TSTP Solution File: SEV083^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV083^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n032.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 16:01:44 EDT 2024

% Result   : Theorem 0.16s 0.33s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   48 (   2 unt;   0 typ;   0 def)
%            Number of atoms       :  474 ( 195 equ;   0 cnn)
%            Maximal formula atoms :    6 (   9 avg)
%            Number of connectives :  401 (  58   ~;  57   |;  36   &; 238   @)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  230 ( 230   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  256 ( 200   ^  37   !;  19   ?; 256   :)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_4,type,
    sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_5,type,
    sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_6,type,
    sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_7,type,
    sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_9,type,
    ph5: 
      !>[X0: $tType] : X0 ).

thf(f129,plain,
    $false,
    inference(avatar_sat_refutation,[],[f50,f80,f124,f128]) ).

thf(f128,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f127]) ).

thf(f127,plain,
    ( $false
    | ~ spl4_1 ),
    inference(trivial_inequality_removal,[],[f126]) ).

thf(f126,plain,
    ( ( $false = $true )
    | ~ spl4_1 ),
    inference(beta_eta_normalization,[],[f125]) ).

thf(f125,plain,
    ( ! [X1: $i] :
        ( ( ^ [Y0: $i] : $false
          @ X1 )
        = ( ^ [Y0: $i] : $true
          @ X1 ) )
    | ~ spl4_1 ),
    inference(argument_congruence,[],[f45]) ).

thf(f45,plain,
    ( ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f43]) ).

thf(f43,plain,
    ( spl4_1
  <=> ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

thf(f124,plain,
    ( spl4_1
    | ~ spl4_2
    | spl4_3 ),
    inference(avatar_split_clause,[],[f123,f77,f47,f43]) ).

thf(f47,plain,
    ( spl4_2
  <=> ( ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

thf(f77,plain,
    ( spl4_3
  <=> ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

thf(f123,plain,
    ( ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ~ spl4_2
    | spl4_3 ),
    inference(subsumption_resolution,[],[f101,f79]) ).

thf(f79,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | spl4_3 ),
    inference(avatar_component_clause,[],[f77]) ).

thf(f101,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ~ spl4_2 ),
    inference(equality_proxy_clausification,[],[f100]) ).

thf(f100,plain,
    ( ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl4_2 ),
    inference(equality_proxy_clausification,[],[f99]) ).

thf(f99,plain,
    ( ( $true
      = ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ~ spl4_2 ),
    inference(trivial_inequality_removal,[],[f98]) ).

thf(f98,plain,
    ( ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
      = ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true != $true )
    | ~ spl4_2 ),
    inference(boolean_simplification,[],[f97]) ).

thf(f97,plain,
    ( ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
      = ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true
     != ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl4_2 ),
    inference(beta_eta_normalization,[],[f92]) ).

thf(f92,plain,
    ( ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ^ [Y0: $i] : $true
        @ ^ [Y0: $i] : $false )
      = $true )
    | ~ spl4_2 ),
    inference(superposition,[],[f16,f49]) ).

thf(f49,plain,
    ( ( ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f47]) ).

thf(f16,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
        = $true )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true )
      | ( $true
       != ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
      | ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
          = $true )
        & ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
         != $true )
        & ( $true
          = ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).

thf(f11,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true )
     => ( $true
       != ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
          ( ( ( X0 @ X4 @ X2 )
            = $true )
          & ( ( X0 @ X3 @ X2 )
           != $true )
          & ( $true
            = ( X0 @ X3 @ X4 ) ) )
     => ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK1 @ X0 ) )
          = $true )
        & ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
         != $true )
        & ( $true
          = ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true )
      | ? [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
          ( ( ( X0 @ X4 @ X2 )
            = $true )
          & ( ( X0 @ X3 @ X2 )
           != $true )
          & ( $true
            = ( X0 @ X3 @ X4 ) ) )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true ) ),
    inference(flattening,[],[f9]) ).

thf(f9,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true )
      | ? [X4: $i > $o,X2: $i > $o,X3: $i > $o] :
          ( ( ( X0 @ X3 @ X2 )
           != $true )
          & ( ( X0 @ X4 @ X2 )
            = $true )
          & ( $true
            = ( X0 @ X3 @ X4 ) ) )
      | ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true ) ),
    inference(ennf_transformation,[],[f8]) ).

thf(f8,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ( ( X0
            @ ^ [Y0: $i] : $true
            @ ^ [Y0: $i] : $false )
         != $true )
        & ! [X4: $i > $o,X2: $i > $o,X3: $i > $o] :
            ( ( ( ( X0 @ X4 @ X2 )
                = $true )
              & ( $true
                = ( X0 @ X3 @ X4 ) ) )
           => ( ( X0 @ X3 @ X2 )
              = $true ) )
        & ! [X1: $i > $o] :
            ( ( X0 @ X1 @ X1 )
            = $true ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ! [X1: $i > $o] :
            ( ( X0 @ X1 @ X1 )
            = $true )
        & ( ( X0
            @ ^ [Y0: $i] : $true
            @ ^ [Y0: $i] : $false )
         != $true )
        & ! [X4: $i > $o,X2: $i > $o,X3: $i > $o] :
            ( ( ( ( X0 @ X4 @ X2 )
                = $true )
              & ( $true
                = ( X0 @ X3 @ X4 ) ) )
           => ( ( X0 @ X3 @ X2 )
              = $true ) ) ),
    inference(true_and_false_elimination,[],[f6]) ).

thf(f6,plain,
    ~ ( ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ! [X1: $i > $o] :
              ( ( X0 @ X1 @ X1 )
              = $true )
          & ( ( X0
              @ ^ [Y0: $i] : $true
              @ ^ [Y0: $i] : $false )
           != $true )
          & ! [X4: $i > $o,X2: $i > $o,X3: $i > $o] :
              ( ( ( ( X0 @ X4 @ X2 )
                  = $true )
                & ( $true
                  = ( X0 @ X3 @ X4 ) ) )
             => ( ( X0 @ X3 @ X2 )
                = $true ) ) )
      & $true ),
    inference(rectify,[],[f5]) ).

thf(f5,plain,
    ~ ( ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ! [X1: $i > $o] :
              ( ( X0 @ X1 @ X1 )
              = $true )
          & ( ( X0
              @ ^ [Y0: $i] : $true
              @ ^ [Y0: $i] : $false )
           != $true )
          & ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
              ( ( ( ( X0 @ X5 @ X6 )
                  = $true )
                & ( ( X0 @ X6 @ X4 )
                  = $true ) )
             => ( $true
                = ( X0 @ X5 @ X4 ) ) ) )
      & $true ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
          & ~ ( X0
              @ ^ [X2: $i] : $true
              @ ^ [X3: $i] : $false )
          & ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
              ( ( ( X0 @ X5 @ X6 )
                & ( X0 @ X6 @ X4 ) )
             => ( X0 @ X5 @ X4 ) ) )
      & $true ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
          ( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
          & ~ ( X0
              @ ^ [X1: $i] : $true
              @ ^ [X1: $i] : $false )
          & ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
              ( ( ( X0 @ X1 @ X2 )
                & ( X0 @ X2 @ X3 ) )
             => ( X0 @ X1 @ X3 ) ) )
      & $true ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
        & ~ ( X0
            @ ^ [X1: $i] : $true
            @ ^ [X1: $i] : $false )
        & ! [X3: $i > $o,X1: $i > $o,X2: $i > $o] :
            ( ( ( X0 @ X1 @ X2 )
              & ( X0 @ X2 @ X3 ) )
           => ( X0 @ X1 @ X3 ) ) )
    & $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_3_pme) ).

thf(f80,plain,
    ( ~ spl4_3
    | spl4_1 ),
    inference(avatar_split_clause,[],[f62,f43,f77]) ).

thf(f62,plain,
    ( ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    inference(equality_proxy_clausification,[],[f61]) ).

thf(f61,plain,
    ( ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ( $true
     != ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[],[f60]) ).

thf(f60,plain,
    ( ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
     != ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(trivial_inequality_removal,[],[f59]) ).

thf(f59,plain,
    ( ( $true != $true )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
     != ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(boolean_simplification,[],[f58]) ).

thf(f58,plain,
    ( ( $true
     != ( ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
     != ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f51]) ).

thf(f51,plain,
    ( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ^ [Y0: $i] : $true
        @ ^ [Y0: $i] : $false )
      = $true )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(primitive_instantiation,[],[f15]) ).

thf(f15,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) )
      | ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
       != $true )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f50,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f41,f47,f43]) ).

thf(f41,plain,
    ( ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ( ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    inference(equality_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ( ( ( ^ [Y0: $i] : $false )
      = ( ^ [Y0: $i] : $true ) )
    | ( $true
      = ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ( ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
      = ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(trivial_inequality_removal,[],[f38]) ).

thf(f38,plain,
    ( ( $true
      = ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true != $true ) ),
    inference(boolean_simplification,[],[f37]) ).

thf(f37,plain,
    ( ( $true
     != ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true
      = ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f17]) ).

thf(f17,plain,
    ( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ^ [Y0: $i] : $true
        @ ^ [Y0: $i] : $false )
      = $true ) ),
    inference(primitive_instantiation,[],[f14]) ).

thf(f14,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
        = ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true )
      | ( $true
       != ( X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : SEV083^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.10  % Command    : run_vampire %s %d THM
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Fri Jun 21 18:36:53 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.10/0.31  This is a TH0_THM_NEQ_NAR problem
% 0.10/0.31  Running higher-order theorem proving
% 0.10/0.31  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
% 0.16/0.32  % (22518)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.16/0.32  % (22519)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 (3000ds/4Mi)
% 0.16/0.32  % (22520)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 (3000ds/27Mi)
% 0.16/0.32  % (22521)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.32  % (22523)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 (3000ds/275Mi)
% 0.16/0.32  % (22522)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 (3000ds/2Mi)
% 0.16/0.32  % (22522)Instruction limit reached!
% 0.16/0.32  % (22522)------------------------------
% 0.16/0.32  % (22522)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.32  % (22522)Termination reason: Unknown
% 0.16/0.32  % (22524)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.16/0.32  % (22522)Termination phase: Saturation
% 0.16/0.32  
% 0.16/0.32  % (22522)Memory used [KB]: 895
% 0.16/0.32  % (22522)Time elapsed: 0.003 s
% 0.16/0.32  % (22522)Instructions burned: 2 (million)
% 0.16/0.32  % (22522)------------------------------
% 0.16/0.32  % (22522)------------------------------
% 0.16/0.32  % (22520)Refutation not found, incomplete strategy
% 0.16/0.32  % (22520)------------------------------
% 0.16/0.32  % (22520)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.32  % (22520)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.32  
% 0.16/0.32  
% 0.16/0.32  % (22520)Memory used [KB]: 5500
% 0.16/0.32  % (22520)Time elapsed: 0.002 s
% 0.16/0.32  % (22520)Instructions burned: 1 (million)
% 0.16/0.32  % (22520)------------------------------
% 0.16/0.32  % (22520)------------------------------
% 0.16/0.32  % (22521)Instruction limit reached!
% 0.16/0.32  % (22521)------------------------------
% 0.16/0.32  % (22521)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.32  % (22521)Termination reason: Unknown
% 0.16/0.32  % (22521)Termination phase: Saturation
% 0.16/0.32  
% 0.16/0.32  % (22521)Memory used [KB]: 5500
% 0.16/0.32  % (22521)Time elapsed: 0.004 s
% 0.16/0.32  % (22521)Instructions burned: 3 (million)
% 0.16/0.32  % (22521)------------------------------
% 0.16/0.32  % (22521)------------------------------
% 0.16/0.32  % (22519)Instruction limit reached!
% 0.16/0.32  % (22519)------------------------------
% 0.16/0.32  % (22519)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.32  % (22519)Termination reason: Unknown
% 0.16/0.32  % (22519)Termination phase: Saturation
% 0.16/0.32  
% 0.16/0.32  % (22519)Memory used [KB]: 5500
% 0.16/0.32  % (22519)Time elapsed: 0.004 s
% 0.16/0.32  % (22519)Instructions burned: 6 (million)
% 0.16/0.32  % (22519)------------------------------
% 0.16/0.32  % (22519)------------------------------
% 0.16/0.32  % (22523)First to succeed.
% 0.16/0.33  % (22523)Refutation found. Thanks to Tanya!
% 0.16/0.33  % SZS status Theorem for theBenchmark
% 0.16/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33  % (22523)------------------------------
% 0.16/0.33  % (22523)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.33  % (22523)Termination reason: Refutation
% 0.16/0.33  
% 0.16/0.33  % (22523)Memory used [KB]: 5500
% 0.16/0.33  % (22523)Time elapsed: 0.007 s
% 0.16/0.33  % (22523)Instructions burned: 9 (million)
% 0.16/0.33  % (22523)------------------------------
% 0.16/0.33  % (22523)------------------------------
% 0.16/0.33  % (22517)Success in time 0.008 s
%------------------------------------------------------------------------------