TSTP Solution File: SYN417+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n007.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  : 600s
% DateTime : Thu Jul 21 08:26:05 EDT 2022

% Result   : Theorem 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   68 (  39 unt;   6 typ;   0 def)
%            Number of atoms       :  357 ( 272 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :  621 ( 164   ~;  84   |;  26   &; 326   @)
%                                         (   3 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   84 (   0   ^  70   !;  14   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_f,type,
    f: $i > $i ).

thf(tp_g,type,
    g: $i > $i ).

thf(tp_sK1_Y,type,
    sK1_Y: $i > $i ).

thf(tp_sK2_X,type,
    sK2_X: $i ).

thf(tp_sK3_Y,type,
    sK3_Y: $i > $i ).

thf(tp_sK4_X,type,
    sK4_X: $i ).

thf(1,conjecture,
    ( ? [X: $i] :
        ( ( X
          = ( f @ ( g @ X ) ) )
        & ! [Y: $i] :
            ( ( Y
              = ( f @ ( g @ Y ) ) )
           => ( X = Y ) ) )
  <=> ? [X: $i] :
        ( ( X
          = ( g @ ( f @ X ) ) )
        & ! [Y: $i] :
            ( ( Y
              = ( g @ ( f @ Y ) ) )
           => ( X = Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cute) ).

thf(2,negated_conjecture,
    ( ( ? [X: $i] :
          ( ( X
            = ( f @ ( g @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( f @ ( g @ Y ) ) )
             => ( X = Y ) ) )
    <=> ? [X: $i] :
          ( ( X
            = ( g @ ( f @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( g @ ( f @ Y ) ) )
             => ( X = Y ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [X: $i] :
          ( ( X
            = ( f @ ( g @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( f @ ( g @ Y ) ) )
             => ( X = Y ) ) )
    <=> ? [X: $i] :
          ( ( X
            = ( g @ ( f @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( g @ ( f @ Y ) ) )
             => ( X = Y ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [X: $i] :
          ( ( X
            = ( f @ ( g @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( f @ ( g @ Y ) ) )
             => ( X = Y ) ) )
     => ? [X: $i] :
          ( ( X
            = ( g @ ( f @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( g @ ( f @ Y ) ) )
             => ( X = Y ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[3]) ).

thf(5,plain,
    ( ( ? [X: $i] :
          ( ( X
            = ( g @ ( f @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( g @ ( f @ Y ) ) )
             => ( X = Y ) ) )
     => ? [X: $i] :
          ( ( X
            = ( f @ ( g @ X ) ) )
          & ! [Y: $i] :
              ( ( Y
                = ( f @ ( g @ Y ) ) )
             => ( X = Y ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[3]) ).

thf(6,plain,
    ( ( ~ ( ? [X: $i] :
              ( ( X
                = ( f @ ( g @ X ) ) )
              & ! [Y: $i] :
                  ( ( Y
                    = ( f @ ( g @ Y ) ) )
                 => ( X = Y ) ) )
         => ? [X: $i] :
              ( ( X
                = ( g @ ( f @ X ) ) )
              & ! [Y: $i] :
                  ( ( Y
                    = ( g @ ( f @ Y ) ) )
                 => ( X = Y ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ~ ( ? [X: $i] :
              ( ( X
                = ( g @ ( f @ X ) ) )
              & ! [Y: $i] :
                  ( ( Y
                    = ( g @ ( f @ Y ) ) )
                 => ( X = Y ) ) )
         => ? [X: $i] :
              ( ( X
                = ( f @ ( g @ X ) ) )
              & ! [Y: $i] :
                  ( ( Y
                    = ( f @ ( g @ Y ) ) )
                 => ( X = Y ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ! [SY4: $i] :
          ( ( SY4
           != ( f @ ( g @ SY4 ) ) )
          | ( sK2_X = SY4 ) )
      & ( sK2_X
        = ( f @ ( g @ sK2_X ) ) )
      & ! [X: $i] :
          ( ( ( ( sK1_Y @ X )
              = ( g @ ( f @ ( sK1_Y @ X ) ) ) )
            & ( X
             != ( sK1_Y @ X ) ) )
          | ( X
           != ( g @ ( f @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(9,plain,
    ( ( ! [SY5: $i] :
          ( ( SY5
           != ( g @ ( f @ SY5 ) ) )
          | ( sK4_X = SY5 ) )
      & ( sK4_X
        = ( g @ ( f @ sK4_X ) ) )
      & ! [X: $i] :
          ( ( ( ( sK3_Y @ X )
              = ( f @ ( g @ ( sK3_Y @ X ) ) ) )
            & ( X
             != ( sK3_Y @ X ) ) )
          | ( X
           != ( f @ ( g @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(10,plain,
    ( ( ! [SY4: $i] :
          ( ( SY4
           != ( f @ ( g @ SY4 ) ) )
          | ( sK2_X = SY4 ) )
      & ( sK2_X
        = ( f @ ( g @ sK2_X ) ) )
      & ! [X: $i] :
          ( ( ( ( sK1_Y @ X )
              = ( g @ ( f @ ( sK1_Y @ X ) ) ) )
            & ( X
             != ( sK1_Y @ X ) ) )
          | ( X
           != ( g @ ( f @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ( SX0
                       != ( f @ ( g @ SX0 ) ) )
                      | ( sK2_X = SX0 ) )
                | ( sK2_X
                 != ( f @ ( g @ sK2_X ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( ( ( sK1_Y @ SX0 )
                     != ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
                    | ~ ( ( SX0
                         != ( sK1_Y @ SX0 ) ) ) )
                | ( SX0
                 != ( g @ ( f @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ( SX0
                   != ( f @ ( g @ SX0 ) ) )
                  | ( sK2_X = SX0 ) )
            | ( sK2_X
             != ( f @ ( g @ sK2_X ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( ( ( sK1_Y @ SX0 )
                 != ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
                | ~ ( ( SX0
                     != ( sK1_Y @ SX0 ) ) ) )
            | ( SX0
             != ( g @ ( f @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ( SX0
                   != ( f @ ( g @ SX0 ) ) )
                  | ( sK2_X = SX0 ) )
            | ( sK2_X
             != ( f @ ( g @ sK2_X ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ( ( sK1_Y @ SX0 )
                 != ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
                | ~ ( ( SX0
                     != ( sK1_Y @ SX0 ) ) ) )
            | ( SX0
             != ( g @ ( f @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( SX0
                 != ( f @ ( g @ SX0 ) ) )
                | ( sK2_X = SX0 ) )
          | ( sK2_X
           != ( f @ ( g @ sK2_X ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ( ( sK1_Y @ SX0 )
               != ( g @ ( f @ ( sK1_Y @ SX0 ) ) ) )
              | ~ ( ( SX0
                   != ( sK1_Y @ SX0 ) ) ) )
          | ( SX0
           != ( g @ ( f @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0
             != ( f @ ( g @ SX0 ) ) )
            | ( sK2_X = SX0 ) )
      | ( sK2_X
       != ( f @ ( g @ sK2_X ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV1: $i] :
      ( ( ~ ( ( ( sK1_Y @ SV1 )
             != ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
            | ~ ( ( SV1
                 != ( sK1_Y @ SV1 ) ) ) )
        | ( SV1
         != ( g @ ( f @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0
             != ( f @ ( g @ SX0 ) ) )
            | ( sK2_X = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ( sK2_X
       != ( f @ ( g @ sK2_X ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ( ( sK1_Y @ SV1 )
               != ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
              | ~ ( ( SV1
                   != ( sK1_Y @ SV1 ) ) ) ) )
        = $true )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0
           != ( f @ ( g @ SX0 ) ) )
          | ( sK2_X = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(23,plain,
    ( ( sK2_X
      = ( f @ ( g @ sK2_X ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: $i] :
      ( ( ( ( ( sK1_Y @ SV1 )
           != ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
          | ~ ( ( SV1
               != ( sK1_Y @ SV1 ) ) ) )
        = $false )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV2: $i] :
      ( ( ( SV2
         != ( f @ ( g @ SV2 ) ) )
        | ( sK2_X = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV1: $i] :
      ( ( ( ( ( sK1_Y @ SV1 )
           != ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) ) )
        = $false )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ( SV1
               != ( sK1_Y @ SV1 ) ) ) )
        = $false )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV2: $i] :
      ( ( ( ( SV2
           != ( f @ ( g @ SV2 ) ) ) )
        = $true )
      | ( ( sK2_X = SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV1: $i] :
      ( ( ( ( sK1_Y @ SV1 )
          = ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
        = $true )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV1: $i] :
      ( ( ( ( SV1
           != ( sK1_Y @ SV1 ) ) )
        = $true )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ( SV2
          = ( f @ ( g @ SV2 ) ) )
        = $false )
      | ( ( sK2_X = SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV1: $i] :
      ( ( ( SV1
          = ( g @ ( f @ SV1 ) ) )
        = $false )
      | ( ( ( sK1_Y @ SV1 )
          = ( g @ ( f @ ( sK1_Y @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(33,plain,
    ! [SV1: $i] :
      ( ( ( SV1
          = ( sK1_Y @ SV1 ) )
        = $false )
      | ( ( ( SV1
           != ( g @ ( f @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV1: $i] :
      ( ( ( SV1
          = ( g @ ( f @ SV1 ) ) )
        = $false )
      | ( ( SV1
          = ( sK1_Y @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(35,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[23,34,32,31]) ).

thf(36,plain,
    ( ( ! [SY5: $i] :
          ( ( SY5
           != ( g @ ( f @ SY5 ) ) )
          | ( sK4_X = SY5 ) )
      & ( sK4_X
        = ( g @ ( f @ sK4_X ) ) )
      & ! [X: $i] :
          ( ( ( ( sK3_Y @ X )
              = ( f @ ( g @ ( sK3_Y @ X ) ) ) )
            & ( X
             != ( sK3_Y @ X ) ) )
          | ( X
           != ( f @ ( g @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(37,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ( SX0
                       != ( g @ ( f @ SX0 ) ) )
                      | ( sK4_X = SX0 ) )
                | ( sK4_X
                 != ( g @ ( f @ sK4_X ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( ( ( sK3_Y @ SX0 )
                     != ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
                    | ~ ( ( SX0
                         != ( sK3_Y @ SX0 ) ) ) )
                | ( SX0
                 != ( f @ ( g @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(38,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ( SX0
                   != ( g @ ( f @ SX0 ) ) )
                  | ( sK4_X = SX0 ) )
            | ( sK4_X
             != ( g @ ( f @ sK4_X ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( ( ( sK3_Y @ SX0 )
                 != ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
                | ~ ( ( SX0
                     != ( sK3_Y @ SX0 ) ) ) )
            | ( SX0
             != ( f @ ( g @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(39,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ( SX0
                   != ( g @ ( f @ SX0 ) ) )
                  | ( sK4_X = SX0 ) )
            | ( sK4_X
             != ( g @ ( f @ sK4_X ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(40,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ( ( sK3_Y @ SX0 )
                 != ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
                | ~ ( ( SX0
                     != ( sK3_Y @ SX0 ) ) ) )
            | ( SX0
             != ( f @ ( g @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( SX0
                 != ( g @ ( f @ SX0 ) ) )
                | ( sK4_X = SX0 ) )
          | ( sK4_X
           != ( g @ ( f @ sK4_X ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ( ( sK3_Y @ SX0 )
               != ( f @ ( g @ ( sK3_Y @ SX0 ) ) ) )
              | ~ ( ( SX0
                   != ( sK3_Y @ SX0 ) ) ) )
          | ( SX0
           != ( f @ ( g @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0
             != ( g @ ( f @ SX0 ) ) )
            | ( sK4_X = SX0 ) )
      | ( sK4_X
       != ( g @ ( f @ sK4_X ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(44,plain,
    ! [SV3: $i] :
      ( ( ~ ( ( ( sK3_Y @ SV3 )
             != ( f @ ( g @ ( sK3_Y @ SV3 ) ) ) )
            | ~ ( ( SV3
                 != ( sK3_Y @ SV3 ) ) ) )
        | ( SV3
         != ( f @ ( g @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(45,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0
             != ( g @ ( f @ SX0 ) ) )
            | ( sK4_X = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(46,plain,
    ( ( ( sK4_X
       != ( g @ ( f @ sK4_X ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( ( sK3_Y @ SV3 )
               != ( f @ ( g @ ( sK3_Y @ SV3 ) ) ) )
              | ~ ( ( SV3
                   != ( sK3_Y @ SV3 ) ) ) ) )
        = $true )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(48,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0
           != ( g @ ( f @ SX0 ) ) )
          | ( sK4_X = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(49,plain,
    ( ( sK4_X
      = ( g @ ( f @ sK4_X ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV3: $i] :
      ( ( ( ( ( sK3_Y @ SV3 )
           != ( f @ ( g @ ( sK3_Y @ SV3 ) ) ) )
          | ~ ( ( SV3
               != ( sK3_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV4: $i] :
      ( ( ( SV4
         != ( g @ ( f @ SV4 ) ) )
        | ( sK4_X = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV3: $i] :
      ( ( ( ( ( sK3_Y @ SV3 )
           != ( f @ ( g @ ( sK3_Y @ SV3 ) ) ) ) )
        = $false )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(53,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( SV3
               != ( sK3_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV4: $i] :
      ( ( ( ( SV4
           != ( g @ ( f @ SV4 ) ) ) )
        = $true )
      | ( ( sK4_X = SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV3: $i] :
      ( ( ( ( sK3_Y @ SV3 )
          = ( f @ ( g @ ( sK3_Y @ SV3 ) ) ) )
        = $true )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(56,plain,
    ! [SV3: $i] :
      ( ( ( ( SV3
           != ( sK3_Y @ SV3 ) ) )
        = $true )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(57,plain,
    ! [SV4: $i] :
      ( ( ( SV4
          = ( g @ ( f @ SV4 ) ) )
        = $false )
      | ( ( sK4_X = SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(58,plain,
    ! [SV3: $i] :
      ( ( ( SV3
          = ( f @ ( g @ SV3 ) ) )
        = $false )
      | ( ( ( sK3_Y @ SV3 )
          = ( f @ ( g @ ( sK3_Y @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(59,plain,
    ! [SV3: $i] :
      ( ( ( SV3
          = ( sK3_Y @ SV3 ) )
        = $false )
      | ( ( ( SV3
           != ( f @ ( g @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(60,plain,
    ! [SV3: $i] :
      ( ( ( SV3
          = ( f @ ( g @ SV3 ) ) )
        = $false )
      | ( ( SV3
          = ( sK3_Y @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(61,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[49,60,58,57]) ).

thf(62,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[61,35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jul 12 02:26:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.40  
% 0.19/0.40  ********************************
% 0.19/0.40  *   All subproblems solved!    *
% 0.19/0.40  ********************************
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40  
% 0.19/0.40  %**** Beginning of derivation protocol ****
% 0.19/0.40  % SZS output start CNFRefutation
% See solution above
% 0.19/0.40  
% 0.19/0.40  %**** End of derivation protocol ****
% 0.19/0.40  %**** no. of clauses in derivation: 62 ****
% 0.19/0.40  %**** clause counter: 61 ****
% 0.19/0.40  
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------