TSTP Solution File: SEV189^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV189^5 : 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 16:02:11 EDT 2024

% Result   : Theorem 0.11s 0.38s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   41 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :  469 ( 120 equ;   0 cnn)
%            Maximal formula atoms :   11 (  11 avg)
%            Number of connectives :  630 (  58   ~;  50   |;  47   &; 347   @)
%                                         (   2 <=>;  88  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  185 ( 185   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   8 usr;   5 con; 0-2 aty)
%                                         (  38  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  164 (  88   ^  64   !;  12   ?; 164   :)

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

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

thf(func_def_1,type,
    cQ: ( b > $o ) > $o ).

thf(func_def_2,type,
    cP: ( b > $o ) > $o ).

thf(func_def_11,type,
    sK0: ( ( b > $o ) > $o ) > b > $o ).

thf(func_def_12,type,
    sK1: ( ( b > $o ) > $o ) > b > $o ).

thf(func_def_13,type,
    sK2: ( b > $o ) > $o ).

thf(func_def_16,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(f50,plain,
    $false,
    inference(avatar_sat_refutation,[],[f29,f39,f49]) ).

thf(f49,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f48]) ).

thf(f48,plain,
    ( $false
    | spl3_2 ),
    inference(subsumption_resolution,[],[f47,f43]) ).

thf(f43,plain,
    ( ( $true
      = ( sK2 @ ( sK0 @ sK2 ) ) )
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f42]) ).

thf(f42,plain,
    ( ( $true != $true )
    | ( $true
      = ( sK2 @ ( sK0 @ sK2 ) ) )
    | spl3_2 ),
    inference(superposition,[],[f28,f19]) ).

thf(f19,plain,
    ! [X0: ( b > $o ) > $o] :
      ( ( $true
        = ( cQ
          @ ^ [Y0: b] :
              ( !! @ ( b > $o )
              @ ^ [Y1: b > $o] :
                  ( ( X0 @ Y1 )
                 => ( Y1 @ Y0 ) ) ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ! [X0: ( b > $o ) > $o] :
        ( ( ( $true
           != ( cQ @ ( sK0 @ X0 ) ) )
          & ( $true
            = ( X0 @ ( sK0 @ X0 ) ) ) )
        | ( $true
          = ( cQ
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X0 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    & ! [X2: ( b > $o ) > $o] :
        ( ( ( ( cP @ ( sK1 @ X2 ) )
           != $true )
          & ( $true
            = ( X2 @ ( sK1 @ X2 ) ) ) )
        | ( $true
          = ( cP
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X2 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    & ( ( ( cP
          @ ^ [Y0: b] :
              ( !! @ ( b > $o )
              @ ^ [Y1: b > $o] :
                  ( ( sK2 @ Y1 )
                 => ( Y1 @ Y0 ) ) ) )
       != $true )
      | ( $true
       != ( cQ
          @ ^ [Y0: b] :
              ( !! @ ( b > $o )
              @ ^ [Y1: b > $o] :
                  ( ( sK2 @ Y1 )
                 => ( Y1 @ Y0 ) ) ) ) ) )
    & ! [X5: b > $o] :
        ( ( ( sK2 @ X5 )
         != $true )
        | ( ( $true
            = ( cP @ X5 ) )
          & ( $true
            = ( cQ @ X5 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).

thf(f10,plain,
    ! [X0: ( b > $o ) > $o] :
      ( ? [X1: b > $o] :
          ( ( ( cQ @ X1 )
           != $true )
          & ( ( X0 @ X1 )
            = $true ) )
     => ( ( $true
         != ( cQ @ ( sK0 @ X0 ) ) )
        & ( $true
          = ( X0 @ ( sK0 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X2: ( b > $o ) > $o] :
      ( ? [X3: b > $o] :
          ( ( $true
           != ( cP @ X3 ) )
          & ( ( X2 @ X3 )
            = $true ) )
     => ( ( ( cP @ ( sK1 @ X2 ) )
         != $true )
        & ( $true
          = ( X2 @ ( sK1 @ X2 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X4: ( b > $o ) > $o] :
        ( ( ( $true
           != ( cP
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) )
          | ( $true
           != ( cQ
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) ) )
        & ! [X5: b > $o] :
            ( ( ( X4 @ X5 )
             != $true )
            | ( ( $true
                = ( cP @ X5 ) )
              & ( $true
                = ( cQ @ X5 ) ) ) ) )
   => ( ( ( ( cP
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( sK2 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) )
         != $true )
        | ( $true
         != ( cQ
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( sK2 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
      & ! [X5: b > $o] :
          ( ( ( sK2 @ X5 )
           != $true )
          | ( ( $true
              = ( cP @ X5 ) )
            & ( $true
              = ( cQ @ X5 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ( ! [X0: ( b > $o ) > $o] :
        ( ? [X1: b > $o] :
            ( ( ( cQ @ X1 )
             != $true )
            & ( ( X0 @ X1 )
              = $true ) )
        | ( $true
          = ( cQ
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X0 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    & ! [X2: ( b > $o ) > $o] :
        ( ? [X3: b > $o] :
            ( ( $true
             != ( cP @ X3 ) )
            & ( ( X2 @ X3 )
              = $true ) )
        | ( $true
          = ( cP
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X2 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    & ? [X4: ( b > $o ) > $o] :
        ( ( ( $true
           != ( cP
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) )
          | ( $true
           != ( cQ
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) ) )
        & ! [X5: b > $o] :
            ( ( ( X4 @ X5 )
             != $true )
            | ( ( $true
                = ( cP @ X5 ) )
              & ( $true
                = ( cQ @ X5 ) ) ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f8,plain,
    ( ! [X2: ( b > $o ) > $o] :
        ( ? [X3: b > $o] :
            ( ( $true
             != ( cQ @ X3 ) )
            & ( ( X2 @ X3 )
              = $true ) )
        | ( $true
          = ( cQ
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X2 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    & ! [X0: ( b > $o ) > $o] :
        ( ? [X1: b > $o] :
            ( ( ( cP @ X1 )
             != $true )
            & ( ( X0 @ X1 )
              = $true ) )
        | ( ( cP
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X0 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) )
          = $true ) )
    & ? [X4: ( b > $o ) > $o] :
        ( ( ( $true
           != ( cP
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) )
          | ( $true
           != ( cQ
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) ) )
        & ! [X5: b > $o] :
            ( ( ( X4 @ X5 )
             != $true )
            | ( ( $true
                = ( cP @ X5 ) )
              & ( $true
                = ( cQ @ X5 ) ) ) ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ( ? [X4: ( b > $o ) > $o] :
        ( ( ( $true
           != ( cP
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) )
          | ( $true
           != ( cQ
              @ ^ [Y0: b] :
                  ( !! @ ( b > $o )
                  @ ^ [Y1: b > $o] :
                      ( ( X4 @ Y1 )
                     => ( Y1 @ Y0 ) ) ) ) ) )
        & ! [X5: b > $o] :
            ( ( ( X4 @ X5 )
             != $true )
            | ( ( $true
                = ( cP @ X5 ) )
              & ( $true
                = ( cQ @ X5 ) ) ) ) )
    & ! [X2: ( b > $o ) > $o] :
        ( ? [X3: b > $o] :
            ( ( $true
             != ( cQ @ X3 ) )
            & ( ( X2 @ X3 )
              = $true ) )
        | ( $true
          = ( cQ
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X2 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) ) ) )
    & ! [X0: ( b > $o ) > $o] :
        ( ? [X1: b > $o] :
            ( ( ( cP @ X1 )
             != $true )
            & ( ( X0 @ X1 )
              = $true ) )
        | ( ( cP
            @ ^ [Y0: b] :
                ( !! @ ( b > $o )
                @ ^ [Y1: b > $o] :
                    ( ( X0 @ Y1 )
                   => ( Y1 @ Y0 ) ) ) )
          = $true ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ( ( ! [X2: ( b > $o ) > $o] :
            ( ! [X3: b > $o] :
                ( ( ( X2 @ X3 )
                  = $true )
               => ( $true
                  = ( cQ @ X3 ) ) )
           => ( $true
              = ( cQ
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X2 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) ) ) )
        & ! [X0: ( b > $o ) > $o] :
            ( ! [X1: b > $o] :
                ( ( ( X0 @ X1 )
                  = $true )
               => ( ( cP @ X1 )
                  = $true ) )
           => ( ( cP
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X0 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) )
              = $true ) ) )
     => ! [X4: ( b > $o ) > $o] :
          ( ! [X5: b > $o] :
              ( ( ( X4 @ X5 )
                = $true )
             => ( ( $true
                  = ( cP @ X5 ) )
                & ( $true
                  = ( cQ @ X5 ) ) ) )
         => ( ( $true
              = ( cP
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X4 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) ) )
            & ( $true
              = ( cQ
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X4 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) ) ) ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ! [X0: ( b > $o ) > $o] :
            ( ! [X1: b > $o] :
                ( ( ( X0 @ X1 )
                  = $true )
               => ( ( cP @ X1 )
                  = $true ) )
           => ( ( cP
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X0 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) )
              = $true ) )
        & ! [X4: ( b > $o ) > $o] :
            ( ! [X5: b > $o] :
                ( ( ( X4 @ X5 )
                  = $true )
               => ( $true
                  = ( cQ @ X5 ) ) )
           => ( $true
              = ( cQ
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X4 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) ) ) ) )
     => ! [X8: ( b > $o ) > $o] :
          ( ! [X9: b > $o] :
              ( ( $true
                = ( X8 @ X9 ) )
             => ( ( $true
                  = ( cP @ X9 ) )
                & ( $true
                  = ( cQ @ X9 ) ) ) )
         => ( ( $true
              = ( cQ
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X8 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) ) )
            & ( ( cP
                @ ^ [Y0: b] :
                    ( !! @ ( b > $o )
                    @ ^ [Y1: b > $o] :
                        ( ( X8 @ Y1 )
                       => ( Y1 @ Y0 ) ) ) )
              = $true ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ( ! [X0: ( b > $o ) > $o] :
            ( ! [X1: b > $o] :
                ( ( X0 @ X1 )
               => ( cP @ X1 ) )
           => ( cP
              @ ^ [X2: b] :
                ! [X3: b > $o] :
                  ( ( X0 @ X3 )
                 => ( X3 @ X2 ) ) ) )
        & ! [X4: ( b > $o ) > $o] :
            ( ! [X5: b > $o] :
                ( ( X4 @ X5 )
               => ( cQ @ X5 ) )
           => ( cQ
              @ ^ [X6: b] :
                ! [X7: b > $o] :
                  ( ( X4 @ X7 )
                 => ( X7 @ X6 ) ) ) ) )
     => ! [X8: ( b > $o ) > $o] :
          ( ! [X9: b > $o] :
              ( ( X8 @ X9 )
             => ( ( cP @ X9 )
                & ( cQ @ X9 ) ) )
         => ( ( cQ
              @ ^ [X10: b] :
                ! [X11: b > $o] :
                  ( ( X8 @ X11 )
                 => ( X11 @ X10 ) ) )
            & ( cP
              @ ^ [X12: b] :
                ! [X13: b > $o] :
                  ( ( X8 @ X13 )
                 => ( X13 @ X12 ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ! [X0: ( b > $o ) > $o] :
            ( ! [X1: b > $o] :
                ( ( X0 @ X1 )
               => ( cP @ X1 ) )
           => ( cP
              @ ^ [X1: b] :
                ! [X2: b > $o] :
                  ( ( X0 @ X2 )
                 => ( X2 @ X1 ) ) ) )
        & ! [X0: ( b > $o ) > $o] :
            ( ! [X1: b > $o] :
                ( ( X0 @ X1 )
               => ( cQ @ X1 ) )
           => ( cQ
              @ ^ [X1: b] :
                ! [X2: b > $o] :
                  ( ( X0 @ X2 )
                 => ( X2 @ X1 ) ) ) ) )
     => ! [X0: ( b > $o ) > $o] :
          ( ! [X1: b > $o] :
              ( ( X0 @ X1 )
             => ( ( cP @ X1 )
                & ( cQ @ X1 ) ) )
         => ( ( cQ
              @ ^ [X1: b] :
                ! [X2: b > $o] :
                  ( ( X0 @ X2 )
                 => ( X2 @ X1 ) ) )
            & ( cP
              @ ^ [X1: b] :
                ! [X2: b > $o] :
                  ( ( X0 @ X2 )
                 => ( X2 @ X1 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ! [X0: ( b > $o ) > $o] :
          ( ! [X1: b > $o] :
              ( ( X0 @ X1 )
             => ( cP @ X1 ) )
         => ( cP
            @ ^ [X1: b] :
              ! [X2: b > $o] :
                ( ( X0 @ X2 )
               => ( X2 @ X1 ) ) ) )
      & ! [X0: ( b > $o ) > $o] :
          ( ! [X1: b > $o] :
              ( ( X0 @ X1 )
             => ( cQ @ X1 ) )
         => ( cQ
            @ ^ [X1: b] :
              ! [X2: b > $o] :
                ( ( X0 @ X2 )
               => ( X2 @ X1 ) ) ) ) )
   => ! [X0: ( b > $o ) > $o] :
        ( ! [X1: b > $o] :
            ( ( X0 @ X1 )
           => ( ( cP @ X1 )
              & ( cQ @ X1 ) ) )
       => ( ( cQ
            @ ^ [X1: b] :
              ! [X2: b > $o] :
                ( ( X0 @ X2 )
               => ( X2 @ X1 ) ) )
          & ( cP
            @ ^ [X1: b] :
              ! [X2: b > $o] :
                ( ( X0 @ X2 )
               => ( X2 @ X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM567_pme) ).

thf(f28,plain,
    ( ( $true
     != ( cQ
        @ ^ [Y0: b] :
            ( !! @ ( b > $o )
            @ ^ [Y1: b > $o] :
                ( ( sK2 @ Y1 )
               => ( Y1 @ Y0 ) ) ) ) )
    | spl3_2 ),
    inference(avatar_component_clause,[],[f26]) ).

thf(f26,plain,
    ( spl3_2
  <=> ( $true
      = ( cQ
        @ ^ [Y0: b] :
            ( !! @ ( b > $o )
            @ ^ [Y1: b > $o] :
                ( ( sK2 @ Y1 )
               => ( Y1 @ Y0 ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f47,plain,
    ( ( $true
     != ( sK2 @ ( sK0 @ sK2 ) ) )
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f46]) ).

thf(f46,plain,
    ( ( $true != $true )
    | ( $true
     != ( sK2 @ ( sK0 @ sK2 ) ) )
    | spl3_2 ),
    inference(superposition,[],[f45,f14]) ).

thf(f14,plain,
    ! [X5: b > $o] :
      ( ( $true
        = ( cQ @ X5 ) )
      | ( ( sK2 @ X5 )
       != $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f45,plain,
    ( ( $true
     != ( cQ @ ( sK0 @ sK2 ) ) )
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f44]) ).

thf(f44,plain,
    ( ( $true
     != ( cQ @ ( sK0 @ sK2 ) ) )
    | ( $true != $true )
    | spl3_2 ),
    inference(superposition,[],[f28,f20]) ).

thf(f20,plain,
    ! [X0: ( b > $o ) > $o] :
      ( ( $true
        = ( cQ
          @ ^ [Y0: b] :
              ( !! @ ( b > $o )
              @ ^ [Y1: b > $o] :
                  ( ( X0 @ Y1 )
                 => ( Y1 @ Y0 ) ) ) ) )
      | ( $true
       != ( cQ @ ( sK0 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f39,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f38]) ).

thf(f38,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f37,f33]) ).

thf(f33,plain,
    ( ( $true
      = ( sK2 @ ( sK1 @ sK2 ) ) )
    | spl3_1 ),
    inference(trivial_inequality_removal,[],[f32]) ).

thf(f32,plain,
    ( ( $true
      = ( sK2 @ ( sK1 @ sK2 ) ) )
    | ( $true != $true )
    | spl3_1 ),
    inference(superposition,[],[f24,f17]) ).

thf(f17,plain,
    ! [X2: ( b > $o ) > $o] :
      ( ( $true
        = ( cP
          @ ^ [Y0: b] :
              ( !! @ ( b > $o )
              @ ^ [Y1: b > $o] :
                  ( ( X2 @ Y1 )
                 => ( Y1 @ Y0 ) ) ) ) )
      | ( $true
        = ( X2 @ ( sK1 @ X2 ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f24,plain,
    ( ( ( cP
        @ ^ [Y0: b] :
            ( !! @ ( b > $o )
            @ ^ [Y1: b > $o] :
                ( ( sK2 @ Y1 )
               => ( Y1 @ Y0 ) ) ) )
     != $true )
    | spl3_1 ),
    inference(avatar_component_clause,[],[f22]) ).

thf(f22,plain,
    ( spl3_1
  <=> ( ( cP
        @ ^ [Y0: b] :
            ( !! @ ( b > $o )
            @ ^ [Y1: b > $o] :
                ( ( sK2 @ Y1 )
               => ( Y1 @ Y0 ) ) ) )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f37,plain,
    ( ( $true
     != ( sK2 @ ( sK1 @ sK2 ) ) )
    | spl3_1 ),
    inference(trivial_inequality_removal,[],[f36]) ).

thf(f36,plain,
    ( ( $true
     != ( sK2 @ ( sK1 @ sK2 ) ) )
    | ( $true != $true )
    | spl3_1 ),
    inference(superposition,[],[f35,f15]) ).

thf(f15,plain,
    ! [X5: b > $o] :
      ( ( $true
        = ( cP @ X5 ) )
      | ( ( sK2 @ X5 )
       != $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f35,plain,
    ( ( $true
     != ( cP @ ( sK1 @ sK2 ) ) )
    | spl3_1 ),
    inference(trivial_inequality_removal,[],[f34]) ).

thf(f34,plain,
    ( ( $true != $true )
    | ( $true
     != ( cP @ ( sK1 @ sK2 ) ) )
    | spl3_1 ),
    inference(superposition,[],[f24,f18]) ).

thf(f18,plain,
    ! [X2: ( b > $o ) > $o] :
      ( ( $true
        = ( cP
          @ ^ [Y0: b] :
              ( !! @ ( b > $o )
              @ ^ [Y1: b > $o] :
                  ( ( X2 @ Y1 )
                 => ( Y1 @ Y0 ) ) ) ) )
      | ( ( cP @ ( sK1 @ X2 ) )
       != $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f29,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f16,f26,f22]) ).

thf(f16,plain,
    ( ( ( cP
        @ ^ [Y0: b] :
            ( !! @ ( b > $o )
            @ ^ [Y1: b > $o] :
                ( ( sK2 @ Y1 )
               => ( Y1 @ Y0 ) ) ) )
     != $true )
    | ( $true
     != ( cQ
        @ ^ [Y0: b] :
            ( !! @ ( b > $o )
            @ ^ [Y1: b > $o] :
                ( ( sK2 @ Y1 )
               => ( Y1 @ Y0 ) ) ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV189^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.11/0.33  % Computer : n021.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri Jun 21 19:27:39 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.35  This is a TH0_THM_NEQ_NAR problem
% 0.11/0.35  Running higher-order theorem proving
% 0.11/0.35  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
% 0.11/0.38  % (21116)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.38  % (21114)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)
% 0.11/0.38  % (21118)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)
% 0.11/0.38  % (21119)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.38  % (21115)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)
% 0.11/0.38  % (21113)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.38  % (21116)Instruction limit reached!
% 0.11/0.38  % (21116)------------------------------
% 0.11/0.38  % (21116)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38  % (21116)Termination reason: Unknown
% 0.11/0.38  % (21116)Termination phase: Preprocessing 3
% 0.11/0.38  
% 0.11/0.38  % (21116)Memory used [KB]: 1023
% 0.11/0.38  % (21116)Time elapsed: 0.003 s
% 0.11/0.38  % (21116)Instructions burned: 2 (million)
% 0.11/0.38  % (21116)------------------------------
% 0.11/0.38  % (21116)------------------------------
% 0.11/0.38  % (21117)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)
% 0.11/0.38  % (21114)Instruction limit reached!
% 0.11/0.38  % (21114)------------------------------
% 0.11/0.38  % (21114)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38  % (21114)Termination reason: Unknown
% 0.11/0.38  % (21114)Termination phase: Saturation
% 0.11/0.38  
% 0.11/0.38  % (21114)Memory used [KB]: 5500
% 0.11/0.38  % (21114)Time elapsed: 0.006 s
% 0.11/0.38  % (21114)Instructions burned: 5 (million)
% 0.11/0.38  % (21114)------------------------------
% 0.11/0.38  % (21114)------------------------------
% 0.11/0.38  % (21117)Instruction limit reached!
% 0.11/0.38  % (21117)------------------------------
% 0.11/0.38  % (21117)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38  % (21117)Termination reason: Unknown
% 0.11/0.38  % (21117)Termination phase: Saturation
% 0.11/0.38  
% 0.11/0.38  % (21117)Memory used [KB]: 895
% 0.11/0.38  % (21117)Time elapsed: 0.004 s
% 0.11/0.38  % (21117)Instructions burned: 2 (million)
% 0.11/0.38  % (21117)------------------------------
% 0.11/0.38  % (21117)------------------------------
% 0.11/0.38  % (21118)First to succeed.
% 0.11/0.38  % (21115)Also succeeded, but the first one will report.
% 0.11/0.38  % (21118)Refutation found. Thanks to Tanya!
% 0.11/0.38  % SZS status Theorem for theBenchmark
% 0.11/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.38  % (21118)------------------------------
% 0.11/0.38  % (21118)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38  % (21118)Termination reason: Refutation
% 0.11/0.38  
% 0.11/0.38  % (21118)Memory used [KB]: 5500
% 0.11/0.38  % (21118)Time elapsed: 0.009 s
% 0.11/0.38  % (21118)Instructions burned: 7 (million)
% 0.11/0.38  % (21118)------------------------------
% 0.11/0.38  % (21118)------------------------------
% 0.11/0.38  % (21107)Success in time 0.024 s
%------------------------------------------------------------------------------