TSTP Solution File: SEV028^5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV028^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n017.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 16:01:31 EDT 2024

% Result   : Theorem 0.22s 0.41s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   79 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :  709 ( 234 equ;   0 cnn)
%            Maximal formula atoms :   19 (   8 avg)
%            Number of connectives :  954 ( 144   ~; 143   |;  98   &; 512   @)
%                                         (  15 <=>;  42  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;  14 con; 0-2 aty)
%            Number of variables   :  209 (   0   ^ 127   !;  82   ?; 209   :)

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

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

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

thf(func_def_5,type,
    sK0: a > a > $o ).

thf(func_def_6,type,
    sK1: a > a ).

thf(func_def_7,type,
    sK2: ( a > $o ) > a ).

thf(func_def_8,type,
    sK3: ( a > $o ) > a ).

thf(func_def_9,type,
    sK4: ( a > $o ) > a ).

thf(func_def_10,type,
    sK5: ( a > $o ) > a ).

thf(func_def_11,type,
    sK6: ( a > $o ) > a ).

thf(func_def_12,type,
    sK7: a ).

thf(func_def_13,type,
    sK8: a ).

thf(func_def_14,type,
    sK9: a ).

thf(func_def_15,type,
    sK10: a ).

thf(func_def_16,type,
    sK11: a ).

thf(func_def_17,type,
    sK12: a ).

thf(func_def_20,type,
    ph14: 
      !>[X0: $tType] : X0 ).

thf(f376,plain,
    $false,
    inference(avatar_sat_refutation,[],[f51,f60,f65,f66,f67,f68,f134,f181,f375]) ).

thf(f375,plain,
    ( ~ spl13_1
    | ~ spl13_5
    | spl13_6 ),
    inference(avatar_contradiction_clause,[],[f374]) ).

thf(f374,plain,
    ( $false
    | ~ spl13_1
    | ~ spl13_5
    | spl13_6 ),
    inference(subsumption_resolution,[],[f362,f30]) ).

thf(f30,plain,
    ! [X0: a] :
      ( $true
      = ( sK0 @ X0 @ X0 ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f19,plain,
    ( ! [X0: a] :
        ( ! [X2: a] :
            ( ! [X3: a] :
                ( ( cQ @ X2 @ X3 )
                = ( sK0 @ X0 @ X3 ) )
            | ( $true
             != ( sK0 @ X0 @ X2 ) ) )
        & ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
          = $true )
        & ( $true
          = ( sK0 @ X0 @ X0 ) )
        & ! [X5: a > $o] :
            ( ( ( sK0 @ X0 )
              = X5 )
            | ! [X6: a] :
                ( $true
               != ( X5 @ X6 ) )
            | ( ( ( X5 @ ( sK2 @ X5 ) )
                = $true )
              & ( ( X5 @ ( sK3 @ X5 ) )
               != ( cQ @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) ) )
            | ( $true
             != ( X5 @ X0 ) ) ) )
    & ! [X9: a > $o] :
        ( ( ( ( X9 @ ( sK5 @ X9 ) )
           != ( cQ @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) )
          & ( $true
            = ( X9 @ ( sK4 @ X9 ) ) ) )
        | ! [X12: a] :
            ( $true
           != ( X9 @ X12 ) )
        | ( $true
          = ( X9 @ ( sK6 @ X9 ) ) ) )
    & ( ( ( $true
         != ( cQ @ sK7 @ sK8 ) )
        & ( ( cQ @ sK8 @ sK7 )
          = $true ) )
      | ( $true
       != ( cQ @ sK9 @ sK9 ) )
      | ( ( $true
          = ( cQ @ sK11 @ sK10 ) )
        & ( $true
          = ( cQ @ sK10 @ sK12 ) )
        & ( ( cQ @ sK11 @ sK12 )
         != $true ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f8,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9]) ).

thf(f9,plain,
    ! [X0: a] :
      ( ? [X1: a > $o] :
          ( ! [X2: a] :
              ( ! [X3: a] :
                  ( ( cQ @ X2 @ X3 )
                  = ( X1 @ X3 ) )
              | ( $true
               != ( X1 @ X2 ) ) )
          & ? [X4: a] :
              ( $true
              = ( X1 @ X4 ) )
          & ( ( X1 @ X0 )
            = $true )
          & ! [X5: a > $o] :
              ( ( X1 = X5 )
              | ! [X6: a] :
                  ( $true
                 != ( X5 @ X6 ) )
              | ? [X7: a] :
                  ( ( $true
                    = ( X5 @ X7 ) )
                  & ? [X8: a] :
                      ( ( X5 @ X8 )
                     != ( cQ @ X7 @ X8 ) ) )
              | ( $true
               != ( X5 @ X0 ) ) ) )
     => ( ! [X2: a] :
            ( ! [X3: a] :
                ( ( cQ @ X2 @ X3 )
                = ( sK0 @ X0 @ X3 ) )
            | ( $true
             != ( sK0 @ X0 @ X2 ) ) )
        & ? [X4: a] :
            ( $true
            = ( sK0 @ X0 @ X4 ) )
        & ( $true
          = ( sK0 @ X0 @ X0 ) )
        & ! [X5: a > $o] :
            ( ( ( sK0 @ X0 )
              = X5 )
            | ! [X6: a] :
                ( $true
               != ( X5 @ X6 ) )
            | ? [X7: a] :
                ( ( $true
                  = ( X5 @ X7 ) )
                & ? [X8: a] :
                    ( ( X5 @ X8 )
                   != ( cQ @ X7 @ X8 ) ) )
            | ( $true
             != ( X5 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ! [X0: a] :
      ( ? [X4: a] :
          ( $true
          = ( sK0 @ X0 @ X4 ) )
     => ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
        = $true ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X5: a > $o] :
      ( ? [X7: a] :
          ( ( $true
            = ( X5 @ X7 ) )
          & ? [X8: a] :
              ( ( X5 @ X8 )
             != ( cQ @ X7 @ X8 ) ) )
     => ( ( ( X5 @ ( sK2 @ X5 ) )
          = $true )
        & ? [X8: a] :
            ( ( cQ @ ( sK2 @ X5 ) @ X8 )
           != ( X5 @ X8 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X5: a > $o] :
      ( ? [X8: a] :
          ( ( cQ @ ( sK2 @ X5 ) @ X8 )
         != ( X5 @ X8 ) )
     => ( ( X5 @ ( sK3 @ X5 ) )
       != ( cQ @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ! [X9: a > $o] :
      ( ? [X10: a] :
          ( ? [X11: a] :
              ( ( cQ @ X10 @ X11 )
             != ( X9 @ X11 ) )
          & ( $true
            = ( X9 @ X10 ) ) )
     => ( ? [X11: a] :
            ( ( cQ @ ( sK4 @ X9 ) @ X11 )
           != ( X9 @ X11 ) )
        & ( $true
          = ( X9 @ ( sK4 @ X9 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f14,plain,
    ! [X9: a > $o] :
      ( ? [X11: a] :
          ( ( cQ @ ( sK4 @ X9 ) @ X11 )
         != ( X9 @ X11 ) )
     => ( ( X9 @ ( sK5 @ X9 ) )
       != ( cQ @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f15,plain,
    ! [X9: a > $o] :
      ( ? [X13: a] :
          ( $true
          = ( X9 @ X13 ) )
     => ( $true
        = ( X9 @ ( sK6 @ X9 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f16,plain,
    ( ? [X14: a,X15: a] :
        ( ( $true
         != ( cQ @ X14 @ X15 ) )
        & ( $true
          = ( cQ @ X15 @ X14 ) ) )
   => ( ( $true
       != ( cQ @ sK7 @ sK8 ) )
      & ( ( cQ @ sK8 @ sK7 )
        = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f17,plain,
    ( ? [X16: a] :
        ( $true
       != ( cQ @ X16 @ X16 ) )
   => ( $true
     != ( cQ @ sK9 @ sK9 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f18,plain,
    ( ? [X17: a,X18: a,X19: a] :
        ( ( $true
          = ( cQ @ X18 @ X17 ) )
        & ( $true
          = ( cQ @ X17 @ X19 ) )
        & ( $true
         != ( cQ @ X18 @ X19 ) ) )
   => ( ( $true
        = ( cQ @ sK11 @ sK10 ) )
      & ( $true
        = ( cQ @ sK10 @ sK12 ) )
      & ( ( cQ @ sK11 @ sK12 )
       != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ! [X0: a] :
      ? [X1: a > $o] :
        ( ! [X2: a] :
            ( ! [X3: a] :
                ( ( cQ @ X2 @ X3 )
                = ( X1 @ X3 ) )
            | ( $true
             != ( X1 @ X2 ) ) )
        & ? [X4: a] :
            ( $true
            = ( X1 @ X4 ) )
        & ( ( X1 @ X0 )
          = $true )
        & ! [X5: a > $o] :
            ( ( X1 = X5 )
            | ! [X6: a] :
                ( $true
               != ( X5 @ X6 ) )
            | ? [X7: a] :
                ( ( $true
                  = ( X5 @ X7 ) )
                & ? [X8: a] :
                    ( ( X5 @ X8 )
                   != ( cQ @ X7 @ X8 ) ) )
            | ( $true
             != ( X5 @ X0 ) ) ) )
    & ! [X9: a > $o] :
        ( ? [X10: a] :
            ( ? [X11: a] :
                ( ( cQ @ X10 @ X11 )
               != ( X9 @ X11 ) )
            & ( $true
              = ( X9 @ X10 ) ) )
        | ! [X12: a] :
            ( $true
           != ( X9 @ X12 ) )
        | ? [X13: a] :
            ( $true
            = ( X9 @ X13 ) ) )
    & ( ? [X14: a,X15: a] :
          ( ( $true
           != ( cQ @ X14 @ X15 ) )
          & ( $true
            = ( cQ @ X15 @ X14 ) ) )
      | ? [X16: a] :
          ( $true
         != ( cQ @ X16 @ X16 ) )
      | ? [X17: a,X18: a,X19: a] :
          ( ( $true
            = ( cQ @ X18 @ X17 ) )
          & ( $true
            = ( cQ @ X17 @ X19 ) )
          & ( $true
           != ( cQ @ X18 @ X19 ) ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ! [X0: a] :
      ? [X1: a > $o] :
        ( ! [X7: a] :
            ( ! [X8: a] :
                ( ( X1 @ X8 )
                = ( cQ @ X7 @ X8 ) )
            | ( $true
             != ( X1 @ X7 ) ) )
        & ? [X6: a] :
            ( ( X1 @ X6 )
            = $true )
        & ( ( X1 @ X0 )
          = $true )
        & ! [X2: a > $o] :
            ( ( X1 = X2 )
            | ! [X3: a] :
                ( ( X2 @ X3 )
               != $true )
            | ? [X4: a] :
                ( ( ( X2 @ X4 )
                  = $true )
                & ? [X5: a] :
                    ( ( cQ @ X4 @ X5 )
                   != ( X2 @ X5 ) ) )
            | ( $true
             != ( X2 @ X0 ) ) ) )
    & ! [X9: a > $o] :
        ( ? [X11: a] :
            ( ? [X12: a] :
                ( ( cQ @ X11 @ X12 )
               != ( X9 @ X12 ) )
            & ( $true
              = ( X9 @ X11 ) ) )
        | ! [X10: a] :
            ( $true
           != ( X9 @ X10 ) )
        | ? [X13: a] :
            ( $true
            = ( X9 @ X13 ) ) )
    & ( ? [X15: a,X14: a] :
          ( ( $true
           != ( cQ @ X15 @ X14 ) )
          & ( $true
            = ( cQ @ X14 @ X15 ) ) )
      | ? [X16: a] :
          ( $true
         != ( cQ @ X16 @ X16 ) )
      | ? [X19: a,X18: a,X17: a] :
          ( ( $true
            = ( cQ @ X18 @ X19 ) )
          & ( $true
            = ( cQ @ X19 @ X17 ) )
          & ( $true
           != ( cQ @ X18 @ X17 ) ) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ( ( ? [X16: a] :
          ( $true
         != ( cQ @ X16 @ X16 ) )
      | ? [X19: a,X18: a,X17: a] :
          ( ( $true
           != ( cQ @ X18 @ X17 ) )
          & ( $true
            = ( cQ @ X18 @ X19 ) )
          & ( $true
            = ( cQ @ X19 @ X17 ) ) )
      | ? [X15: a,X14: a] :
          ( ( $true
           != ( cQ @ X15 @ X14 ) )
          & ( $true
            = ( cQ @ X14 @ X15 ) ) ) )
    & ! [X0: a] :
      ? [X1: a > $o] :
        ( ! [X2: a > $o] :
            ( ( X1 = X2 )
            | ( $true
             != ( X2 @ X0 ) )
            | ! [X3: a] :
                ( ( X2 @ X3 )
               != $true )
            | ? [X4: a] :
                ( ( ( X2 @ X4 )
                  = $true )
                & ? [X5: a] :
                    ( ( cQ @ X4 @ X5 )
                   != ( X2 @ X5 ) ) ) )
        & ! [X7: a] :
            ( ! [X8: a] :
                ( ( X1 @ X8 )
                = ( cQ @ X7 @ X8 ) )
            | ( $true
             != ( X1 @ X7 ) ) )
        & ? [X6: a] :
            ( ( X1 @ X6 )
            = $true )
        & ( ( X1 @ X0 )
          = $true ) )
    & ! [X9: a > $o] :
        ( ? [X13: a] :
            ( $true
            = ( X9 @ X13 ) )
        | ? [X11: a] :
            ( ? [X12: a] :
                ( ( cQ @ X11 @ X12 )
               != ( X9 @ X12 ) )
            & ( $true
              = ( X9 @ X11 ) ) )
        | ! [X10: a] :
            ( $true
           != ( X9 @ X10 ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ! [X0: a] :
          ? [X1: a > $o] :
            ( ! [X2: a > $o] :
                ( ( ( $true
                    = ( X2 @ X0 ) )
                  & ? [X3: a] :
                      ( ( X2 @ X3 )
                      = $true )
                  & ! [X4: a] :
                      ( ( ( X2 @ X4 )
                        = $true )
                     => ! [X5: a] :
                          ( ( cQ @ X4 @ X5 )
                          = ( X2 @ X5 ) ) ) )
               => ( X1 = X2 ) )
            & ! [X7: a] :
                ( ( $true
                  = ( X1 @ X7 ) )
               => ! [X8: a] :
                    ( ( X1 @ X8 )
                    = ( cQ @ X7 @ X8 ) ) )
            & ? [X6: a] :
                ( ( X1 @ X6 )
                = $true )
            & ( ( X1 @ X0 )
              = $true ) )
        & ! [X9: a > $o] :
            ( ( ! [X11: a] :
                  ( ( $true
                    = ( X9 @ X11 ) )
                 => ! [X12: a] :
                      ( ( cQ @ X11 @ X12 )
                      = ( X9 @ X12 ) ) )
              & ? [X10: a] :
                  ( $true
                  = ( X9 @ X10 ) ) )
           => ? [X13: a] :
                ( $true
                = ( X9 @ X13 ) ) ) )
     => ( ! [X16: a] :
            ( $true
            = ( cQ @ X16 @ X16 ) )
        & ! [X19: a,X18: a,X17: a] :
            ( ( ( $true
                = ( cQ @ X18 @ X19 ) )
              & ( $true
                = ( cQ @ X19 @ X17 ) ) )
           => ( $true
              = ( cQ @ X18 @ X17 ) ) )
        & ! [X14: a,X15: a] :
            ( ( $true
              = ( cQ @ X14 @ X15 ) )
           => ( $true
              = ( cQ @ X15 @ X14 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

thf(f2,negated_conjecture,
    ~ ( ( ! [X2: a] :
          ? [X0: a > $o] :
            ( ( X0 @ X2 )
            & ! [X5: a > $o] :
                ( ( ? [X1: a] : ( X5 @ X1 )
                  & ! [X4: a] :
                      ( ( X5 @ X4 )
                     => ! [X3: a] :
                          ( ( cQ @ X4 @ X3 )
                        <=> ( X5 @ X3 ) ) )
                  & ( X5 @ X2 ) )
               => ( X0 = X5 ) )
            & ? [X1: a] : ( X0 @ X1 )
            & ! [X4: a] :
                ( ( X0 @ X4 )
               => ! [X3: a] :
                    ( ( cQ @ X4 @ X3 )
                  <=> ( X0 @ X3 ) ) ) )
        & ! [X0: a > $o] :
            ( ( ? [X1: a] : ( X0 @ X1 )
              & ! [X2: a] :
                  ( ( X0 @ X2 )
                 => ! [X3: a] :
                      ( ( cQ @ X2 @ X3 )
                    <=> ( X0 @ X3 ) ) ) )
           => ? [X1: a] : ( X0 @ X1 ) ) )
     => ( ! [X2: a,X3: a] :
            ( ( cQ @ X2 @ X3 )
           => ( cQ @ X3 @ X2 ) )
        & ! [X2: a] : ( cQ @ X2 @ X2 )
        & ! [X1: a,X2: a,X3: a] :
            ( ( ( cQ @ X2 @ X3 )
              & ( cQ @ X3 @ X1 ) )
           => ( cQ @ X2 @ X1 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ! [X2: a] :
        ? [X0: a > $o] :
          ( ( X0 @ X2 )
          & ! [X5: a > $o] :
              ( ( ? [X1: a] : ( X5 @ X1 )
                & ! [X4: a] :
                    ( ( X5 @ X4 )
                   => ! [X3: a] :
                        ( ( cQ @ X4 @ X3 )
                      <=> ( X5 @ X3 ) ) )
                & ( X5 @ X2 ) )
             => ( X0 = X5 ) )
          & ? [X1: a] : ( X0 @ X1 )
          & ! [X4: a] :
              ( ( X0 @ X4 )
             => ! [X3: a] :
                  ( ( cQ @ X4 @ X3 )
                <=> ( X0 @ X3 ) ) ) )
      & ! [X0: a > $o] :
          ( ( ? [X1: a] : ( X0 @ X1 )
            & ! [X2: a] :
                ( ( X0 @ X2 )
               => ! [X3: a] :
                    ( ( cQ @ X2 @ X3 )
                  <=> ( X0 @ X3 ) ) ) )
         => ? [X1: a] : ( X0 @ X1 ) ) )
   => ( ! [X2: a,X3: a] :
          ( ( cQ @ X2 @ X3 )
         => ( cQ @ X3 @ X2 ) )
      & ! [X2: a] : ( cQ @ X2 @ X2 )
      & ! [X1: a,X2: a,X3: a] :
          ( ( ( cQ @ X2 @ X3 )
            & ( cQ @ X3 @ X1 ) )
         => ( cQ @ X2 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM558_pme) ).

thf(f362,plain,
    ( ( $true
     != ( sK0 @ sK11 @ sK11 ) )
    | ~ spl13_1
    | ~ spl13_5
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f357]) ).

thf(f357,plain,
    ( ( $true
     != ( sK0 @ sK11 @ sK11 ) )
    | ( $true = $false )
    | ~ spl13_1
    | ~ spl13_5
    | spl13_6 ),
    inference(superposition,[],[f59,f349]) ).

thf(f349,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK10 )
          = $false )
        | ( $true
         != ( sK0 @ sK11 @ X0 ) ) )
    | ~ spl13_1
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f342]) ).

thf(f342,plain,
    ( ! [X0: a] :
        ( ( $true
         != ( sK0 @ sK11 @ X0 ) )
        | ( $true != $true )
        | ( ( cQ @ X0 @ sK10 )
          = $false ) )
    | ~ spl13_1
    | spl13_6 ),
    inference(superposition,[],[f336,f36]) ).

thf(f36,plain,
    ! [X2: a,X3: a,X0: a] :
      ( ( $true
        = ( sK0 @ X0 @ X3 ) )
      | ( ( cQ @ X2 @ X3 )
        = $false )
      | ( $true
       != ( sK0 @ X0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f32]) ).

thf(f32,plain,
    ! [X2: a,X3: a,X0: a] :
      ( ( ( cQ @ X2 @ X3 )
        = ( sK0 @ X0 @ X3 ) )
      | ( $true
       != ( sK0 @ X0 @ X2 ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f336,plain,
    ( ( $true
     != ( sK0 @ sK11 @ sK10 ) )
    | ~ spl13_1
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f326]) ).

thf(f326,plain,
    ( ( $true
     != ( sK0 @ sK11 @ sK10 ) )
    | ( $true = $false )
    | ~ spl13_1
    | spl13_6 ),
    inference(superposition,[],[f42,f299]) ).

thf(f299,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK12 )
          = $false )
        | ( $true
         != ( sK0 @ sK11 @ X0 ) ) )
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f290]) ).

thf(f290,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK12 )
          = $false )
        | ( $true != $true )
        | ( $true
         != ( sK0 @ sK11 @ X0 ) ) )
    | spl13_6 ),
    inference(superposition,[],[f285,f36]) ).

thf(f285,plain,
    ( ( $true
     != ( sK0 @ sK11 @ sK12 ) )
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f277]) ).

thf(f277,plain,
    ( ( $true != $true )
    | ( $true
     != ( sK0 @ sK11 @ sK12 ) )
    | spl13_6 ),
    inference(superposition,[],[f249,f30]) ).

thf(f249,plain,
    ( ! [X0: a] :
        ( ( $true
         != ( sK0 @ sK12 @ X0 ) )
        | ( $true
         != ( sK0 @ sK11 @ X0 ) ) )
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f241]) ).

thf(f241,plain,
    ( ! [X0: a] :
        ( ( $true
         != ( sK0 @ sK12 @ X0 ) )
        | ( $true = $false )
        | ( $true
         != ( sK0 @ sK11 @ X0 ) ) )
    | spl13_6 ),
    inference(superposition,[],[f130,f215]) ).

thf(f215,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK11 )
          = $false )
        | ( $true
         != ( sK0 @ sK12 @ X0 ) ) )
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f211]) ).

thf(f211,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK11 )
          = $false )
        | ( $true != $true )
        | ( $true
         != ( sK0 @ sK12 @ X0 ) ) )
    | spl13_6 ),
    inference(superposition,[],[f198,f36]) ).

thf(f198,plain,
    ( ( $true
     != ( sK0 @ sK12 @ sK11 ) )
    | spl13_6 ),
    inference(trivial_inequality_removal,[],[f192]) ).

thf(f192,plain,
    ( ( $true != $true )
    | ( $true
     != ( sK0 @ sK12 @ sK11 ) )
    | spl13_6 ),
    inference(superposition,[],[f64,f130]) ).

thf(f64,plain,
    ( ( ( cQ @ sK11 @ sK12 )
     != $true )
    | spl13_6 ),
    inference(avatar_component_clause,[],[f62]) ).

thf(f62,plain,
    ( spl13_6
  <=> ( ( cQ @ sK11 @ sK12 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

thf(f130,plain,
    ! [X0: a,X1: a] :
      ( ( $true
        = ( cQ @ X1 @ X0 ) )
      | ( $true
       != ( sK0 @ X0 @ X1 ) ) ),
    inference(trivial_inequality_removal,[],[f111]) ).

thf(f111,plain,
    ! [X0: a,X1: a] :
      ( ( $true
       != ( sK0 @ X0 @ X1 ) )
      | ( $true = $false )
      | ( $true
        = ( cQ @ X1 @ X0 ) ) ),
    inference(superposition,[],[f35,f30]) ).

thf(f35,plain,
    ! [X2: a,X3: a,X0: a] :
      ( ( ( sK0 @ X0 @ X3 )
        = $false )
      | ( ( cQ @ X2 @ X3 )
        = $true )
      | ( $true
       != ( sK0 @ X0 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f32]) ).

thf(f42,plain,
    ( ( $true
      = ( cQ @ sK10 @ sK12 ) )
    | ~ spl13_1 ),
    inference(avatar_component_clause,[],[f40]) ).

thf(f40,plain,
    ( spl13_1
  <=> ( $true
      = ( cQ @ sK10 @ sK12 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

thf(f59,plain,
    ( ( $true
      = ( cQ @ sK11 @ sK10 ) )
    | ~ spl13_5 ),
    inference(avatar_component_clause,[],[f57]) ).

thf(f57,plain,
    ( spl13_5
  <=> ( $true
      = ( cQ @ sK11 @ sK10 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

thf(f181,plain,
    ( spl13_2
    | ~ spl13_4 ),
    inference(avatar_contradiction_clause,[],[f180]) ).

thf(f180,plain,
    ( $false
    | spl13_2
    | ~ spl13_4 ),
    inference(subsumption_resolution,[],[f171,f30]) ).

thf(f171,plain,
    ( ( $true
     != ( sK0 @ sK8 @ sK8 ) )
    | spl13_2
    | ~ spl13_4 ),
    inference(trivial_inequality_removal,[],[f163]) ).

thf(f163,plain,
    ( ( $true = $false )
    | ( $true
     != ( sK0 @ sK8 @ sK8 ) )
    | spl13_2
    | ~ spl13_4 ),
    inference(superposition,[],[f55,f155]) ).

thf(f155,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK7 )
          = $false )
        | ( $true
         != ( sK0 @ sK8 @ X0 ) ) )
    | spl13_2 ),
    inference(trivial_inequality_removal,[],[f154]) ).

thf(f154,plain,
    ( ! [X0: a] :
        ( ( ( cQ @ X0 @ sK7 )
          = $false )
        | ( $true
         != ( sK0 @ sK8 @ X0 ) )
        | ( $true != $true ) )
    | spl13_2 ),
    inference(superposition,[],[f138,f36]) ).

thf(f138,plain,
    ( ( $true
     != ( sK0 @ sK8 @ sK7 ) )
    | spl13_2 ),
    inference(trivial_inequality_removal,[],[f135]) ).

thf(f135,plain,
    ( ( $true
     != ( sK0 @ sK8 @ sK7 ) )
    | ( $true != $true )
    | spl13_2 ),
    inference(superposition,[],[f46,f130]) ).

thf(f46,plain,
    ( ( $true
     != ( cQ @ sK7 @ sK8 ) )
    | spl13_2 ),
    inference(avatar_component_clause,[],[f44]) ).

thf(f44,plain,
    ( spl13_2
  <=> ( $true
      = ( cQ @ sK7 @ sK8 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

thf(f55,plain,
    ( ( ( cQ @ sK8 @ sK7 )
      = $true )
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f53]) ).

thf(f53,plain,
    ( spl13_4
  <=> ( ( cQ @ sK8 @ sK7 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

thf(f134,plain,
    spl13_3,
    inference(avatar_contradiction_clause,[],[f133]) ).

thf(f133,plain,
    ( $false
    | spl13_3 ),
    inference(subsumption_resolution,[],[f132,f30]) ).

thf(f132,plain,
    ( ( $true
     != ( sK0 @ sK9 @ sK9 ) )
    | spl13_3 ),
    inference(trivial_inequality_removal,[],[f131]) ).

thf(f131,plain,
    ( ( $true
     != ( sK0 @ sK9 @ sK9 ) )
    | ( $true != $true )
    | spl13_3 ),
    inference(superposition,[],[f50,f130]) ).

thf(f50,plain,
    ( ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | spl13_3 ),
    inference(avatar_component_clause,[],[f48]) ).

thf(f48,plain,
    ( spl13_3
  <=> ( $true
      = ( cQ @ sK9 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

thf(f68,plain,
    ( ~ spl13_2
    | spl13_5
    | ~ spl13_3 ),
    inference(avatar_split_clause,[],[f25,f48,f57,f44]) ).

thf(f25,plain,
    ( ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | ( $true
     != ( cQ @ sK7 @ sK8 ) )
    | ( $true
      = ( cQ @ sK11 @ sK10 ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f67,plain,
    ( spl13_4
    | ~ spl13_3
    | spl13_1 ),
    inference(avatar_split_clause,[],[f21,f40,f48,f53]) ).

thf(f21,plain,
    ( ( $true
      = ( cQ @ sK10 @ sK12 ) )
    | ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | ( ( cQ @ sK8 @ sK7 )
      = $true ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f66,plain,
    ( spl13_4
    | ~ spl13_3
    | ~ spl13_6 ),
    inference(avatar_split_clause,[],[f20,f62,f48,f53]) ).

thf(f20,plain,
    ( ( ( cQ @ sK8 @ sK7 )
      = $true )
    | ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | ( ( cQ @ sK11 @ sK12 )
     != $true ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f65,plain,
    ( ~ spl13_2
    | ~ spl13_6
    | ~ spl13_3 ),
    inference(avatar_split_clause,[],[f23,f48,f62,f44]) ).

thf(f23,plain,
    ( ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | ( $true
     != ( cQ @ sK7 @ sK8 ) )
    | ( ( cQ @ sK11 @ sK12 )
     != $true ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f60,plain,
    ( spl13_4
    | spl13_5
    | ~ spl13_3 ),
    inference(avatar_split_clause,[],[f22,f48,f57,f53]) ).

thf(f22,plain,
    ( ( ( cQ @ sK8 @ sK7 )
      = $true )
    | ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | ( $true
      = ( cQ @ sK11 @ sK10 ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f51,plain,
    ( spl13_1
    | ~ spl13_2
    | ~ spl13_3 ),
    inference(avatar_split_clause,[],[f24,f48,f44,f40]) ).

thf(f24,plain,
    ( ( $true
      = ( cQ @ sK10 @ sK12 ) )
    | ( $true
     != ( cQ @ sK9 @ sK9 ) )
    | ( $true
     != ( cQ @ sK7 @ sK8 ) ) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEV028^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Jun 21 18:45:24 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.36  This is a TH0_THM_EQU_NAR problem
% 0.12/0.36  Running higher-order theorem proving
% 0.12/0.36  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
% 0.12/0.38  % (29828)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38  % (29829)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)
% 0.12/0.38  % (29830)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)
% 0.12/0.38  % (29832)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)
% 0.12/0.38  % (29831)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.38  % (29833)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)
% 0.12/0.38  % (29834)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.39  % (29831)Instruction limit reached!
% 0.12/0.39  % (29831)------------------------------
% 0.12/0.39  % (29831)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (29831)Termination reason: Unknown
% 0.12/0.39  % (29831)Termination phase: Property scanning
% 0.12/0.39  
% 0.12/0.39  % (29831)Memory used [KB]: 1023
% 0.12/0.39  % (29831)Time elapsed: 0.004 s
% 0.12/0.39  % (29831)Instructions burned: 2 (million)
% 0.12/0.39  % (29831)------------------------------
% 0.12/0.39  % (29831)------------------------------
% 0.12/0.39  % (29832)Instruction limit reached!
% 0.12/0.39  % (29832)------------------------------
% 0.12/0.39  % (29832)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (29832)Termination reason: Unknown
% 0.12/0.39  % (29832)Termination phase: Saturation
% 0.12/0.39  
% 0.12/0.39  % (29832)Memory used [KB]: 1023
% 0.12/0.39  % (29832)Time elapsed: 0.004 s
% 0.12/0.39  % (29832)Instructions burned: 3 (million)
% 0.12/0.39  % (29832)------------------------------
% 0.12/0.39  % (29832)------------------------------
% 0.12/0.39  % (29829)Instruction limit reached!
% 0.12/0.39  % (29829)------------------------------
% 0.12/0.39  % (29829)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (29829)Termination reason: Unknown
% 0.12/0.39  % (29829)Termination phase: Saturation
% 0.12/0.39  
% 0.12/0.39  % (29829)Memory used [KB]: 5500
% 0.12/0.39  % (29829)Time elapsed: 0.006 s
% 0.12/0.39  % (29829)Instructions burned: 5 (million)
% 0.12/0.39  % (29829)------------------------------
% 0.12/0.39  % (29829)------------------------------
% 0.12/0.40  % (29834)Instruction limit reached!
% 0.12/0.40  % (29834)------------------------------
% 0.12/0.40  % (29834)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40  % (29834)Termination reason: Unknown
% 0.12/0.40  % (29834)Termination phase: Saturation
% 0.12/0.40  
% 0.12/0.40  % (29834)Memory used [KB]: 5628
% 0.12/0.40  % (29834)Time elapsed: 0.015 s
% 0.12/0.40  % (29834)Instructions burned: 18 (million)
% 0.12/0.40  % (29834)------------------------------
% 0.12/0.40  % (29834)------------------------------
% 0.12/0.40  % (29836)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.12/0.40  % (29835)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)
% 0.12/0.40  % (29837)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.12/0.40  % (29835)Instruction limit reached!
% 0.12/0.40  % (29835)------------------------------
% 0.12/0.40  % (29835)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40  % (29835)Termination reason: Unknown
% 0.12/0.40  % (29835)Termination phase: Saturation
% 0.12/0.40  
% 0.12/0.40  % (29835)Memory used [KB]: 5500
% 0.12/0.40  % (29835)Time elapsed: 0.004 s
% 0.12/0.40  % (29835)Instructions burned: 3 (million)
% 0.12/0.40  % (29835)------------------------------
% 0.12/0.40  % (29835)------------------------------
% 0.12/0.40  % (29830)Instruction limit reached!
% 0.12/0.40  % (29830)------------------------------
% 0.12/0.40  % (29830)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40  % (29830)Termination reason: Unknown
% 0.12/0.40  % (29830)Termination phase: Saturation
% 0.12/0.40  
% 0.12/0.40  % (29830)Memory used [KB]: 5756
% 0.12/0.40  % (29830)Time elapsed: 0.023 s
% 0.12/0.40  % (29830)Instructions burned: 28 (million)
% 0.12/0.40  % (29830)------------------------------
% 0.12/0.40  % (29830)------------------------------
% 0.12/0.41  % (29828)First to succeed.
% 0.22/0.41  % (29828)Refutation found. Thanks to Tanya!
% 0.22/0.41  % SZS status Theorem for theBenchmark
% 0.22/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41  % (29828)------------------------------
% 0.22/0.41  % (29828)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41  % (29828)Termination reason: Refutation
% 0.22/0.41  
% 0.22/0.41  % (29828)Memory used [KB]: 6012
% 0.22/0.41  % (29828)Time elapsed: 0.031 s
% 0.22/0.41  % (29828)Instructions burned: 52 (million)
% 0.22/0.41  % (29828)------------------------------
% 0.22/0.41  % (29828)------------------------------
% 0.22/0.41  % (29827)Success in time 0.041 s
%------------------------------------------------------------------------------