TSTP Solution File: SET600^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET600^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n020.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 : Tue Jul 19 03:03:17 EDT 2022

% Result   : Theorem 0.13s 0.42s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  198 (  57 unt;   9 typ;   0 def)
%            Number of atoms       : 1584 ( 525 equ;   0 cnn)
%            Maximal formula atoms :    4 (   8 avg)
%            Number of connectives :  887 ( 231   ~; 335   |;  15   &; 297   @)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :  209 ( 138   ^  71   !;   0   ?; 209   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $tType ).

thf(tp_sK1_X,type,
    sK1_X: a > $o ).

thf(tp_sK2_SY6,type,
    sK2_SY6: a > $o ).

thf(tp_sK3_SV3,type,
    sK3_SV3: a ).

thf(tp_sK4_SV4,type,
    sK4_SV4: a ).

thf(tp_sK5_SV5,type,
    sK5_SV5: a ).

thf(tp_sK6_SV6,type,
    sK6_SV6: a ).

thf(tp_sK7_SV7,type,
    sK7_SV7: a ).

thf(tp_sK8_SV8,type,
    sK8_SV8: a ).

thf(1,conjecture,
    ! [X: a > $o,Y: a > $o] :
      ( ( ( ^ [Xz: a] :
              ( ( X @ Xz )
              | ( Y @ Xz ) ) )
        = ( ^ [Xx: a] : $false ) )
    <=> ( ( X
          = ( ^ [Xx: a] : $false ) )
        & ( Y
          = ( ^ [Xx: a] : $false ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_59_pme) ).

thf(2,negated_conjecture,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ( ( ^ [Xz: a] :
                  ( ( X @ Xz )
                  | ( Y @ Xz ) ) )
            = ( ^ [Xx: a] : $false ) )
        <=> ( ( X
              = ( ^ [Xx: a] : $false ) )
            & ( Y
              = ( ^ [Xx: a] : $false ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X: a > $o,Y: a > $o] :
          ( ( ( ^ [Xz: a] :
                  ( ( X @ Xz )
                  | ( Y @ Xz ) ) )
            = ( ^ [Xx: a] : $false ) )
        <=> ( ( X
              = ( ^ [Xx: a] : $false ) )
            & ( Y
              = ( ^ [Xx: a] : $false ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY6: a > $o] :
          ( ( ( ^ [SY7: a] :
                  ( ( sK1_X @ SY7 )
                  | ( SY6 @ SY7 ) ) )
            = ( ^ [Xx: a] : $false ) )
        <=> ( ( sK1_X
              = ( ^ [Xx: a] : $false ) )
            & ( SY6
              = ( ^ [Xx: a] : $false ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
        = ( ^ [Xx: a] : $false ) )
    <=> ( ( sK1_X
          = ( ^ [Xx: a] : $false ) )
        & ( sK2_SY6
          = ( ^ [Xx: a] : $false ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
        = ( ^ [Xx: a] : $false ) )
     => ( ( sK1_X
          = ( ^ [Xx: a] : $false ) )
        & ( sK2_SY6
          = ( ^ [Xx: a] : $false ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(7,plain,
    ( ( ( ( sK1_X
          = ( ^ [Xx: a] : $false ) )
        & ( sK2_SY6
          = ( ^ [Xx: a] : $false ) ) )
     => ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
        = ( ^ [Xx: a] : $false ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(8,plain,
    ( ( ~ ( ( ( ^ [SY11: a] :
                  ( ( sK1_X @ SY11 )
                  | ( sK2_SY6 @ SY11 ) ) )
            = ( ^ [Xx: a] : $false ) )
         => ( ( sK1_X
              = ( ^ [Xx: a] : $false ) )
            & ( sK2_SY6
              = ( ^ [Xx: a] : $false ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ( ( ( sK1_X
              = ( ^ [Xx: a] : $false ) )
            & ( sK2_SY6
              = ( ^ [Xx: a] : $false ) ) )
         => ( ( ^ [SY11: a] :
                  ( ( sK1_X @ SY11 )
                  | ( sK2_SY6 @ SY11 ) ) )
            = ( ^ [Xx: a] : $false ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
        = ( ^ [Xx: a] : $false ) )
      & ( ( sK1_X
         != ( ^ [Xx: a] : $false ) )
        | ( sK2_SY6
         != ( ^ [Xx: a] : $false ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(11,plain,
    ( ( ( sK1_X
        = ( ^ [Xx: a] : $false ) )
      & ( sK2_SY6
        = ( ^ [Xx: a] : $false ) )
      & ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
       != ( ^ [Xx: a] : $false ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
        = ( ^ [Xx: a] : $false ) )
      & ( ( sK1_X
         != ( ^ [Xx: a] : $false ) )
        | ( sK2_SY6
         != ( ^ [Xx: a] : $false ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ~ ( ( ( ^ [SX0: a] :
                  ( ( sK1_X @ SX0 )
                  | ( sK2_SY6 @ SX0 ) ) )
           != ( ^ [SX0: a] : $false ) )
          | ~ ( ( sK1_X
               != ( ^ [SX0: a] : $false ) )
              | ( sK2_SY6
               != ( ^ [SX0: a] : $false ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ( ( ^ [SX0: a] :
              ( ( sK1_X @ SX0 )
              | ( sK2_SY6 @ SX0 ) ) )
       != ( ^ [SX0: a] : $false ) )
      | ~ ( ( sK1_X
           != ( ^ [SX0: a] : $false ) )
          | ( sK2_SY6
           != ( ^ [SX0: a] : $false ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ( ( ^ [SX0: a] :
              ( ( sK1_X @ SX0 )
              | ( sK2_SY6 @ SX0 ) ) )
       != ( ^ [SX0: a] : $false ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ~ ( ( sK1_X
           != ( ^ [SX0: a] : $false ) )
          | ( sK2_SY6
           != ( ^ [SX0: a] : $false ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ( ^ [SX0: a] :
            ( ( sK1_X @ SX0 )
            | ( sK2_SY6 @ SX0 ) ) )
      = ( ^ [SX0: a] : $false ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ( sK1_X
       != ( ^ [SX0: a] : $false ) )
      | ( sK2_SY6
       != ( ^ [SX0: a] : $false ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ! [SV1: a] :
          ( ( ( sK1_X @ SV1 )
            | ( sK2_SY6 @ SV1 ) )
          = $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ( ^ [SX0: a] :
            ( ( sK1_X @ SX0 )
            | ( sK2_SY6 @ SX0 ) ) )
      = ( ^ [SX0: a] : $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ( ( sK1_X
         != ( ^ [SX0: a] : $false ) ) )
      = $true )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 ) )
        = $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV2: a] :
      ( ( ~ ( ( sK1_X @ SV2 )
            | ( sK2_SY6 @ SV2 )
            | $false )
        | ~ ( ~ ( ( sK1_X @ SV2 )
                | ( sK2_SY6 @ SV2 ) )
            | ~ $false ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 ) )
        = $false )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ( ! [SV3: a] :
            ( ( sK1_X @ SV3 )
            = $false ) )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[23]) ).

thf(27,plain,
    ( ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ( ( sK1_X @ SV2 )
                  | ( sK2_SY6 @ SV2 ) )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[26]) ).

thf(30,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_X @ SV2 )
                  | ( sK2_SY6 @ SV2 ) )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ( ( ( ~ ( ( sK1_X @ sK3_SV3 )
            | $false )
        | ~ ( ~ ( sK1_X @ sK3_SV3 )
            | ~ $false ) )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[29]) ).

thf(33,plain,
    ( ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[29]) ).

thf(34,plain,
    ( ( ( ! [SV4: a] :
            ( ( sK2_SY6 @ SV4 )
            = $false ) )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[30]) ).

thf(35,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 ) )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_X @ SV2 )
                  | ( sK2_SY6 @ SV2 ) )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV2: a] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ( ( sK1_X @ SV2 )
                  | ( sK2_SY6 @ SV2 ) )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(38,plain,
    ( ( ( ~ ( ( sK1_X @ sK3_SV3 )
            | $false ) )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(39,plain,
    ( ( ( ~ ( ~ ( sK1_X @ sK3_SV3 )
            | ~ $false ) )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(40,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(41,plain,
    ( ( ( ( sK2_SY6 @ sK4_SV4 )
        = $false )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[34]) ).

thf(42,plain,
    ! [SV2: a] :
      ( ( ( sK1_X @ SV2 )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_X @ SV2 )
                  | ( sK2_SY6 @ SV2 ) )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV2: a] :
      ( ( ( sK2_SY6 @ SV2 )
        = $false )
      | ( ( ~ ( ~ ( ( sK1_X @ SV2 )
                  | ( sK2_SY6 @ SV2 ) )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(44,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 ) )
          | ~ $false )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(45,plain,
    ( ( ( ( sK1_X @ sK3_SV3 )
        | $false )
      = $true )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(46,plain,
    ( ( ( ~ ( sK1_X @ sK3_SV3 )
        | ~ $false )
      = $true )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(47,plain,
    ( ( ( ! [SV5: a] :
            ( ( sK2_SY6 @ SV5 )
            = $false ) )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[40]) ).

thf(48,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[40]) ).

thf(49,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK4_SV4 )
            | $false )
        | ~ ( ~ ( sK2_SY6 @ sK4_SV4 )
            | ~ $false ) )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[41]) ).

thf(50,plain,
    ( ( ( ( sK2_SY6 @ sK4_SV4 )
        = $false )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[41]) ).

thf(51,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 ) )
          | ~ $false )
        = $false )
      | ( ( sK1_X @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(52,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 ) )
          | ~ $false )
        = $false )
      | ( ( sK2_SY6 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(53,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 ) ) )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(54,plain,
    ( ( ( ~ $false )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(55,plain,
    ( ( ( sK1_X @ sK3_SV3 )
      = $true )
    | ( $false = $true )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(56,plain,
    ( ( ( ~ ( sK1_X @ sK3_SV3 ) )
      = $true )
    | ( ( ~ $false )
      = $true )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(57,plain,
    ( ( ( ( sK2_SY6 @ sK5_SV5 )
        = $false )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[47]) ).

thf(58,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK4_SV4 )
            | $false ) )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(59,plain,
    ( ( ( ~ ( ~ ( sK2_SY6 @ sK4_SV4 )
            | ~ $false ) )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(60,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 ) ) )
        = $false )
      | ( ( sK1_X @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[51]) ).

thf(61,plain,
    ! [SV2: a] :
      ( ( ( ~ $false )
        = $false )
      | ( ( sK1_X @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[51]) ).

thf(62,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( sK1_X @ SV2 )
              | ( sK2_SY6 @ SV2 ) ) )
        = $false )
      | ( ( sK2_SY6 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[52]) ).

thf(63,plain,
    ! [SV2: a] :
      ( ( ( ~ $false )
        = $false )
      | ( ( sK2_SY6 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[52]) ).

thf(64,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 ) )
        = $true )
      | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(65,plain,
    ( ( $false = $true )
    | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(66,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(67,plain,
    ( ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( ( ~ $false )
      = $true )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(68,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK5_SV5 )
            | $false )
        | ~ ( ~ ( sK2_SY6 @ sK5_SV5 )
            | ~ $false ) )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[57]) ).

thf(69,plain,
    ( ( ( ( sK2_SY6 @ sK5_SV5 )
        = $false )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[57]) ).

thf(70,plain,
    ( ( ( ( sK2_SY6 @ sK4_SV4 )
        | $false )
      = $true )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(71,plain,
    ( ( ( ~ ( sK2_SY6 @ sK4_SV4 )
        | ~ $false )
      = $true )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[59]) ).

thf(72,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 ) )
        = $true )
      | ( ( sK1_X @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(73,plain,
    ! [SV2: a] :
      ( ( $false = $true )
      | ( ( sK1_X @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[61]) ).

thf(74,plain,
    ! [SV2: a] :
      ( ( ( ( sK1_X @ SV2 )
          | ( sK2_SY6 @ SV2 ) )
        = $true )
      | ( ( sK2_SY6 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[62]) ).

thf(75,plain,
    ! [SV2: a] :
      ( ( $false = $true )
      | ( ( sK2_SY6 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[63]) ).

thf(76,plain,
    ! [SV2: a] :
      ( ( ( sK1_X @ SV2 )
        = $true )
      | ( ( sK2_SY6 @ SV2 )
        = $true )
      | ( $false = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(77,plain,
    ( ( ( ! [SV6: a] :
            ( ( sK2_SY6 @ SV6 )
            = $false ) )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[66]) ).

thf(78,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[66]) ).

thf(79,plain,
    ( ( $false = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( ( ( sK2_SY6
         != ( ^ [SX0: a] : $false ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(80,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK5_SV5 )
            | $false ) )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[68]) ).

thf(81,plain,
    ( ( ( ~ ( ~ ( sK2_SY6 @ sK5_SV5 )
            | ~ $false ) )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[68]) ).

thf(82,plain,
    ( ( ( sK2_SY6 @ sK4_SV4 )
      = $true )
    | ( $false = $true )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(83,plain,
    ( ( ( ~ ( sK2_SY6 @ sK4_SV4 ) )
      = $true )
    | ( ( ~ $false )
      = $true )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(84,plain,
    ! [SV2: a] :
      ( ( ( sK1_X @ SV2 )
        = $true )
      | ( ( sK2_SY6 @ SV2 )
        = $true )
      | ( ( sK1_X @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(85,plain,
    ! [SV2: a] :
      ( ( ( sK1_X @ SV2 )
        = $true )
      | ( ( sK2_SY6 @ SV2 )
        = $true )
      | ( ( sK2_SY6 @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(86,plain,
    ( ( ( ( sK2_SY6 @ sK6_SV6 )
        = $false )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[77]) ).

thf(87,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(88,plain,
    ( ( ( ( sK2_SY6 @ sK5_SV5 )
        | $false )
      = $true )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(89,plain,
    ( ( ( ~ ( sK2_SY6 @ sK5_SV5 )
        | ~ $false )
      = $true )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[81]) ).

thf(90,plain,
    ( ( ( sK2_SY6 @ sK4_SV4 )
      = $false )
    | ( ( ~ $false )
      = $true )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(91,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK6_SV6 )
            | $false )
        | ~ ( ~ ( sK2_SY6 @ sK6_SV6 )
            | ~ $false ) )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[86]) ).

thf(92,plain,
    ( ( ( ( sK2_SY6 @ sK6_SV6 )
        = $false )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[86]) ).

thf(93,plain,
    ( ( ( ! [SV7: a] :
            ( ( sK2_SY6 @ SV7 )
            = $false ) )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[87]) ).

thf(94,plain,
    ( ( ( sK2_SY6
        = ( ^ [SX0: a] : $false ) )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[87]) ).

thf(95,plain,
    ( ( ( sK2_SY6 @ sK5_SV5 )
      = $true )
    | ( $false = $true )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(96,plain,
    ( ( ( ~ ( sK2_SY6 @ sK5_SV5 ) )
      = $true )
    | ( ( ~ $false )
      = $true )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(97,plain,
    ( ( $false = $false )
    | ( ( sK2_SY6 @ sK4_SV4 )
      = $false )
    | ( ( sK1_X
        = ( ^ [SX0: a] : $false ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(98,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK6_SV6 )
            | $false ) )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(99,plain,
    ( ( ( ~ ( ~ ( sK2_SY6 @ sK6_SV6 )
            | ~ $false ) )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(100,plain,
    ( ( ( ( sK2_SY6 @ sK7_SV7 )
        = $false )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[93]) ).

thf(101,plain,
    ( ( ( sK2_SY6 @ sK5_SV5 )
      = $false )
    | ( ( ~ $false )
      = $true )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(102,plain,
    ( ( ( ( sK2_SY6 @ sK6_SV6 )
        | $false )
      = $true )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[98]) ).

thf(103,plain,
    ( ( ( ~ ( sK2_SY6 @ sK6_SV6 )
        | ~ $false )
      = $true )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[99]) ).

thf(104,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK7_SV7 )
            | $false )
        | ~ ( ~ ( sK2_SY6 @ sK7_SV7 )
            | ~ $false ) )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[100]) ).

thf(105,plain,
    ( ( ( ( sK2_SY6 @ sK7_SV7 )
        = $false )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[100]) ).

thf(106,plain,
    ( ( $false = $false )
    | ( ( sK2_SY6 @ sK5_SV5 )
      = $false )
    | ( ( ( sK1_X @ sK3_SV3 )
        = $false )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(107,plain,
    ( ( ( sK2_SY6 @ sK6_SV6 )
      = $true )
    | ( $false = $true )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(108,plain,
    ( ( ( ~ ( sK2_SY6 @ sK6_SV6 ) )
      = $true )
    | ( ( ~ $false )
      = $true )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[103]) ).

thf(109,plain,
    ( ( ( ~ ( ( sK2_SY6 @ sK7_SV7 )
            | $false ) )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[104]) ).

thf(110,plain,
    ( ( ( ~ ( ~ ( sK2_SY6 @ sK7_SV7 )
            | ~ $false ) )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[104]) ).

thf(111,plain,
    ( ( ( sK2_SY6 @ sK6_SV6 )
      = $false )
    | ( ( ~ $false )
      = $true )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[108]) ).

thf(112,plain,
    ( ( ( ( sK2_SY6 @ sK7_SV7 )
        | $false )
      = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[109]) ).

thf(113,plain,
    ( ( ( ~ ( sK2_SY6 @ sK7_SV7 )
        | ~ $false )
      = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[110]) ).

thf(114,plain,
    ( ( $false = $false )
    | ( ( sK2_SY6 @ sK6_SV6 )
      = $false )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(115,plain,
    ( ( ( sK2_SY6 @ sK7_SV7 )
      = $true )
    | ( $false = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[112]) ).

thf(116,plain,
    ( ( ( ~ ( sK2_SY6 @ sK7_SV7 ) )
      = $true )
    | ( ( ~ $false )
      = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(117,plain,
    ( ( ( sK2_SY6 @ sK7_SV7 )
      = $false )
    | ( ( ~ $false )
      = $true )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(118,plain,
    ( ( $false = $false )
    | ( ( sK2_SY6 @ sK7_SV7 )
      = $false )
    | ( ( sK1_X @ sK3_SV3 )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(119,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,118,115,114,107,106,105,97,95,94,92,85,84,82,78,76,75,73,69,65,50,48,35,25]) ).

thf(120,plain,
    ( ( ( sK1_X
        = ( ^ [Xx: a] : $false ) )
      & ( sK2_SY6
        = ( ^ [Xx: a] : $false ) )
      & ( ( ^ [SY11: a] :
              ( ( sK1_X @ SY11 )
              | ( sK2_SY6 @ SY11 ) ) )
       != ( ^ [Xx: a] : $false ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(121,plain,
    ( ( ~ ( ~ ~ ( ( sK1_X
                 != ( ^ [SX0: a] : $false ) )
                | ( sK2_SY6
                 != ( ^ [SX0: a] : $false ) ) )
          | ~ ( ( ( ^ [SX0: a] :
                      ( ( sK1_X @ SX0 )
                      | ( sK2_SY6 @ SX0 ) ) )
               != ( ^ [SX0: a] : $false ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[120]) ).

thf(122,plain,
    ( ( ~ ~ ( ( sK1_X
             != ( ^ [SX0: a] : $false ) )
            | ( sK2_SY6
             != ( ^ [SX0: a] : $false ) ) )
      | ~ ( ( ( ^ [SX0: a] :
                  ( ( sK1_X @ SX0 )
                  | ( sK2_SY6 @ SX0 ) ) )
           != ( ^ [SX0: a] : $false ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(123,plain,
    ( ( ~ ~ ( ( sK1_X
             != ( ^ [SX0: a] : $false ) )
            | ( sK2_SY6
             != ( ^ [SX0: a] : $false ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[122]) ).

thf(124,plain,
    ( ( ~ ( ( ( ^ [SX0: a] :
                  ( ( sK1_X @ SX0 )
                  | ( sK2_SY6 @ SX0 ) ) )
           != ( ^ [SX0: a] : $false ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[122]) ).

thf(125,plain,
    ( ( ~ ( ( sK1_X
           != ( ^ [SX0: a] : $false ) )
          | ( sK2_SY6
           != ( ^ [SX0: a] : $false ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[123]) ).

thf(126,plain,
    ( ( ( ( ^ [SX0: a] :
              ( ( sK1_X @ SX0 )
              | ( sK2_SY6 @ SX0 ) ) )
       != ( ^ [SX0: a] : $false ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[124]) ).

thf(127,plain,
    ( ( ( sK1_X
       != ( ^ [SX0: a] : $false ) )
      | ( sK2_SY6
       != ( ^ [SX0: a] : $false ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(128,plain,
    ( ( ( ^ [SX0: a] :
            ( ( sK1_X @ SX0 )
            | ( sK2_SY6 @ SX0 ) ) )
      = ( ^ [SX0: a] : $false ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[126]) ).

thf(129,plain,
    ( ( ( sK1_X
       != ( ^ [SX0: a] : $false ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[127]) ).

thf(130,plain,
    ( ( ( sK2_SY6
       != ( ^ [SX0: a] : $false ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[127]) ).

thf(131,plain,
    ( ( ! [SV8: a] :
          ( ( ( sK1_X @ SV8 )
            | ( sK2_SY6 @ SV8 ) )
          = $false ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[128]) ).

thf(132,plain,
    ( ( ( ^ [SX0: a] :
            ( ( sK1_X @ SX0 )
            | ( sK2_SY6 @ SX0 ) ) )
      = ( ^ [SX0: a] : $false ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[128]) ).

thf(133,plain,
    ( ( sK1_X
      = ( ^ [SX0: a] : $false ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[129]) ).

thf(134,plain,
    ( ( sK2_SY6
      = ( ^ [SX0: a] : $false ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[130]) ).

thf(135,plain,
    ( ( ( ( sK1_X @ sK8_SV8 )
        | ( sK2_SY6 @ sK8_SV8 ) )
      = $false )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[131]) ).

thf(136,plain,
    ( ( ! [SV9: a] :
          ( ( sK1_X @ SV9 )
          = $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[133]) ).

thf(137,plain,
    ( ( sK1_X
      = ( ^ [SX0: a] : $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[133]) ).

thf(138,plain,
    ( ( ! [SV10: a] :
          ( ( sK2_SY6 @ SV10 )
          = $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[134]) ).

thf(139,plain,
    ( ( sK2_SY6
      = ( ^ [SX0: a] : $false ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[134]) ).

thf(140,plain,
    ( ( ~ ( ( sK1_X @ sK8_SV8 )
          | ( sK2_SY6 @ sK8_SV8 )
          | $false )
      | ~ ( ~ ( ( sK1_X @ sK8_SV8 )
              | ( sK2_SY6 @ sK8_SV8 ) )
          | ~ $false ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[135]) ).

thf(141,plain,
    ( ( ( ( sK1_X @ sK8_SV8 )
        | ( sK2_SY6 @ sK8_SV8 ) )
      = $false )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[135]) ).

thf(142,plain,
    ! [SV11: a] :
      ( ( ( sK1_X @ SV11 )
        = $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(143,plain,
    ! [SV12: a] :
      ( ( ( sK2_SY6 @ SV12 )
        = $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(144,plain,
    ( ( ~ ( ( sK1_X @ sK8_SV8 )
          | ( sK2_SY6 @ sK8_SV8 )
          | $false ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[140]) ).

thf(145,plain,
    ( ( ~ ( ~ ( ( sK1_X @ sK8_SV8 )
              | ( sK2_SY6 @ sK8_SV8 ) )
          | ~ $false ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[140]) ).

thf(146,plain,
    ! [SV11: a] :
      ( ( ~ ( ( sK1_X @ SV11 )
            | $false )
        | ~ ( ~ ( sK1_X @ SV11 )
            | ~ $false ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[142]) ).

thf(147,plain,
    ! [SV11: a] :
      ( ( ( sK1_X @ SV11 )
        = $false )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[142]) ).

thf(148,plain,
    ! [SV12: a] :
      ( ( ~ ( ( sK2_SY6 @ SV12 )
            | $false )
        | ~ ( ~ ( sK2_SY6 @ SV12 )
            | ~ $false ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[143]) ).

thf(149,plain,
    ! [SV12: a] :
      ( ( ( sK2_SY6 @ SV12 )
        = $false )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[143]) ).

thf(150,plain,
    ( ( ( sK1_X @ sK8_SV8 )
      | ( sK2_SY6 @ sK8_SV8 )
      | $false )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[144]) ).

thf(151,plain,
    ( ( ~ ( ( sK1_X @ sK8_SV8 )
          | ( sK2_SY6 @ sK8_SV8 ) )
      | ~ $false )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[145]) ).

thf(152,plain,
    ! [SV11: a] :
      ( ( ( ~ ( ( sK1_X @ SV11 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ( sK1_X @ SV11 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[146]) ).

thf(153,plain,
    ! [SV12: a] :
      ( ( ( ~ ( ( sK2_SY6 @ SV12 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[148]) ).

thf(154,plain,
    ( ( ( ( sK1_X @ sK8_SV8 )
        | ( sK2_SY6 @ sK8_SV8 ) )
      = $true )
    | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(155,plain,
    ( ( ( ~ ( ( sK1_X @ sK8_SV8 )
            | ( sK2_SY6 @ sK8_SV8 ) ) )
      = $true )
    | ( ( ~ $false )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(156,plain,
    ! [SV11: a] :
      ( ( ( ( sK1_X @ SV11 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ( sK1_X @ SV11 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(157,plain,
    ! [SV12: a] :
      ( ( ( ( sK2_SY6 @ SV12 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(158,plain,
    ( ( ( sK1_X @ sK8_SV8 )
      = $true )
    | ( ( sK2_SY6 @ sK8_SV8 )
      = $true )
    | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(159,plain,
    ( ( ( ( sK1_X @ sK8_SV8 )
        | ( sK2_SY6 @ sK8_SV8 ) )
      = $false )
    | ( ( ~ $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(160,plain,
    ! [SV11: a] :
      ( ( ( sK1_X @ SV11 )
        = $false )
      | ( ( ~ ( ~ ( sK1_X @ SV11 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[156]) ).

thf(161,plain,
    ! [SV11: a] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ( sK1_X @ SV11 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[156]) ).

thf(162,plain,
    ! [SV12: a] :
      ( ( ( sK2_SY6 @ SV12 )
        = $false )
      | ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[157]) ).

thf(163,plain,
    ! [SV12: a] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
              | ~ $false ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[157]) ).

thf(164,plain,
    ( ( ( sK1_X @ sK8_SV8 )
      = $false )
    | ( ( ~ $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[159]) ).

thf(165,plain,
    ( ( ( sK2_SY6 @ sK8_SV8 )
      = $false )
    | ( ( ~ $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[159]) ).

thf(166,plain,
    ! [SV11: a] :
      ( ( ( ~ ( sK1_X @ SV11 )
          | ~ $false )
        = $false )
      | ( ( sK1_X @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[160]) ).

thf(167,plain,
    ! [SV11: a] :
      ( ( ( ~ ( sK1_X @ SV11 )
          | ~ $false )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(168,plain,
    ! [SV12: a] :
      ( ( ( ~ ( sK2_SY6 @ SV12 )
          | ~ $false )
        = $false )
      | ( ( sK2_SY6 @ SV12 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(169,plain,
    ! [SV12: a] :
      ( ( ( ~ ( sK2_SY6 @ SV12 )
          | ~ $false )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(170,plain,
    ( ( $false = $false )
    | ( ( sK1_X @ sK8_SV8 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[164]) ).

thf(171,plain,
    ( ( $false = $false )
    | ( ( sK2_SY6 @ sK8_SV8 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[165]) ).

thf(172,plain,
    ! [SV11: a] :
      ( ( ( ~ ( sK1_X @ SV11 ) )
        = $false )
      | ( ( sK1_X @ SV11 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[166]) ).

thf(173,plain,
    ! [SV11: a] :
      ( ( ( ~ $false )
        = $false )
      | ( ( sK1_X @ SV11 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[166]) ).

thf(174,plain,
    ! [SV11: a] :
      ( ( ( ~ ( sK1_X @ SV11 ) )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[167]) ).

thf(175,plain,
    ( ( ( ~ $false )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[167]) ).

thf(176,plain,
    ! [SV12: a] :
      ( ( ( ~ ( sK2_SY6 @ SV12 ) )
        = $false )
      | ( ( sK2_SY6 @ SV12 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[168]) ).

thf(177,plain,
    ! [SV12: a] :
      ( ( ( ~ $false )
        = $false )
      | ( ( sK2_SY6 @ SV12 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[168]) ).

thf(178,plain,
    ! [SV12: a] :
      ( ( ( ~ ( sK2_SY6 @ SV12 ) )
        = $false )
      | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[169]) ).

thf(179,plain,
    ( ( ( ~ $false )
      = $false )
    | ( $false = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[169]) ).

thf(180,plain,
    ! [SV11: a] :
      ( ( ( sK1_X @ SV11 )
        = $true )
      | ( ( sK1_X @ SV11 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[172]) ).

thf(181,plain,
    ! [SV11: a] :
      ( ( $false = $true )
      | ( ( sK1_X @ SV11 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[173]) ).

thf(182,plain,
    ! [SV11: a] :
      ( ( ( sK1_X @ SV11 )
        = $true )
      | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[174]) ).

thf(183,plain,
    ( ( $false = $true )
    | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[175]) ).

thf(184,plain,
    ! [SV12: a] :
      ( ( ( sK2_SY6 @ SV12 )
        = $true )
      | ( ( sK2_SY6 @ SV12 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[176]) ).

thf(185,plain,
    ! [SV12: a] :
      ( ( $false = $true )
      | ( ( sK2_SY6 @ SV12 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[177]) ).

thf(186,plain,
    ! [SV12: a] :
      ( ( ( sK2_SY6 @ SV12 )
        = $true )
      | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[178]) ).

thf(187,plain,
    ( ( $false = $true )
    | ( $false = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[179]) ).

thf(188,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[132,187,186,185,184,183,182,181,180,171,170,158,149,147,141,139,137]) ).

thf(189,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[188,119]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET600^5 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sat Jul  9 23:19:58 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.42  
% 0.13/0.42  ********************************
% 0.13/0.42  *   All subproblems solved!    *
% 0.13/0.42  ********************************
% 0.13/0.42  % SZS status Theorem for /export/starexec/sandbox/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:188,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.44  
% 0.20/0.44  %**** Beginning of derivation protocol ****
% 0.20/0.44  % SZS output start CNFRefutation
% See solution above
% 0.20/0.44  
% 0.20/0.44  %**** End of derivation protocol ****
% 0.20/0.44  %**** no. of clauses in derivation: 189 ****
% 0.20/0.44  %**** clause counter: 188 ****
% 0.20/0.44  
% 0.20/0.44  % SZS status Theorem for /export/starexec/sandbox/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:188,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------