TSTP Solution File: SYO245^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO245^5 : 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 : n019.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 09:03:38 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   68 (   2 unt;  11 typ;   0 def)
%            Number of atoms       :  399 ( 191 equ;   0 cnn)
%            Maximal formula atoms :    6 (   7 avg)
%            Number of connectives :  860 ( 155   ~;  88   |;  71   &; 485   @)
%                                         (   2 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  213 ( 213   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  13 usr;   5 con; 0-2 aty)
%                                         (   0  !!;  39  ??;   0 @@+;   0 @@-)
%            Number of variables   :  187 (  83   ^  73   !;  30   ?; 187   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_10,type,
    sK0: ( ( $i > $o ) > $i ) > $i > $o ).

thf(func_def_11,type,
    sK1: ( $i > $o ) > $i ).

thf(func_def_13,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK4: $i > $i > $o ).

thf(func_def_15,type,
    sK5: $i > $o ).

thf(func_def_16,type,
    sK6: $i > $o ).

thf(func_def_17,type,
    sK7: $i > $i > $o ).

thf(func_def_18,type,
    sK8: $i > $i > $o ).

thf(func_def_19,type,
    sK9: $i > $o ).

thf(func_def_20,type,
    sK10: $i > $o ).

thf(func_def_21,type,
    sK11: $i > $o ).

thf(f201,plain,
    $false,
    inference(avatar_sat_refutation,[],[f26,f170,f199]) ).

thf(f199,plain,
    ( spl2_1
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f196,f23,f20]) ).

thf(f20,plain,
    ( spl2_1
  <=> ! [X1: $i > $o] :
        ( ( ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) )
         != ( sK1 @ X1 ) )
        | ( $true
          = ( X1 @ ( sK1 @ X1 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f23,plain,
    ( spl2_2
  <=> ! [X0: $i > $o] :
        ( ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) )
        | ( ( ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ( ( sK1 @ Y1 )
                      = Y0 )
                    & ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
          = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f196,plain,
    ( ! [X0: $i > $o] :
        ( ( $true
          = ( X0 @ ( sK1 @ X0 ) ) )
        | ( ( sK1 @ X0 )
         != ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) ) ) )
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f193]) ).

thf(f193,plain,
    ( ! [X0: $i > $o] :
        ( ( $true
          = ( X0 @ ( sK1 @ X0 ) ) )
        | ( ( sK1 @ X0 )
         != ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) ) )
        | ( $true != $true ) )
    | ~ spl2_2 ),
    inference(superposition,[],[f15,f91]) ).

thf(f91,plain,
    ( ( $true
      = ( sK0 @ sK1 @ ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f90]) ).

thf(f90,plain,
    ( ( ( sK1 @ ( sK0 @ sK1 ) )
     != ( sK1 @ ( sK0 @ sK1 ) ) )
    | ( $true != $true )
    | ( $true
      = ( sK0 @ sK1 @ ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(equality_factoring,[],[f78]) ).

thf(f78,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( $true
          = ( sK0 @ sK1 @ X1 ) )
        | ( $true
          = ( X0 @ ( sK1 @ X0 ) ) )
        | ( ( sK1 @ X0 )
         != X1 ) )
    | ~ spl2_2 ),
    inference(equality_resolution,[],[f43]) ).

thf(f43,plain,
    ( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
        ( ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) )
        | ( ( sK1 @ X2 )
         != X1 )
        | ( ( X0 @ X1 )
          = $true )
        | ( $true
          = ( X2 @ ( sK1 @ X2 ) ) ) )
    | ~ spl2_2 ),
    inference(equality_proxy_clausification,[],[f42]) ).

thf(f42,plain,
    ( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
        ( ( ( ( sK1 @ X2 )
            = X1 )
          = $false )
        | ( ( X0 @ X1 )
          = $true )
        | ( $true
          = ( X2 @ ( sK1 @ X2 ) ) )
        | ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(not_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
        ( ( ( X0 @ X1 )
          = $true )
        | ( ( ~ ( X2 @ ( sK1 @ X2 ) ) )
          = $false )
        | ( ( ( sK1 @ X2 )
            = X1 )
          = $false )
        | ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
        ( ( ( X0 @ X1 )
          = $true )
        | ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) )
        | ( $false
          = ( ( ( sK1 @ X2 )
              = X1 )
            & ~ ( X2 @ ( sK1 @ X2 ) ) ) ) )
    | ~ spl2_2 ),
    inference(beta_eta_normalization,[],[f39]) ).

thf(f39,plain,
    ( ! [X2: $i > $o,X0: $i > $o,X1: $i] :
        ( ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) )
        | ( $false
          = ( ^ [Y0: $i > $o] :
                ( ( ( sK1 @ Y0 )
                  = X1 )
                & ~ ( Y0 @ ( sK1 @ Y0 ) ) )
            @ X2 ) )
        | ( ( X0 @ X1 )
          = $true ) )
    | ~ spl2_2 ),
    inference(pi_clausification,[],[f31]) ).

thf(f31,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( ( ?? @ ( $i > $o )
            @ ^ [Y0: $i > $o] :
                ( ( ( sK1 @ Y0 )
                  = X1 )
                & ~ ( Y0 @ ( sK1 @ Y0 ) ) ) )
          = $false )
        | ( ( X0 @ X1 )
          = $true )
        | ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(binary_proxy_clausification,[],[f30]) ).

thf(f30,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( ( X0 @ X1 )
          = ( ?? @ ( $i > $o )
            @ ^ [Y0: $i > $o] :
                ( ( ( sK1 @ Y0 )
                  = X1 )
                & ~ ( Y0 @ ( sK1 @ Y0 ) ) ) ) )
        | ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(beta_eta_normalization,[],[f27]) ).

thf(f27,plain,
    ( ! [X0: $i > $o,X1: $i] :
        ( ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) )
        | ( ( X0 @ X1 )
          = ( ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ( ( sK1 @ Y1 )
                      = Y0 )
                    & ~ ( Y1 @ ( sK1 @ Y1 ) ) ) )
            @ X1 ) ) )
    | ~ spl2_2 ),
    inference(argument_congruence,[],[f24]) ).

thf(f24,plain,
    ( ! [X0: $i > $o] :
        ( ( ( ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ( ( sK1 @ Y1 )
                      = Y0 )
                    & ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
          = X0 )
        | ( ( sK1 @ X0 )
         != ( sK1 @ ( sK0 @ sK1 ) ) ) )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f23]) ).

thf(f15,plain,
    ! [X2: $i > $o,X0: ( $i > $o ) > $i] :
      ( ( $true
       != ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
      | ( $true
        = ( X2 @ ( X0 @ X2 ) ) )
      | ( ( X0
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( X0 @ Y1 ) )
                  & ( ( X0 @ Y1 )
                    = Y0 ) ) ) )
       != ( X0 @ X2 ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ! [X0: ( $i > $o ) > $i] :
        ( ( ( $true
           != ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
          & ( ( X0
              @ ^ [Y0: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y1: $i > $o] :
                      ( ( ( X0 @ Y1 )
                        = Y0 )
                      & ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) )
            = ( X0 @ ( sK0 @ X0 ) ) ) )
        | ! [X2: $i > $o] :
            ( ( ( X0
                @ ^ [Y0: $i] :
                    ( ?? @ ( $i > $o )
                    @ ^ [Y1: $i > $o] :
                        ( ~ ( Y1 @ ( X0 @ Y1 ) )
                        & ( ( X0 @ Y1 )
                          = Y0 ) ) ) )
             != ( X0 @ X2 ) )
            | ( $true
              = ( X2 @ ( X0 @ X2 ) ) ) ) )
    & ! [X4: $i > $o,X5: $i > $o] :
        ( ( X4 = X5 )
        | ( ( sK1 @ X5 )
         != ( sK1 @ X4 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).

thf(f10,plain,
    ! [X0: ( $i > $o ) > $i] :
      ( ? [X1: $i > $o] :
          ( ( ( X1 @ ( X0 @ X1 ) )
           != $true )
          & ( ( X0 @ X1 )
            = ( X0
              @ ^ [Y0: $i] :
                  ( ?? @ ( $i > $o )
                  @ ^ [Y1: $i > $o] :
                      ( ( ( X0 @ Y1 )
                        = Y0 )
                      & ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) ) )
     => ( ( $true
         != ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
        & ( ( X0
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ( ( X0 @ Y1 )
                      = Y0 )
                    & ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) )
          = ( X0 @ ( sK0 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X3: ( $i > $o ) > $i] :
      ! [X4: $i > $o,X5: $i > $o] :
        ( ( X4 = X5 )
        | ( ( X3 @ X5 )
         != ( X3 @ X4 ) ) )
   => ! [X5: $i > $o,X4: $i > $o] :
        ( ( X4 = X5 )
        | ( ( sK1 @ X5 )
         != ( sK1 @ X4 ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

thf(f7,plain,
    ~ ( ! [X0: ( $i > $o ) > $i] :
          ( ? [X1: $i > $o] :
              ( ( ( X0 @ X1 )
                = ( X0
                  @ ^ [Y0: $i] :
                      ( ?? @ ( $i > $o )
                      @ ^ [Y1: $i > $o] :
                          ( ~ ( Y1 @ ( X0 @ Y1 ) )
                          & ( ( X0 @ Y1 )
                            = Y0 ) ) ) ) )
              & ( ( X1 @ ( X0 @ X1 ) )
               != $true ) )
         => ? [X2: $i > $o] :
              ( ( $true
               != ( X2 @ ( X0 @ X2 ) ) )
              & ( ( X0 @ X2 )
                = ( X0
                  @ ^ [Y0: $i] :
                      ( ?? @ ( $i > $o )
                      @ ^ [Y1: $i > $o] :
                          ( ( ( X0 @ Y1 )
                            = Y0 )
                          & ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) ) ) )
     => ~ ? [X3: ( $i > $o ) > $i] :
          ! [X4: $i > $o,X5: $i > $o] :
            ( ( ( X3 @ X5 )
              = ( X3 @ X4 ) )
           => ( X4 = X5 ) ) ),
    inference(flattening,[],[f6]) ).

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

thf(f5,plain,
    ~ ( ! [X0: ( $i > $o ) > $i] :
          ( ? [X1: $i > $o] :
              ( ( ( X0 @ X1 )
                = ( X0
                  @ ^ [Y0: $i] :
                      ( ?? @ ( $i > $o )
                      @ ^ [Y1: $i > $o] :
                          ( ~ ( Y1 @ ( X0 @ Y1 ) )
                          & ( ( X0 @ Y1 )
                            = Y0 ) ) ) ) )
              & ( ( X1 @ ( X0 @ X1 ) )
               != $true ) )
         => ? [X4: $i > $o] :
              ( ( ( X0 @ X4 )
                = ( X0
                  @ ^ [Y0: $i] :
                      ( ?? @ ( $i > $o )
                      @ ^ [Y1: $i > $o] :
                          ( ( ( X0 @ Y1 )
                            = Y0 )
                          & ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
              & ( $true
               != ( X4 @ ( X0 @ X4 ) ) ) ) )
     => ~ ? [X7: ( $i > $o ) > $i] :
          ! [X8: $i > $o,X9: $i > $o] :
            ( ( ( X7 @ X9 )
              = ( X7 @ X8 ) )
           => ( X8 = X9 ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ! [X0: ( $i > $o ) > $i] :
          ( ? [X1: $i > $o] :
              ( ( ( X0 @ X1 )
                = ( X0
                  @ ^ [X2: $i] :
                    ? [X3: $i > $o] :
                      ( ( ( X0 @ X3 )
                        = X2 )
                      & ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
              & ~ ( X1 @ ( X0 @ X1 ) ) )
         => ? [X4: $i > $o] :
              ( ( ( X0 @ X4 )
                = ( X0
                  @ ^ [X5: $i] :
                    ? [X6: $i > $o] :
                      ( ~ ( X6 @ ( X0 @ X6 ) )
                      & ( ( X0 @ X6 )
                        = X5 ) ) ) )
              & ~ ( X4 @ ( X0 @ X4 ) ) ) )
     => ~ ? [X7: ( $i > $o ) > $i] :
          ! [X8: $i > $o,X9: $i > $o] :
            ( ( ( X7 @ X9 )
              = ( X7 @ X8 ) )
           => ( X8 = X9 ) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ( ! [X0: ( $i > $o ) > $i] :
        ( ? [X1: $i > $o] :
            ( ( ( X0 @ X1 )
              = ( X0
                @ ^ [X2: $i] :
                  ? [X3: $i > $o] :
                    ( ( ( X0 @ X3 )
                      = X2 )
                    & ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
            & ~ ( X1 @ ( X0 @ X1 ) ) )
       => ? [X1: $i > $o] :
            ( ( ( X0 @ X1 )
              = ( X0
                @ ^ [X2: $i] :
                  ? [X3: $i > $o] :
                    ( ~ ( X3 @ ( X0 @ X3 ) )
                    & ( ( X0 @ X3 )
                      = X2 ) ) ) )
            & ~ ( X1 @ ( X0 @ X1 ) ) ) )
   => ~ ? [X0: ( $i > $o ) > $i] :
        ! [X4: $i > $o,X5: $i > $o] :
          ( ( ( X0 @ X4 )
            = ( X0 @ X5 ) )
         => ( X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM193A) ).

thf(f170,plain,
    ~ spl2_1,
    inference(avatar_contradiction_clause,[],[f169]) ).

thf(f169,plain,
    ( $false
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f168]) ).

thf(f168,plain,
    ( ( $true = $false )
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f148,f125]) ).

thf(f125,plain,
    ( ( $false
      = ( sK9 @ ( sK1 @ sK5 ) ) )
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f123,f124]) ).

thf(f124,plain,
    ( ( ( sK1 @ sK9 )
      = ( sK1 @ sK5 ) )
    | ~ spl2_1 ),
    inference(equality_proxy_clausification,[],[f121]) ).

thf(f121,plain,
    ( ( $true
      = ( ( sK1 @ sK9 )
        = ( sK1 @ sK5 ) ) )
    | ~ spl2_1 ),
    inference(binary_proxy_clausification,[],[f120]) ).

thf(f120,plain,
    ( ( $true
      = ( ~ ( sK9 @ ( sK1 @ sK9 ) )
        & ( ( sK1 @ sK9 )
          = ( sK1 @ sK5 ) ) ) )
    | ~ spl2_1 ),
    inference(beta_eta_normalization,[],[f119]) ).

thf(f119,plain,
    ( ( $true
      = ( ^ [Y0: $i > $o] :
            ( ~ ( Y0 @ ( sK1 @ Y0 ) )
            & ( ( sK1 @ Y0 )
              = ( sK1 @ sK5 ) ) )
        @ sK9 ) )
    | ~ spl2_1 ),
    inference(sigma_clausification,[],[f118]) ).

thf(f118,plain,
    ( ( ( ?? @ ( $i > $o )
        @ ^ [Y0: $i > $o] :
            ( ~ ( Y0 @ ( sK1 @ Y0 ) )
            & ( ( sK1 @ Y0 )
              = ( sK1 @ sK5 ) ) ) )
      = $true )
    | ~ spl2_1 ),
    inference(beta_eta_normalization,[],[f117]) ).

thf(f117,plain,
    ( ( $true
      = ( ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) )
        @ ( sK1 @ sK5 ) ) )
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f99]) ).

thf(f99,plain,
    ( ( $true
      = ( ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) )
        @ ( sK1 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
     != ( sK1 @ sK5 ) )
    | ~ spl2_1 ),
    inference(superposition,[],[f21,f65]) ).

thf(f65,plain,
    ( ( ( sK1
        @ ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) ) )
      = ( sK1 @ sK5 ) )
    | ~ spl2_1 ),
    inference(equality_proxy_clausification,[],[f62]) ).

thf(f62,plain,
    ( ( ( ( sK1 @ sK5 )
        = ( sK1
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                  & ( ( sK1 @ Y1 )
                    = Y0 ) ) ) ) )
      = $true )
    | ~ spl2_1 ),
    inference(binary_proxy_clausification,[],[f61]) ).

thf(f61,plain,
    ( ( $true
      = ( ~ ( sK5 @ ( sK1 @ sK5 ) )
        & ( ( sK1 @ sK5 )
          = ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) ) ) ) )
    | ~ spl2_1 ),
    inference(beta_eta_normalization,[],[f60]) ).

thf(f60,plain,
    ( ( $true
      = ( ^ [Y0: $i > $o] :
            ( ~ ( Y0 @ ( sK1 @ Y0 ) )
            & ( ( sK1 @ Y0 )
              = ( sK1
                @ ^ [Y1: $i] :
                    ( ?? @ ( $i > $o )
                    @ ^ [Y2: $i > $o] :
                        ( ~ ( Y2 @ ( sK1 @ Y2 ) )
                        & ( ( sK1 @ Y2 )
                          = Y1 ) ) ) ) ) )
        @ sK5 ) )
    | ~ spl2_1 ),
    inference(sigma_clausification,[],[f59]) ).

thf(f59,plain,
    ( ( $true
      = ( ?? @ ( $i > $o )
        @ ^ [Y0: $i > $o] :
            ( ~ ( Y0 @ ( sK1 @ Y0 ) )
            & ( ( sK1 @ Y0 )
              = ( sK1
                @ ^ [Y1: $i] :
                    ( ?? @ ( $i > $o )
                    @ ^ [Y2: $i > $o] :
                        ( ~ ( Y2 @ ( sK1 @ Y2 ) )
                        & ( ( sK1 @ Y2 )
                          = Y1 ) ) ) ) ) ) ) )
    | ~ spl2_1 ),
    inference(beta_eta_normalization,[],[f58]) ).

thf(f58,plain,
    ( ( $true
      = ( ^ [Y0: $i] :
            ( ?? @ ( $i > $o )
            @ ^ [Y1: $i > $o] :
                ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                & ( ( sK1 @ Y1 )
                  = Y0 ) ) )
        @ ( sK1
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                  & ( ( sK1 @ Y1 )
                    = Y0 ) ) ) ) ) )
    | ~ spl2_1 ),
    inference(equality_resolution,[],[f21]) ).

thf(f21,plain,
    ( ! [X1: $i > $o] :
        ( ( ( sK1
            @ ^ [Y0: $i] :
                ( ?? @ ( $i > $o )
                @ ^ [Y1: $i > $o] :
                    ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                    & ( ( sK1 @ Y1 )
                      = Y0 ) ) ) )
         != ( sK1 @ X1 ) )
        | ( $true
          = ( X1 @ ( sK1 @ X1 ) ) ) )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f20]) ).

thf(f123,plain,
    ( ( ( sK9 @ ( sK1 @ sK9 ) )
      = $false )
    | ~ spl2_1 ),
    inference(not_proxy_clausification,[],[f122]) ).

thf(f122,plain,
    ( ( ( ~ ( sK9 @ ( sK1 @ sK9 ) ) )
      = $true )
    | ~ spl2_1 ),
    inference(binary_proxy_clausification,[],[f120]) ).

thf(f148,plain,
    ( ( $true
      = ( sK9 @ ( sK1 @ sK5 ) ) )
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f144]) ).

thf(f144,plain,
    ( ( $true
      = ( sK9 @ ( sK1 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
     != ( sK1 @ sK5 ) )
    | ~ spl2_1 ),
    inference(superposition,[],[f103,f124]) ).

thf(f103,plain,
    ( ! [X0: $i > $o] :
        ( ( ( sK1 @ X0 )
         != ( sK1 @ sK5 ) )
        | ( $true
          = ( X0 @ ( sK1 @ X0 ) ) ) )
    | ~ spl2_1 ),
    inference(superposition,[],[f21,f65]) ).

thf(f26,plain,
    ( spl2_2
    | spl2_1 ),
    inference(avatar_split_clause,[],[f17,f20,f23]) ).

thf(f17,plain,
    ! [X0: $i > $o,X1: $i > $o] :
      ( ( ( sK1
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( sK1 @ Y1 ) )
                  & ( ( sK1 @ Y1 )
                    = Y0 ) ) ) )
       != ( sK1 @ X1 ) )
      | ( ( sK1 @ X0 )
       != ( sK1 @ ( sK0 @ sK1 ) ) )
      | ( $true
        = ( X1 @ ( sK1 @ X1 ) ) )
      | ( ( ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ( ( sK1 @ Y1 )
                    = Y0 )
                  & ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
        = X0 ) ),
    inference(superposition,[],[f13,f14]) ).

thf(f14,plain,
    ! [X2: $i > $o,X0: ( $i > $o ) > $i] :
      ( ( ( X0
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ( ( X0 @ Y1 )
                    = Y0 )
                  & ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) )
        = ( X0 @ ( sK0 @ X0 ) ) )
      | ( $true
        = ( X2 @ ( X0 @ X2 ) ) )
      | ( ( X0
          @ ^ [Y0: $i] :
              ( ?? @ ( $i > $o )
              @ ^ [Y1: $i > $o] :
                  ( ~ ( Y1 @ ( X0 @ Y1 ) )
                  & ( ( X0 @ Y1 )
                    = Y0 ) ) ) )
       != ( X0 @ X2 ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f13,plain,
    ! [X4: $i > $o,X5: $i > $o] :
      ( ( ( sK1 @ X5 )
       != ( sK1 @ X4 ) )
      | ( X4 = X5 ) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYO245^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14  % 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
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon May 20 10:34:23 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  This is a TH0_CAX_EQU_NAR problem
% 0.14/0.35  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
% 0.14/0.36  % (26395)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)
% 0.14/0.36  % (26396)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.36  % (26397)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)
% 0.14/0.37  % (26391)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)
% 0.14/0.37  % (26394)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)
% 0.14/0.37  % (26394)Instruction limit reached!
% 0.14/0.37  % (26394)------------------------------
% 0.14/0.37  % (26394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (26394)Termination reason: Unknown
% 0.14/0.37  % (26394)Termination phase: Property scanning
% 0.14/0.37  
% 0.14/0.37  % (26394)Memory used [KB]: 895
% 0.14/0.37  % (26394)Time elapsed: 0.003 s
% 0.14/0.37  % (26394)Instructions burned: 2 (million)
% 0.14/0.37  % (26394)------------------------------
% 0.14/0.37  % (26394)------------------------------
% 0.14/0.37  % (26390)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.37  % (26391)Instruction limit reached!
% 0.14/0.37  % (26391)------------------------------
% 0.14/0.37  % (26391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (26391)Termination reason: Unknown
% 0.14/0.37  % (26391)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (26391)Memory used [KB]: 5500
% 0.14/0.37  % (26391)Time elapsed: 0.005 s
% 0.14/0.37  % (26391)Instructions burned: 4 (million)
% 0.14/0.37  % (26391)------------------------------
% 0.14/0.37  % (26391)------------------------------
% 0.14/0.37  % (26397)Instruction limit reached!
% 0.14/0.37  % (26397)------------------------------
% 0.14/0.37  % (26397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (26397)Termination reason: Unknown
% 0.14/0.37  % (26397)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (26397)Memory used [KB]: 5500
% 0.14/0.37  % (26397)Time elapsed: 0.004 s
% 0.14/0.37  % (26397)Instructions burned: 3 (million)
% 0.14/0.37  % (26397)------------------------------
% 0.14/0.37  % (26397)------------------------------
% 0.14/0.37  % (26393)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37  % (26393)Instruction limit reached!
% 0.14/0.37  % (26393)------------------------------
% 0.14/0.37  % (26393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (26393)Termination reason: Unknown
% 0.14/0.37  % (26393)Termination phase: Property scanning
% 0.14/0.37  
% 0.14/0.37  % (26393)Memory used [KB]: 895
% 0.14/0.37  % (26393)Time elapsed: 0.002 s
% 0.14/0.37  % (26393)Instructions burned: 2 (million)
% 0.14/0.37  % (26393)------------------------------
% 0.14/0.37  % (26393)------------------------------
% 0.14/0.37  % (26396)Instruction limit reached!
% 0.14/0.37  % (26396)------------------------------
% 0.14/0.37  % (26396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (26396)Termination reason: Unknown
% 0.14/0.37  % (26396)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (26396)Memory used [KB]: 5628
% 0.14/0.37  % (26396)Time elapsed: 0.010 s
% 0.14/0.37  % (26396)Instructions burned: 19 (million)
% 0.14/0.37  % (26396)------------------------------
% 0.14/0.37  % (26396)------------------------------
% 0.14/0.37  % (26392)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)
% 0.14/0.37  % (26395)First to succeed.
% 0.14/0.38  % (26395)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (26395)------------------------------
% 0.14/0.38  % (26395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (26395)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (26395)Memory used [KB]: 5628
% 0.14/0.38  % (26395)Time elapsed: 0.015 s
% 0.14/0.38  % (26395)Instructions burned: 23 (million)
% 0.14/0.38  % (26395)------------------------------
% 0.14/0.38  % (26395)------------------------------
% 0.14/0.38  % (26389)Success in time 0.024 s
% 0.14/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------