( ( ! [X13: b > $o] :
                      ( ( ( ^ [Y0: b] :
                              ~ ( X11 @ Y0 ) )
                        = X13 )
                     => ( ( X0 @ X13 )
                        = $true ) )
                  & ! [X12: b] :
                      ( ( $true
                        = ( X9 @ X12 ) )
                     => ( $true
                        = ( X11 @ X12 ) ) ) )
               => ( $true
                  = ( X11 @ X10 ) ) ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: ( b > $o ) > $o] :
        ( ( ! [X1: b > $o] :
              ( ( ( ^ [Y0: b] : ~ $false )
                = X1 )
             => ( ( X0 @ X1 )
                = $true ) )
          & ! [X3: ( b > $o ) > $o,X4: b > $o] :
              ( ( ! [X5: b > $o] :
                    ( ( ( X3 @ X5 )
                      = $true )
                   => ( ( X0 @ X5 )
                      = $true ) )
                & ( ( ^ [Y0: b] :
                        ( ?? @ ( b > $o )
                        @ ^ [Y1: b > $o] :
                            ( ( Y1 @ Y0 )
                            & ( X3 @ Y1 ) ) ) )
                  = X4 ) )
             => ( ( X0 @ X4 )
                = $true ) )
          & ! [X8: b > $o,X9: b > $o,X10: b > $o] :
              ( ( ( ( X0 @ X10 )
                  = $true )
                & ( ( ^ [Y0: b] :
                        ( ( X9 @ Y0 )
                        & ( X10 @ Y0 ) ) )
                  = X8 )
                & ( $true
                  = ( X0 @ X9 ) ) )
             => ( ( X0 @ X8 )
                = $true ) )
          & ! [X12: b > $o] :
              ( ( ( ^ [Y0: b] : $false )
                = X12 )
             => ( $true
                = ( X0 @ X12 ) ) ) )
       => ! [X14: b > $o,X15: b] :
            ( ( ( X14 @ X15 )
              = $true )
           => ! [X16: b > $o] :
                ( ( ! [X17: b] :
                      ( ( $true
                        = ( X14 @ X17 ) )
                     => ( ( X16 @ X17 )
                        = $true ) )
                  & ! [X18: b > $o] :
                      ( ( ( ^ [Y0: b] :
                              ~ ( X16 @ Y0 ) )
                        = X18 )
                     => ( ( X0 @ X18 )
                        = $true ) ) )
               => ( $true
                  = ( X16 @ X15 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: ( b > $o ) > $o] :
        ( ( ! [X1: b > $o] :
              ( ( ( ^ [X2: b] : ~ $false )
                = X1 )
             => ( X0 @ X1 ) )
          & ! [X3: ( b > $o ) > $o,X4: b > $o] :
              ( ( ! [X5: b > $o] :
                    ( ( X3 @ X5 )
                   => ( X0 @ X5 ) )
                & ( ( ^ [X6: b] :
                      ? [X7: b > $o] :
                        ( ( X3 @ X7 )
                        & ( X7 @ X6 ) ) )
                  = X4 ) )
             => ( X0 @ X4 ) )
          & ! [X8: b > $o,X9: b > $o,X10: b > $o] :
              ( ( ( X0 @ X10 )
                & ( ( ^ [X11: b] :
                        ( ( X10 @ X11 )
                        & ( X9 @ X11 ) ) )
                  = X8 )
                & ( X0 @ X9 ) )
             => ( X0 @ X8 ) )
          & ! [X12: b > $o] :
              ( ( ( ^ [X13: b] : $false )
                = X12 )
             => ( X0 @ X12 ) ) )
       => ! [X14: b > $o,X15: b] :
            ( ( X14 @ X15 )
           => ! [X16: b > $o] :
                ( ( ! [X17: b] :
                      ( ( X14 @ X17 )
                     => ( X16 @ X17 ) )
                  & ! [X18: b > $o] :
                      ( ( X18
                        = ( ^ [X19: b] :
                              ~ ( X16 @ X19 ) ) )
                     => ( X0 @ X18 ) ) )
               => ( X16 @ X15 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: ( b > $o ) > $o] :
        ( ( ! [X1: b > $o] :
              ( ( ( ^ [X2: b] : ~ $false )
                = X1 )
             => ( X0 @ X1 ) )
          & ! [X3: ( b > $o ) > $o,X1: b > $o] :
              ( ( ! [X2: b > $o] :
                    ( ( X3 @ X2 )
                   => ( X0 @ X2 ) )
                & ( ( ^ [X2: b] :
                      ? [X4: b > $o] :
                        ( ( X3 @ X4 )
                        & ( X4 @ X2 ) ) )
                  = X1 ) )
             => ( X0 @ X1 ) )
          & ! [X4: b > $o,X6: b > $o,X5: b > $o] :
              ( ( ( X0 @ X5 )
                & ( ( ^ [X2: b] :
                        ( ( X5 @ X2 )
                        & ( X6 @ X2 ) ) )
                  = X4 )
                & ( X0 @ X6 ) )
             => ( X0 @ X4 ) )
          & ! [X1: b > $o] :
              ( ( ( ^ [X2: b] : $false )
                = X1 )
             => ( X0 @ X1 ) ) )
       => ! [X7: b > $o,X2: b] :
            ( ( X7 @ X2 )
           => ! [X4: b > $o] :
                ( ( ! [X8: b] :
                      ( ( X7 @ X8 )
                     => ( X4 @ X8 ) )
                  & ! [X1: b > $o] :
                      ( ( X1
                        = ( ^ [X8: b] :
                              ~ ( X4 @ X8 ) ) )
                     => ( X0 @ X1 ) ) )
               => ( X4 @ X2 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: ( b > $o ) > $o] :
      ( ( ! [X1: b > $o] :
            ( ( ( ^ [X2: b] : ~ $false )
              = X1 )
           => ( X0 @ X1 ) )
        & ! [X3: ( b > $o ) > $o,X1: b > $o] :
            ( ( ! [X2: b > $o] :
                  ( ( X3 @ X2 )
                 => ( X0 @ X2 ) )
              & ( ( ^ [X2: b] :
                    ? [X4: b > $o] :
                      ( ( X3 @ X4 )
                      & ( X4 @ X2 ) ) )
                = X1 ) )
           => ( X0 @ X1 ) )
        & ! [X4: b > $o,X6: b > $o,X5: b > $o] :
            ( ( ( X0 @ X5 )
              & ( ( ^ [X2: b] :
                      ( ( X5 @ X2 )
                      & ( X6 @ X2 ) ) )
                = X4 )
              & ( X0 @ X6 ) )
           => ( X0 @ X4 ) )
        & ! [X1: b > $o] :
            ( ( ( ^ [X2: b] : $false )
              = X1 )
           => ( X0 @ X1 ) ) )
     => ! [X7: b > $o,X2: b] :
          ( ( X7 @ X2 )
         => ! [X4: b > $o] :
              ( ( ! [X8: b] :
                    ( ( X7 @ X8 )
                   => ( X4 @ X8 ) )
                & ! [X1: b > $o] :
                    ( ( X1
                      = ( ^ [X8: b] :
                            ~ ( X4 @ X8 ) ) )
                   => ( X0 @ X1 ) ) )
             => ( X4 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCLOSURE_THM0_pme) ).

thf(f32,plain,
    ( ( sK1 @ sK2 )
   != $true ),
    inference(trivial_inequality_removal,[],[f31]) ).

thf(f31,plain,
    ( ( $true != $true )
    | ( ( sK1 @ sK2 )
     != $true ) ),
    inference(superposition,[],[f20,f19]) ).

thf(f19,plain,
    ! [X9: b] :
      ( ( ( sK3 @ X9 )
        = $true )
      | ( ( sK1 @ X9 )
       != $true ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f20,plain,
    ( ( sK3 @ sK2 )
   != $true ),
    inference(cnf_transformation,[],[f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SEV259^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 21 18:40:09 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a TH0_THM_EQU_NAR problem
% 0.12/0.35  Running higher-order theorem proving
% 0.12/0.35  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.37  % (24925)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)
% 0.12/0.37  % (24926)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37  % (24924)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)
% 0.12/0.37  % (24927)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)
% 0.12/0.37  % (24923)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37  % (24928)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)
% 0.12/0.37  % (24929)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37  % (24927)Instruction limit reached!
% 0.12/0.37  % (24927)------------------------------
% 0.12/0.37  % (24927)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37  % (24927)Termination reason: Unknown
% 0.12/0.37  % (24927)Termination phase: shuffling
% 0.12/0.37  
% 0.12/0.37  % (24927)Memory used [KB]: 895
% 0.12/0.37  % (24927)Time elapsed: 0.003 s
% 0.12/0.37  % (24927)Instructions burned: 2 (million)
% 0.12/0.37  % (24927)------------------------------
% 0.12/0.37  % (24927)------------------------------
% 0.12/0.37  % (24926)Instruction limit reached!
% 0.12/0.37  % (24926)------------------------------
% 0.12/0.37  % (24926)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37  % (24926)Termination reason: Unknown
% 0.12/0.37  % (24926)Termination phase: Saturation
% 0.12/0.37  
% 0.12/0.37  % (24926)Memory used [KB]: 1023
% 0.12/0.37  % (24926)Time elapsed: 0.004 s
% 0.12/0.37  % (24926)Instructions burned: 3 (million)
% 0.12/0.37  % (24926)------------------------------
% 0.12/0.37  % (24926)------------------------------
% 0.12/0.38  % (24923)First to succeed.
% 0.12/0.38  % (24924)Instruction limit reached!
% 0.12/0.38  % (24924)------------------------------
% 0.12/0.38  % (24924)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (24924)Termination reason: Unknown
% 0.12/0.38  % (24924)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (24924)Memory used [KB]: 5500
% 0.12/0.38  % (24924)Time elapsed: 0.006 s
% 0.12/0.38  % (24924)Instructions burned: 4 (million)
% 0.12/0.38  % (24924)------------------------------
% 0.12/0.38  % (24924)------------------------------
% 0.12/0.38  % (24925)Also succeeded, but the first one will report.
% 0.12/0.38  % (24928)Also succeeded, but the first one will report.
% 0.12/0.38  % (24923)Refutation found. Thanks to Tanya!
% 0.12/0.38  % SZS status Theorem for theBenchmark
% 0.12/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38  % (24923)------------------------------
% 0.12/0.38  % (24923)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (24923)Termination reason: Refutation
% 0.12/0.38  
% 0.12/0.38  % (24923)Memory used [KB]: 5500
% 0.12/0.38  % (24923)Time elapsed: 0.007 s
% 0.12/0.38  % (24923)Instructions burned: 3 (million)
% 0.12/0.38  % (24923)------------------------------
% 0.12/0.38  % (24923)------------------------------
% 0.12/0.38  % (24922)Success in time 0.009 s
%------------------------------------------------------------------------------