TSTP Solution File: SEV052^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV052^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% 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 : Tue May 21 04:11:51 EDT 2024

% Result   : Theorem 0.18s 0.37s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   52 (   2 unt;   5 typ;   0 def)
%            Number of atoms       :  455 ( 188 equ;   0 cnn)
%            Maximal formula atoms :    6 (   9 avg)
%            Number of connectives :  379 (  57   ~;  58   |;  28   &; 226   @)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  242 ( 242   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  248 ( 196   ^  33   !;  18   ?; 248   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% 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,[],[f49,f83,f128]) ).

thf(f128,plain,
    ( spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f127]) ).

thf(f127,plain,
    ( $false
    | spl4_1
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f126,f43]) ).

thf(f43,plain,
    ( ( ( ^ [Y0: $i] : $true )
     != ( ^ [Y0: $i] : $false ) )
    | spl4_1 ),
    inference(avatar_component_clause,[],[f42]) ).

thf(f42,plain,
    ( spl4_1
  <=> ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

thf(f126,plain,
    ( ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | spl4_1
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f125,f109]) ).

thf(f109,plain,
    ( ( ( sK0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | spl4_1 ),
    inference(subsumption_resolution,[],[f104,f43]) ).

thf(f104,plain,
    ( ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | ( ( sK0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    inference(equality_proxy_clausification,[],[f103]) ).

thf(f103,plain,
    ( ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) ) ),
    inference(equality_proxy_clausification,[],[f102]) ).

thf(f102,plain,
    ( ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true ) ),
    inference(trivial_inequality_removal,[],[f101]) ).

thf(f101,plain,
    ( ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ( $true != $true ) ),
    inference(boolean_simplification,[],[f100]) ).

thf(f100,plain,
    ( ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [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 ) )
        = ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true ) ),
    inference(beta_eta_normalization,[],[f84]) ).

thf(f84,plain,
    ( ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK1
          @ ^ [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 )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true ) ),
    inference(primitive_instantiation,[],[f15]) ).

thf(f15,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
       != $true )
      | ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
       != $true )
      | ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
         != $true )
        & ( ( X0 @ ( sK2 @ X0 ) @ ( sK0 @ X0 ) )
          = $true )
        & ( ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) )
          = $true ) )
      | ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
       != $true )
      | ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).

thf(f10,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
          ( ( ( X0 @ X2 @ X1 )
           != $true )
          & ( ( X0 @ X3 @ X1 )
            = $true )
          & ( ( X0 @ X2 @ X3 )
            = $true ) )
     => ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
         != $true )
        & ( ( X0 @ ( sK2 @ X0 ) @ ( sK0 @ X0 ) )
          = $true )
        & ( ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X4: $i > $o] :
          ( ( X0 @ X4 @ X4 )
         != $true )
     => ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
       != $true ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

thf(f5,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ( $true
         != ( X0
            @ ^ [Y0: $i] : $true
            @ ^ [Y0: $i] : $false ) )
        & ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
            ( ( ( $true
                = ( X0 @ X4 @ X5 ) )
              & ( ( X0 @ X5 @ X3 )
                = $true ) )
           => ( ( X0 @ X4 @ X3 )
              = $true ) )
        & ! [X6: $i > $o] :
            ( ( X0 @ X6 @ X6 )
            = $true ) ),
    inference(fool_elimination,[],[f4]) ).

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

thf(f2,negated_conjecture,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ~ ( 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 ) )
        & ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ~ ( 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 ) )
      & ! [X1: $i > $o] : ( X0 @ X1 @ X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120B_pme) ).

thf(f125,plain,
    ( ( ( sK0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | ~ spl4_2 ),
    inference(equality_proxy_clausification,[],[f124]) ).

thf(f124,plain,
    ( ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( sK0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl4_2 ),
    inference(equality_proxy_clausification,[],[f123]) ).

thf(f123,plain,
    ( ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ~ spl4_2 ),
    inference(trivial_inequality_removal,[],[f122]) ).

thf(f122,plain,
    ( ( $true != $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ~ spl4_2 ),
    inference(boolean_simplification,[],[f121]) ).

thf(f121,plain,
    ( ( ( ( sK0
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [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 ) )
        = ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ~ spl4_2 ),
    inference(beta_eta_normalization,[],[f114]) ).

thf(f114,plain,
    ( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK3
          @ ^ [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 )
        @ ( sK1
          @ ^ [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 )
    | ~ spl4_2 ),
    inference(superposition,[],[f14,f48]) ).

thf(f48,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f46]) ).

thf(f46,plain,
    ( spl4_2
  <=> ( ( 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_2])]) ).

thf(f14,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( X0 @ ( sK2 @ X0 ) @ ( sK0 @ X0 ) )
        = $true )
      | ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
       != $true ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f83,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f82]) ).

thf(f82,plain,
    ( $false
    | ~ spl4_1 ),
    inference(trivial_inequality_removal,[],[f81]) ).

thf(f81,plain,
    ( ( $false = $true )
    | ~ spl4_1 ),
    inference(beta_eta_normalization,[],[f80]) ).

thf(f80,plain,
    ( ! [X1: $i] :
        ( ( ^ [Y0: $i] : $true
          @ X1 )
        = ( ^ [Y0: $i] : $false
          @ X1 ) )
    | ~ spl4_1 ),
    inference(argument_congruence,[],[f44]) ).

thf(f44,plain,
    ( ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f42]) ).

thf(f49,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f40,f46,f42]) ).

thf(f40,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) ) ),
    inference(equality_proxy_clausification,[],[f39]) ).

thf(f39,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,[],[f38]) ).

thf(f38,plain,
    ( ( ( ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true ) ),
    inference(trivial_inequality_removal,[],[f37]) ).

thf(f37,plain,
    ( ( $true != $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true ) ),
    inference(boolean_simplification,[],[f36]) ).

thf(f36,plain,
    ( ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ( ( ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true ) ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ^ [Y0: $i] : $true
        @ ^ [Y0: $i] : $false )
      = $true )
    | ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true ) ),
    inference(primitive_instantiation,[],[f13]) ).

thf(f13,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) )
        = $true )
      | ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
       != $true ) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEV052^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 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
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Sun May 19 19:14:53 EDT 2024
% 0.11/0.34  % CPUTime    : 
% 0.11/0.34  This is a TH0_THM_NEQ_NAR problem
% 0.11/0.34  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35  % (18914)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)
% 0.18/0.36  % (18919)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.18/0.36  % (18920)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.18/0.36  % (18918)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)
% 0.18/0.36  % (18915)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)
% 0.18/0.36  % (18917)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)
% 0.18/0.36  % (18920)Instruction limit reached!
% 0.18/0.36  % (18920)------------------------------
% 0.18/0.36  % (18920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36  % (18920)Termination reason: Unknown
% 0.18/0.36  % (18920)Termination phase: Saturation
% 0.18/0.36  
% 0.18/0.36  % (18920)Memory used [KB]: 5500
% 0.18/0.36  % (18920)Time elapsed: 0.004 s
% 0.18/0.36  % (18920)Instructions burned: 4 (million)
% 0.18/0.36  % (18920)------------------------------
% 0.18/0.36  % (18920)------------------------------
% 0.18/0.36  % (18915)Refutation not found, incomplete strategy
% 0.18/0.36  % (18915)------------------------------
% 0.18/0.36  % (18915)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36  % (18915)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.36  
% 0.18/0.36  
% 0.18/0.36  % (18915)Memory used [KB]: 5500
% 0.18/0.36  % (18915)Time elapsed: 0.002 s
% 0.18/0.36  % (18915)Instructions burned: 2 (million)
% 0.18/0.36  % (18915)------------------------------
% 0.18/0.36  % (18915)------------------------------
% 0.18/0.36  % (18917)Instruction limit reached!
% 0.18/0.36  % (18917)------------------------------
% 0.18/0.36  % (18917)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36  % (18917)Termination reason: Unknown
% 0.18/0.36  % (18917)Termination phase: Saturation
% 0.18/0.36  
% 0.18/0.36  % (18917)Memory used [KB]: 5500
% 0.18/0.36  % (18917)Time elapsed: 0.003 s
% 0.18/0.36  % (18917)Instructions burned: 2 (million)
% 0.18/0.36  % (18917)------------------------------
% 0.18/0.36  % (18917)------------------------------
% 0.18/0.36  % (18913)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.18/0.36  % (18914)Instruction limit reached!
% 0.18/0.36  % (18914)------------------------------
% 0.18/0.36  % (18914)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36  % (18914)Termination reason: Unknown
% 0.18/0.36  % (18914)Termination phase: Saturation
% 0.18/0.36  
% 0.18/0.36  % (18914)Memory used [KB]: 5500
% 0.18/0.36  % (18914)Time elapsed: 0.004 s
% 0.18/0.36  % (18914)Instructions burned: 4 (million)
% 0.18/0.36  % (18914)------------------------------
% 0.18/0.36  % (18914)------------------------------
% 0.18/0.36  % (18918)First to succeed.
% 0.18/0.36  % (18919)Instruction limit reached!
% 0.18/0.36  % (18919)------------------------------
% 0.18/0.36  % (18919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (18919)Termination reason: Unknown
% 0.18/0.37  % (18919)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (18919)Memory used [KB]: 5628
% 0.18/0.37  % (18919)Time elapsed: 0.011 s
% 0.18/0.37  % (18919)Instructions burned: 18 (million)
% 0.18/0.37  % (18919)------------------------------
% 0.18/0.37  % (18919)------------------------------
% 0.18/0.37  % (18918)Refutation found. Thanks to Tanya!
% 0.18/0.37  % SZS status Theorem for theBenchmark
% 0.18/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.37  % (18918)------------------------------
% 0.18/0.37  % (18918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (18918)Termination reason: Refutation
% 0.18/0.37  
% 0.18/0.37  % (18918)Memory used [KB]: 5500
% 0.18/0.37  % (18918)Time elapsed: 0.011 s
% 0.18/0.37  % (18918)Instructions burned: 10 (million)
% 0.18/0.37  % (18918)------------------------------
% 0.18/0.37  % (18918)------------------------------
% 0.18/0.37  % (18912)Success in time 0.022 s
% 0.18/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------