TSTP Solution File: SEU504^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU504^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n022.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 12:12:24 EDT 2022

% Result   : Theorem 0.18s 0.38s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   65 (  29 unt;   6 typ;   2 def)
%            Number of atoms       :  334 ( 183 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  604 ( 156   ~; 129   |;  17   &; 282   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  48   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  144 (   4   ^ 126   !;  14   ?; 144   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_exu,type,
    exu: ( $i > $o ) > $o ).

thf(tp_exuE1,type,
    exuE1: $o ).

thf(tp_sK1_SY0,type,
    sK1_SY0: $i > $o ).

thf(tp_sK2_SY24,type,
    sK2_SY24: $i ).

thf(tp_sK3_Xx,type,
    sK3_Xx: ( $i > $o ) > $i ).

thf(tp_sK4_SY8,type,
    sK4_SY8: $i > ( $i > $o ) > $i ).

thf(exu,definition,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ( Xphi @ Xx )
          & ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).

thf(exuE1,definition,
    ( exuE1
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( Xphi @ Xx )
              & ! [Xy: $i] :
                  ( ( Xphi @ Xy )
                 => ( Xx = Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).

thf(1,conjecture,
    ( exuE1
   => ! [Xphi: $i > $o] :
        ( ( exu
          @ ^ [Xx: $i] : ( Xphi @ Xx ) )
       => ? [Xx: $i] : ( Xphi @ Xx ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).

thf(2,negated_conjecture,
    ( ( exuE1
     => ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] : ( Xphi @ Xx ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY5: $i > $o] :
          ( ? [SY7: $i] :
              ( ( SY5 @ SY7 )
              & ! [SY8: $i] :
                  ( ( SY5 @ SY8 )
                 => ( SY7 = SY8 ) ) )
         => ? [Xx: $i] :
              ( ( SY5 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY5 @ Xy )
                 => ( Xx = Xy ) ) ) )
     => ! [SY0: $i > $o] :
          ( ? [SY2: $i] :
              ( ( SY0 @ SY2 )
              & ! [SY3: $i] :
                  ( ( SY0 @ SY3 )
                 => ( SY2 = SY3 ) ) )
         => ? [Xx: $i] : ( SY0 @ Xx ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,exu,exuE1]) ).

thf(4,plain,
    ( ( ! [SY5: $i > $o] :
          ( ? [SY7: $i] :
              ( ( SY5 @ SY7 )
              & ! [SY8: $i] :
                  ( ( SY5 @ SY8 )
                 => ( SY7 = SY8 ) ) )
         => ? [Xx: $i] :
              ( ( SY5 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY5 @ Xy )
                 => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [SY0: $i > $o] :
          ( ? [SY2: $i] :
              ( ( SY0 @ SY2 )
              & ! [SY3: $i] :
                  ( ( SY0 @ SY3 )
                 => ( SY2 = SY3 ) ) )
         => ? [Xx: $i] : ( SY0 @ Xx ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [SY0: $i > $o] :
            ( ? [SY2: $i] :
                ( ( SY0 @ SY2 )
                & ! [SY3: $i] :
                    ( ( SY0 @ SY3 )
                   => ( SY2 = SY3 ) ) )
           => ? [Xx: $i] : ( SY0 @ Xx ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY27: $i] :
          ( ~ ( sK1_SY0 @ SY27 )
          | ( sK2_SY24 = SY27 ) )
      & ( sK1_SY0 @ sK2_SY24 )
      & ! [SY26: $i] :
          ~ ( sK1_SY0 @ SY26 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY5: $i > $o] :
          ( ! [SY7: $i] :
              ( ( ( SY5 @ ( sK4_SY8 @ SY7 @ SY5 ) )
                & ( SY7
                 != ( sK4_SY8 @ SY7 @ SY5 ) ) )
              | ~ ( SY5 @ SY7 ) )
          | ( ! [SY28: $i] :
                ( ~ ( SY5 @ SY28 )
                | ( ( sK3_Xx @ SY5 )
                  = SY28 ) )
            & ( SY5 @ ( sK3_Xx @ SY5 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [SY5: $i > $o] :
          ( ! [SY7: $i] :
              ( ( ( SY5 @ ( sK4_SY8 @ SY7 @ SY5 ) )
                & ( SY7
                 != ( sK4_SY8 @ SY7 @ SY5 ) ) )
              | ~ ( SY5 @ SY7 ) )
          | ( ! [SY28: $i] :
                ( ~ ( SY5 @ SY28 )
                | ( ( sK3_Xx @ SY5 )
                  = SY28 ) )
            & ( SY5 @ ( sK3_Xx @ SY5 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ! [SY27: $i] :
          ( ~ ( sK1_SY0 @ SY27 )
          | ( sK2_SY24 = SY27 ) )
      & ( sK1_SY0 @ sK2_SY24 )
      & ! [SY26: $i] :
          ~ ( sK1_SY0 @ SY26 ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK4_SY8 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK4_SY8 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ~ ( ~ ! [SX1: $i] :
                    ( ~ ( SX0 @ SX1 )
                    | ( ( sK3_Xx @ SX0 )
                      = SX1 ) )
              | ~ ( SX0 @ ( sK3_Xx @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9,exu,exuE1]) ).

thf(12,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( sK1_SY0 @ SX0 )
                      | ( sK2_SY24 = SX0 ) )
                | ~ ( sK1_SY0 @ sK2_SY24 ) )
          | ~ ! [SX0: $i] :
                ~ ( sK1_SY0 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,exu,exuE1]) ).

thf(13,plain,
    ! [SV1: $i > $o] :
      ( ( ! [SY29: $i] :
            ( ~ ( ~ ( SV1 @ ( sK4_SY8 @ SY29 @ SV1 ) )
                | ~ ( ( SY29
                     != ( sK4_SY8 @ SY29 @ SV1 ) ) ) )
            | ~ ( SV1 @ SY29 ) )
        | ~ ( ~ ! [SY30: $i] :
                  ( ~ ( SV1 @ SY30 )
                  | ( ( sK3_Xx @ SV1 )
                    = SY30 ) )
            | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK1_SY0 @ SX0 )
                  | ( sK2_SY24 = SX0 ) )
            | ~ ( sK1_SY0 @ sK2_SY24 ) )
      | ~ ! [SX0: $i] :
            ~ ( sK1_SY0 @ SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i > $o] :
      ( ( ( ! [SY29: $i] :
              ( ~ ( ~ ( SV1 @ ( sK4_SY8 @ SY29 @ SV1 ) )
                  | ~ ( ( SY29
                       != ( sK4_SY8 @ SY29 @ SV1 ) ) ) )
              | ~ ( SV1 @ SY29 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK1_SY0 @ SX0 )
                  | ( sK2_SY24 = SX0 ) )
            | ~ ( sK1_SY0 @ sK2_SY24 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ( sK1_SY0 @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
              | ~ ( ( SV2
                   != ( sK4_SY8 @ SV2 @ SV1 ) ) ) )
          | ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( sK1_SY0 @ SX0 )
                | ( sK2_SY24 = SX0 ) )
          | ~ ( sK1_SY0 @ sK2_SY24 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ! [SX0: $i] :
          ~ ( sK1_SY0 @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ( ~ ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
              | ~ ( ( SV2
                   != ( sK4_SY8 @ SV2 @ SV1 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_SY0 @ SX0 )
            | ( sK2_SY24 = SX0 ) )
      | ~ ( sK1_SY0 @ sK2_SY24 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV3: $i] :
      ( ( ~ ( sK1_SY0 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
          | ~ ( ( SV2
               != ( sK4_SY8 @ SV2 @ SV1 ) ) ) )
        = $false )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_SY0 @ SX0 )
            | ( sK2_SY24 = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ~ ( sK1_SY0 @ sK2_SY24 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV3: $i] :
      ( ( sK1_SY0 @ SV3 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) ) )
        = $false )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV1: $i > $o,SV2: $i] :
      ( ( ( ~ ( ( SV2
               != ( sK4_SY8 @ SV2 @ SV1 ) ) ) )
        = $false )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(30,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK1_SY0 @ SX0 )
          | ( sK2_SY24 = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(31,plain,
    ( ( sK1_SY0 @ sK2_SY24 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(32,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV1: $i > $o,SV2: $i] :
      ( ( ( ( SV2
           != ( sK4_SY8 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV4: $i] :
      ( ( ~ ( sK1_SY0 @ SV4 )
        | ( sK2_SY24 = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV2 )
        = $false )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV1: $i > $o,SV2: $i] :
      ( ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( ~ ( SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK1_SY0 @ SV4 ) )
        = $true )
      | ( ( sK2_SY24 = SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(38,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ! [SY30: $i] :
                ( ~ ( SV1 @ SY30 )
                | ( ( sK3_Xx @ SV1 )
                  = SY30 ) )
          | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) )
        = $false )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV2 )
        = $false )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY30: $i] :
                    ( ~ ( SV1 @ SY30 )
                    | ( ( sK3_Xx @ SV1 )
                      = SY30 ) )
              | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(40,plain,
    ! [SV4: $i] :
      ( ( ( sK1_SY0 @ SV4 )
        = $false )
      | ( ( sK2_SY24 = SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(41,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ! [SY30: $i] :
                ( ~ ( SV1 @ SY30 )
                | ( ( sK3_Xx @ SV1 )
                  = SY30 ) ) )
        = $false )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) )
        = $false )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ! [SY30: $i] :
                ( ~ ( SV1 @ SY30 )
                | ( ( sK3_Xx @ SV1 )
                  = SY30 ) )
          | ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) )
        = $false )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ! [SY30: $i] :
              ( ~ ( SV1 @ SY30 )
              | ( ( sK3_Xx @ SV1 )
                = SY30 ) ) )
        = $true )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(45,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( SV1 @ ( sK3_Xx @ SV1 ) )
        = $true )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(46,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ! [SY30: $i] :
                ( ~ ( SV1 @ SY30 )
                | ( ( sK3_Xx @ SV1 )
                  = SY30 ) ) )
        = $false )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ ( sK3_Xx @ SV1 ) ) )
        = $false )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV2: $i,SV5: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV5 )
          | ( ( sK3_Xx @ SV1 )
            = SV5 ) )
        = $true )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( ! [SY30: $i] :
              ( ~ ( SV1 @ SY30 )
              | ( ( sK3_Xx @ SV1 )
                = SY30 ) ) )
        = $true )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV2: $i,SV1: $i > $o] :
      ( ( ( SV1 @ ( sK3_Xx @ SV1 ) )
        = $true )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV2: $i,SV5: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV5 ) )
        = $true )
      | ( ( ( sK3_Xx @ SV1 )
          = SV5 )
        = $true )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV2: $i,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 )
          | ( ( sK3_Xx @ SV1 )
            = SV6 ) )
        = $true )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV2: $i,SV5: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV5 )
        = $false )
      | ( ( ( sK3_Xx @ SV1 )
          = SV5 )
        = $true )
      | ( ( SV1 @ ( sK4_SY8 @ SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(54,plain,
    ! [SV2: $i,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 ) )
        = $true )
      | ( ( ( sK3_Xx @ SV1 )
          = SV6 )
        = $true )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV2: $i,SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $false )
      | ( ( ( sK3_Xx @ SV1 )
          = SV6 )
        = $true )
      | ( ( SV2
          = ( sK4_SY8 @ SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(56,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[27,55,53,50,45,40,31]) ).

thf(57,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU504^2 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n022.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
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 20 08:29:31 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.34  
% 0.18/0.34   No.of.Axioms: 0
% 0.18/0.34  
% 0.18/0.34   Length.of.Defs: 387
% 0.18/0.34  
% 0.18/0.34   Contains.Choice.Funs: false
% 0.18/0.34  (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: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)...
% 0.18/0.38  
% 0.18/0.38  ********************************
% 0.18/0.38  *   All subproblems solved!    *
% 0.18/0.38  ********************************
% 0.18/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.38  
% 0.18/0.38  %**** Beginning of derivation protocol ****
% 0.18/0.38  % SZS output start CNFRefutation
% See solution above
% 0.18/0.38  
% 0.18/0.38  %**** End of derivation protocol ****
% 0.18/0.38  %**** no. of clauses in derivation: 57 ****
% 0.18/0.38  %**** clause counter: 56 ****
% 0.18/0.38  
% 0.18/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------