TSTP Solution File: SEV082^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV082^5 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n027.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 04:11:55 EDT 2024

% Result   : Theorem 0.16s 0.34s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   61 (   2 unt;   6 typ;   0 def)
%            Number of atoms       :  431 ( 171 equ;   0 cnn)
%            Maximal formula atoms :    6 (   7 avg)
%            Number of connectives :  424 (  70   ~;  56   |;  37   &; 247   @)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  273 ( 273   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  223 ( 150   ^  43   !;  29   ?; 223   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_4,type,
    sP0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $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_8,type,
    sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_10,type,
    ph6: 
      !>[X0: $tType] : X0 ).

thf(f88,plain,
    $false,
    inference(avatar_sat_refutation,[],[f52,f56,f76,f81,f86,f87]) ).

thf(f87,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK2
        @ ^ [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 ) ) )
    | ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(theory_tautology_sat_conflict,[]) ).

thf(f86,plain,
    ( spl5_5
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f65,f45,f83]) ).

thf(f83,plain,
    ( spl5_5
  <=> ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

thf(f45,plain,
    ( spl5_1
  <=> ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

thf(f65,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl5_1 ),
    inference(equality_proxy_clausification,[],[f64]) ).

thf(f64,plain,
    ( ( ( ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ~ spl5_1 ),
    inference(beta_eta_normalization,[],[f63]) ).

thf(f63,plain,
    ( ( ( ^ [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 ) ) )
      = $true )
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f60]) ).

thf(f60,plain,
    ( ( ( ^ [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 ) ) )
      = $true )
    | ( $true != $true )
    | ~ spl5_1 ),
    inference(superposition,[],[f20,f47]) ).

thf(f47,plain,
    ( ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f45]) ).

thf(f20,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
        = ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) )
      | ( ( sP0 @ X0 )
       != $true ) ),
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) )
         != $true )
        & ( $true
          = ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) )
        & ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
          = $true ) )
      | ( ( sP0 @ X0 )
       != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f14,f15]) ).

thf(f15,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
          ( ( ( X0 @ X1 @ X3 )
           != $true )
          & ( ( X0 @ X1 @ X2 )
            = $true )
          & ( ( X0 @ X2 @ X3 )
            = $true ) )
     => ( ( ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) )
         != $true )
        & ( $true
          = ( X0 @ ( sK1 @ X0 ) @ ( sK2 @ X0 ) ) )
        & ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f14,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
          ( ( ( X0 @ X1 @ X3 )
           != $true )
          & ( ( X0 @ X1 @ X2 )
            = $true )
          & ( ( X0 @ X2 @ X3 )
            = $true ) )
      | ( ( sP0 @ X0 )
       != $true ) ),
    inference(rectify,[],[f13]) ).

thf(f13,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X2: $i > $o,X4: $i > $o,X3: $i > $o] :
          ( ( ( X0 @ X2 @ X3 )
           != $true )
          & ( ( X0 @ X2 @ X4 )
            = $true )
          & ( ( X0 @ X4 @ X3 )
            = $true ) )
      | ( ( sP0 @ X0 )
       != $true ) ),
    inference(nnf_transformation,[],[f11]) ).

thf(f11,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X2: $i > $o,X4: $i > $o,X3: $i > $o] :
          ( ( ( X0 @ X2 @ X3 )
           != $true )
          & ( ( X0 @ X2 @ X4 )
            = $true )
          & ( ( X0 @ X4 @ X3 )
            = $true ) )
      | ( ( sP0 @ X0 )
       != $true ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f81,plain,
    ( spl5_4
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f68,f45,f78]) ).

thf(f78,plain,
    ( spl5_4
  <=> ( ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

thf(f68,plain,
    ( ( ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl5_1 ),
    inference(equality_proxy_clausification,[],[f67]) ).

thf(f67,plain,
    ( ( ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
      = $true )
    | ~ spl5_1 ),
    inference(beta_eta_normalization,[],[f66]) ).

thf(f66,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 )
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f61]) ).

thf(f61,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 != $true )
    | ~ spl5_1 ),
    inference(superposition,[],[f19,f47]) ).

thf(f19,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) )
        = $true )
      | ( ( sP0 @ X0 )
       != $true ) ),
    inference(cnf_transformation,[],[f16]) ).

thf(f76,plain,
    ( ~ spl5_3
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f71,f45,f73]) ).

thf(f73,plain,
    ( spl5_3
  <=> ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

thf(f71,plain,
    ( ( ( sK1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl5_1 ),
    inference(equality_proxy_clausification,[],[f70]) ).

thf(f70,plain,
    ( ( ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ~ spl5_1 ),
    inference(beta_eta_normalization,[],[f69]) ).

thf(f69,plain,
    ( ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl5_1 ),
    inference(trivial_inequality_removal,[],[f62]) ).

thf(f62,plain,
    ( ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK1
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true != $true )
    | ~ spl5_1 ),
    inference(superposition,[],[f21,f47]) ).

thf(f21,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( sP0 @ X0 )
       != $true )
      | ( ( X0 @ ( sK1 @ X0 ) @ ( sK3 @ X0 ) )
       != $true ) ),
    inference(cnf_transformation,[],[f16]) ).

thf(f56,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f55]) ).

thf(f55,plain,
    ( $false
    | ~ spl5_2 ),
    inference(trivial_inequality_removal,[],[f54]) ).

thf(f54,plain,
    ( ( $false = $true )
    | ~ spl5_2 ),
    inference(beta_eta_normalization,[],[f53]) ).

thf(f53,plain,
    ( ! [X1: $i] :
        ( ( ^ [Y0: $i] : $false
          @ X1 )
        = ( ^ [Y0: $i] : $true
          @ X1 ) )
    | ~ spl5_2 ),
    inference(argument_congruence,[],[f51]) ).

thf(f51,plain,
    ( ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f49]) ).

thf(f49,plain,
    ( spl5_2
  <=> ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

thf(f52,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f42,f49,f45]) ).

thf(f42,plain,
    ( ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true )
    | ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) ) ),
    inference(equality_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true ) ),
    inference(trivial_inequality_removal,[],[f40]) ).

thf(f40,plain,
    ( ( $true != $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true )
    | ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true ) ),
    inference(boolean_simplification,[],[f39]) ).

thf(f39,plain,
    ( ( ( ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true )
    | ( ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) )
      = $true ) ),
    inference(beta_eta_normalization,[],[f24]) ).

thf(f24,plain,
    ( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ^ [Y0: $i] : $true
        @ ^ [Y0: $i] : $false )
      = $true )
    | ( ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = $true )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true ) ),
    inference(primitive_instantiation,[],[f22]) ).

thf(f22,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( X0 @ ( sK4 @ X0 ) @ ( sK4 @ X0 ) ) )
      | ( ( sP0 @ X0 )
        = $true )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true ) ),
    inference(cnf_transformation,[],[f18]) ).

thf(f18,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( X0 @ ( sK4 @ X0 ) @ ( sK4 @ X0 ) ) )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true )
      | ( ( sP0 @ X0 )
        = $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f12,f17]) ).

thf(f17,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true )
     => ( $true
       != ( X0 @ ( sK4 @ X0 ) @ ( sK4 @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true )
      | ( ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false )
        = $true )
      | ( ( sP0 @ X0 )
        = $true ) ),
    inference(definition_folding,[],[f10,f11]) ).

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

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

thf(f8,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ( ( X0
            @ ^ [Y0: $i] : $true
            @ ^ [Y0: $i] : $false )
         != $true )
        & ! [X1: $i > $o] :
            ( ( X0 @ X1 @ X1 )
            = $true )
        & ! [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
            ( ( ( ( X0 @ X4 @ X3 )
                = $true )
              & ( ( X0 @ X2 @ X4 )
                = $true ) )
           => ( ( X0 @ X2 @ X3 )
              = $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 )
        & ! [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
            ( ( ( ( X0 @ X4 @ X3 )
                = $true )
              & ( ( X0 @ X2 @ X4 )
                = $true ) )
           => ( ( X0 @ X2 @ X3 )
              = $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 )
          & ! [X3: $i > $o,X2: $i > $o,X4: $i > $o] :
              ( ( ( ( X0 @ X4 @ X3 )
                  = $true )
                & ( ( X0 @ X2 @ X4 )
                  = $true ) )
             => ( ( X0 @ X2 @ X3 )
                = $true ) ) )
      | $false ),
    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] :
              ( ( ( $true
                  = ( X0 @ X4 @ X6 ) )
                & ( ( X0 @ X6 @ X5 )
                  = $true ) )
             => ( ( X0 @ X4 @ X5 )
                = $true ) ) )
      | $false ),
    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 @ X4 @ X6 )
                & ( X0 @ X6 @ X5 ) )
             => ( X0 @ X4 @ X5 ) ) )
      | $false ),
    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 )
          & ! [X1: $i > $o,X3: $i > $o,X2: $i > $o] :
              ( ( ( X0 @ X1 @ X2 )
                & ( X0 @ X2 @ X3 ) )
             => ( X0 @ X1 @ X3 ) ) )
      | $false ),
    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 )
        & ! [X1: $i > $o,X3: $i > $o,X2: $i > $o] :
            ( ( ( X0 @ X1 @ X2 )
              & ( X0 @ X2 @ X3 ) )
           => ( X0 @ X1 @ X3 ) ) )
    | $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_4_pme) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SEV082^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30  % Computer : n027.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   : Sun May 19 18:55:07 EDT 2024
% 0.15/0.31  % CPUTime    : 
% 0.15/0.31  This is a TH0_THM_NEQ_NAR problem
% 0.15/0.31  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/sandbox/benchmark/theBenchmark.p
% 0.16/0.32  % (31375)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  % (31373)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)
% 0.16/0.33  % (31374)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.33  % (31371)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.16/0.33  % (31372)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)
% 0.16/0.33  % (31374)Instruction limit reached!
% 0.16/0.33  % (31374)------------------------------
% 0.16/0.33  % (31374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (31374)Termination reason: Unknown
% 0.16/0.33  % (31374)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (31375)Instruction limit reached!
% 0.16/0.33  % (31375)------------------------------
% 0.16/0.33  % (31375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (31374)Memory used [KB]: 5500
% 0.16/0.33  % (31374)Time elapsed: 0.003 s
% 0.16/0.33  % (31374)Instructions burned: 2 (million)
% 0.16/0.33  % (31374)------------------------------
% 0.16/0.33  % (31374)------------------------------
% 0.16/0.33  % (31375)Termination reason: Unknown
% 0.16/0.33  % (31375)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (31375)Memory used [KB]: 5500
% 0.16/0.33  % (31375)Time elapsed: 0.003 s
% 0.16/0.33  % (31375)Instructions burned: 2 (million)
% 0.16/0.33  % (31375)------------------------------
% 0.16/0.33  % (31375)------------------------------
% 0.16/0.33  % (31373)Refutation not found, incomplete strategy
% 0.16/0.33  % (31373)------------------------------
% 0.16/0.33  % (31373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (31373)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.33  
% 0.16/0.33  
% 0.16/0.33  % (31373)Memory used [KB]: 5500
% 0.16/0.33  % (31377)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.16/0.33  % (31373)Time elapsed: 0.003 s
% 0.16/0.33  % (31373)Instructions burned: 2 (million)
% 0.16/0.33  % (31373)------------------------------
% 0.16/0.33  % (31373)------------------------------
% 0.16/0.33  % (31378)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)
% 0.16/0.33  % (31372)Instruction limit reached!
% 0.16/0.33  % (31372)------------------------------
% 0.16/0.33  % (31372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (31372)Termination reason: Unknown
% 0.16/0.33  % (31372)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (31372)Memory used [KB]: 5500
% 0.16/0.33  % (31372)Time elapsed: 0.005 s
% 0.16/0.33  % (31372)Instructions burned: 5 (million)
% 0.16/0.33  % (31372)------------------------------
% 0.16/0.33  % (31372)------------------------------
% 0.16/0.33  % (31378)Instruction limit reached!
% 0.16/0.33  % (31378)------------------------------
% 0.16/0.33  % (31378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (31378)Termination reason: Unknown
% 0.16/0.33  % (31378)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (31378)Memory used [KB]: 5500
% 0.16/0.33  % (31378)Time elapsed: 0.005 s
% 0.16/0.33  % (31378)Instructions burned: 4 (million)
% 0.16/0.33  % (31378)------------------------------
% 0.16/0.33  % (31378)------------------------------
% 0.16/0.33  % (31377)Instruction limit reached!
% 0.16/0.33  % (31377)------------------------------
% 0.16/0.33  % (31377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33  % (31377)Termination reason: Unknown
% 0.16/0.33  % (31377)Termination phase: Saturation
% 0.16/0.33  
% 0.16/0.33  % (31377)Memory used [KB]: 5628
% 0.16/0.33  % (31377)Time elapsed: 0.010 s
% 0.16/0.34  % (31377)Instructions burned: 18 (million)
% 0.16/0.34  % (31377)------------------------------
% 0.16/0.34  % (31377)------------------------------
% 0.16/0.34  % (31376)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)
% 0.16/0.34  % (31380)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)
% 0.16/0.34  % (31380)First to succeed.
% 0.16/0.34  % (31379)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)
% 0.16/0.34  % (31380)Refutation found. Thanks to Tanya!
% 0.16/0.34  % SZS status Theorem for theBenchmark
% 0.16/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.34  % (31380)------------------------------
% 0.16/0.34  % (31380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34  % (31380)Termination reason: Refutation
% 0.16/0.34  
% 0.16/0.34  % (31380)Memory used [KB]: 5628
% 0.16/0.34  % (31380)Time elapsed: 0.004 s
% 0.16/0.34  % (31380)Instructions burned: 4 (million)
% 0.16/0.34  % (31380)------------------------------
% 0.16/0.34  % (31380)------------------------------
% 0.16/0.34  % (31370)Success in time 0.025 s
% 0.16/0.34  % Vampire---4.8 exiting
%------------------------------------------------------------------------------