TSTP Solution File: SEU550^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU550^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n025.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 12:12:48 EDT 2022

% Result   : Theorem 0.20s 0.42s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  113 (  67 unt;   7 typ;   1 def)
%            Number of atoms       :  647 ( 269 equ;   0 cnn)
%            Maximal formula atoms :    3 (   6 avg)
%            Number of connectives :  804 ( 254   ~; 180   |;  32   &; 294   @)
%                                         (  12 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  206 (   5   ^ 184   !;  17   ?; 206   :)

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

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

thf(tp_sK2_SY18,type,
    sK2_SY18: $i > $o ).

thf(tp_sK3_SY30,type,
    sK3_SY30: $i > $i ).

thf(tp_sK4_SY21,type,
    sK4_SY21: $i ).

thf(tp_sK5_SY22,type,
    sK5_SY22: $i > $i ).

thf(tp_sK6_SY29,type,
    sK6_SY29: $i ).

thf(exu,definition,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ( Xphi @ Xx )
          & ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).

thf(1,conjecture,
    ! [Xphi: $i > $o,Xpsi: $i > $o] :
      ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( Xphi @ Xx )
          <=> ( Xpsi @ Xy ) ) )
     => ( ( exu
          @ ^ [Xx: $i] : ( Xphi @ Xx ) )
      <=> ( exu
          @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).

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

thf(3,plain,
    ( ( ! [SY0: $i > $o,SY1: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY0 @ Xx )
              <=> ( SY1 @ Xy ) ) )
         => ( ? [SY5: $i] :
                ( ( SY0 @ SY5 )
                & ! [SY6: $i] :
                    ( ( SY0 @ SY6 )
                   => ( SY5 = SY6 ) ) )
          <=> ? [SY8: $i] :
                ( ( SY1 @ SY8 )
                & ! [SY9: $i] :
                    ( ( SY1 @ SY9 )
                   => ( SY8 = SY9 ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,exu]) ).

thf(4,plain,
    ( ( ! [SY18: $i > $o] :
          ( ! [SY19: $i,SY20: $i] :
              ( ( SY19 = SY20 )
             => ( ( sK1_SY0 @ SY19 )
              <=> ( SY18 @ SY20 ) ) )
         => ( ? [SY21: $i] :
                ( ( sK1_SY0 @ SY21 )
                & ! [SY22: $i] :
                    ( ( sK1_SY0 @ SY22 )
                   => ( SY21 = SY22 ) ) )
          <=> ? [SY8: $i] :
                ( ( SY18 @ SY8 )
                & ! [SY9: $i] :
                    ( ( SY18 @ SY9 )
                   => ( SY8 = SY9 ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY25: $i,SY26: $i] :
          ( ( SY25 = SY26 )
         => ( ( sK1_SY0 @ SY25 )
          <=> ( sK2_SY18 @ SY26 ) ) )
     => ( ? [SY21: $i] :
            ( ( sK1_SY0 @ SY21 )
            & ! [SY22: $i] :
                ( ( sK1_SY0 @ SY22 )
               => ( SY21 = SY22 ) ) )
      <=> ? [SY29: $i] :
            ( ( sK2_SY18 @ SY29 )
            & ! [SY30: $i] :
                ( ( sK2_SY18 @ SY30 )
               => ( SY29 = SY30 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY25: $i,SY26: $i] :
          ( ( SY25 = SY26 )
         => ( ( sK1_SY0 @ SY25 )
          <=> ( sK2_SY18 @ SY26 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ? [SY21: $i] :
          ( ( sK1_SY0 @ SY21 )
          & ! [SY22: $i] :
              ( ( sK1_SY0 @ SY22 )
             => ( SY21 = SY22 ) ) )
    <=> ? [SY29: $i] :
          ( ( sK2_SY18 @ SY29 )
          & ! [SY30: $i] :
              ( ( sK2_SY18 @ SY30 )
             => ( SY29 = SY30 ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ? [SY21: $i] :
          ( ( sK1_SY0 @ SY21 )
          & ! [SY22: $i] :
              ( ( sK1_SY0 @ SY22 )
             => ( SY21 = SY22 ) ) )
     => ? [SY29: $i] :
          ( ( sK2_SY18 @ SY29 )
          & ! [SY30: $i] :
              ( ( sK2_SY18 @ SY30 )
             => ( SY29 = SY30 ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[7]) ).

thf(9,plain,
    ( ( ? [SY29: $i] :
          ( ( sK2_SY18 @ SY29 )
          & ! [SY30: $i] :
              ( ( sK2_SY18 @ SY30 )
             => ( SY29 = SY30 ) ) )
     => ? [SY21: $i] :
          ( ( sK1_SY0 @ SY21 )
          & ! [SY22: $i] :
              ( ( sK1_SY0 @ SY22 )
             => ( SY21 = SY22 ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[7]) ).

thf(10,plain,
    ( ( ~ ( ? [SY21: $i] :
              ( ( sK1_SY0 @ SY21 )
              & ! [SY22: $i] :
                  ( ( sK1_SY0 @ SY22 )
                 => ( SY21 = SY22 ) ) )
         => ? [SY29: $i] :
              ( ( sK2_SY18 @ SY29 )
              & ! [SY30: $i] :
                  ( ( sK2_SY18 @ SY30 )
                 => ( SY29 = SY30 ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ( ? [SY29: $i] :
              ( ( sK2_SY18 @ SY29 )
              & ! [SY30: $i] :
                  ( ( sK2_SY18 @ SY30 )
                 => ( SY29 = SY30 ) ) )
         => ? [SY21: $i] :
              ( ( sK1_SY0 @ SY21 )
              & ! [SY22: $i] :
                  ( ( sK1_SY0 @ SY22 )
                 => ( SY21 = SY22 ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ! [SY31: $i] :
          ( ~ ( sK1_SY0 @ SY31 )
          | ( sK4_SY21 = SY31 ) )
      & ( sK1_SY0 @ sK4_SY21 )
      & ! [SY29: $i] :
          ( ( ( sK2_SY18 @ ( sK3_SY30 @ SY29 ) )
            & ( SY29
             != ( sK3_SY30 @ SY29 ) ) )
          | ~ ( sK2_SY18 @ SY29 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(13,plain,
    ( ( ! [SY32: $i] :
          ( ~ ( sK2_SY18 @ SY32 )
          | ( sK6_SY29 = SY32 ) )
      & ( sK2_SY18 @ sK6_SY29 )
      & ! [SY21: $i] :
          ( ( ( sK1_SY0 @ ( sK5_SY22 @ SY21 ) )
            & ( SY21
             != ( sK5_SY22 @ SY21 ) ) )
          | ~ ( sK1_SY0 @ SY21 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(14,plain,
    ( ( ! [SY25: $i,SY26: $i] :
          ( ( SY25 != SY26 )
          | ~ ( sK1_SY0 @ SY25 )
          | ( sK2_SY18 @ SY26 ) )
      & ! [SY25: $i,SY26: $i] :
          ( ( SY25 != SY26 )
          | ~ ( sK2_SY18 @ SY26 )
          | ( sK1_SY0 @ SY25 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(15,plain,
    ( ( ! [SY25: $i,SY26: $i] :
          ( ( SY25 != SY26 )
          | ~ ( sK1_SY0 @ SY25 )
          | ( sK2_SY18 @ SY26 ) )
      & ! [SY25: $i,SY26: $i] :
          ( ( SY25 != SY26 )
          | ~ ( sK2_SY18 @ SY26 )
          | ( sK1_SY0 @ SY25 ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ! [SY31: $i] :
          ( ~ ( sK1_SY0 @ SY31 )
          | ( sK4_SY21 = SY31 ) )
      & ( sK1_SY0 @ sK4_SY21 )
      & ! [SY29: $i] :
          ( ( ( sK2_SY18 @ ( sK3_SY30 @ SY29 ) )
            & ( SY29
             != ( sK3_SY30 @ SY29 ) ) )
          | ~ ( sK2_SY18 @ SY29 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(17,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( sK1_SY0 @ SX0 )
                      | ( sK4_SY21 = SX0 ) )
                | ~ ( sK1_SY0 @ sK4_SY21 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
                    | ~ ( ( SX0
                         != ( sK3_SY30 @ SX0 ) ) ) )
                | ~ ( sK2_SY18 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16,exu]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ~ ( sK1_SY0 @ SX0 )
                | ( sK2_SY18 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ~ ( sK2_SY18 @ SX1 )
                | ( sK1_SY0 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15,exu]) ).

thf(19,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK1_SY0 @ SX0 )
                  | ( sK4_SY21 = SX0 ) )
            | ~ ( sK1_SY0 @ sK4_SY21 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
                | ~ ( ( SX0
                     != ( sK3_SY30 @ SX0 ) ) ) )
            | ~ ( sK2_SY18 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK1_SY0 @ SX0 )
            | ( sK2_SY18 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK2_SY18 @ SX1 )
            | ( sK1_SY0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK1_SY0 @ SX0 )
                  | ( sK4_SY21 = SX0 ) )
            | ~ ( sK1_SY0 @ sK4_SY21 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(22,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
                | ~ ( ( SX0
                     != ( sK3_SY30 @ SX0 ) ) ) )
            | ~ ( sK2_SY18 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(23,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK1_SY0 @ SX0 )
            | ( sK2_SY18 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK2_SY18 @ SX1 )
            | ( sK1_SY0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( sK1_SY0 @ SX0 )
                | ( sK4_SY21 = SX0 ) )
          | ~ ( sK1_SY0 @ sK4_SY21 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SX0 ) )
              | ~ ( ( SX0
                   != ( sK3_SY30 @ SX0 ) ) ) )
          | ~ ( sK2_SY18 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( sK1_SY0 @ SX0 )
          | ( sK2_SY18 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( sK2_SY18 @ SX1 )
          | ( sK1_SY0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_SY0 @ SX0 )
            | ( sK4_SY21 = SX0 ) )
      | ~ ( sK1_SY0 @ sK4_SY21 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV1: $i] :
      ( ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
            | ~ ( ( SV1
                 != ( sK3_SY30 @ SV1 ) ) ) )
        | ~ ( sK2_SY18 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ! [SY33: $i] :
            ( ( SV2 != SY33 )
            | ~ ( sK1_SY0 @ SV2 )
            | ( sK2_SY18 @ SY33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV3: $i] :
      ( ( ! [SY34: $i] :
            ( ( SV3 != SY34 )
            | ~ ( sK2_SY18 @ SY34 )
            | ( sK1_SY0 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(33,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK1_SY0 @ SX0 )
            | ( sK4_SY21 = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[29]) ).

thf(34,plain,
    ( ( ~ ( sK1_SY0 @ sK4_SY21 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[29]) ).

thf(35,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
              | ~ ( ( SV1
                   != ( sK3_SY30 @ SV1 ) ) ) ) )
        = $true )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( SV2 != SV4 )
        | ~ ( sK1_SY0 @ SV2 )
        | ( sK2_SY18 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( SV3 != SV5 )
        | ~ ( sK2_SY18 @ SV5 )
        | ( sK1_SY0 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(38,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK1_SY0 @ SX0 )
          | ( sK4_SY21 = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(39,plain,
    ( ( sK1_SY0 @ sK4_SY21 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
          | ~ ( ( SV1
               != ( sK3_SY30 @ SV1 ) ) ) )
        = $false )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ( SV2 != SV4 ) )
        = $true )
      | ( ( ~ ( sK1_SY0 @ SV2 )
          | ( sK2_SY18 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( ( SV3 != SV5 ) )
        = $true )
      | ( ( ~ ( sK2_SY18 @ SV5 )
          | ( sK1_SY0 @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(43,plain,
    ! [SV6: $i] :
      ( ( ~ ( sK1_SY0 @ SV6 )
        | ( sK4_SY21 = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) ) )
        = $false )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ( SV1
               != ( sK3_SY30 @ SV1 ) ) ) )
        = $false )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( SV2 = SV4 )
        = $false )
      | ( ( ~ ( sK1_SY0 @ SV2 )
          | ( sK2_SY18 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( ( SV3 = SV5 )
        = $false )
      | ( ( ~ ( sK2_SY18 @ SV5 )
          | ( sK1_SY0 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( sK1_SY0 @ SV6 ) )
        = $true )
      | ( ( sK4_SY21 = SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV1: $i] :
      ( ( ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
        = $true )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV1: $i] :
      ( ( ( ( SV1
           != ( sK3_SY30 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ~ ( sK1_SY0 @ SV2 ) )
        = $true )
      | ( ( sK2_SY18 @ SV4 )
        = $true )
      | ( ( SV2 = SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( sK2_SY18 @ SV5 ) )
        = $true )
      | ( ( sK1_SY0 @ SV3 )
        = $true )
      | ( ( SV3 = SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV6: $i] :
      ( ( ( sK1_SY0 @ SV6 )
        = $false )
      | ( ( sK4_SY21 = SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(54,plain,
    ! [SV1: $i] :
      ( ( ( sK2_SY18 @ SV1 )
        = $false )
      | ( ( sK2_SY18 @ ( sK3_SY30 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV1: $i] :
      ( ( ( SV1
          = ( sK3_SY30 @ SV1 ) )
        = $false )
      | ( ( ~ ( sK2_SY18 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( sK1_SY0 @ SV2 )
        = $false )
      | ( ( sK2_SY18 @ SV4 )
        = $true )
      | ( ( SV2 = SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( sK2_SY18 @ SV5 )
        = $false )
      | ( ( sK1_SY0 @ SV3 )
        = $true )
      | ( ( SV3 = SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV1: $i] :
      ( ( ( sK2_SY18 @ SV1 )
        = $false )
      | ( ( SV1
          = ( sK3_SY30 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(59,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[39,58,57,56,54,53]) ).

thf(60,plain,
    ( ( ! [SY25: $i,SY26: $i] :
          ( ( SY25 != SY26 )
          | ~ ( sK1_SY0 @ SY25 )
          | ( sK2_SY18 @ SY26 ) )
      & ! [SY25: $i,SY26: $i] :
          ( ( SY25 != SY26 )
          | ~ ( sK2_SY18 @ SY26 )
          | ( sK1_SY0 @ SY25 ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(61,plain,
    ( ( ! [SY32: $i] :
          ( ~ ( sK2_SY18 @ SY32 )
          | ( sK6_SY29 = SY32 ) )
      & ( sK2_SY18 @ sK6_SY29 )
      & ! [SY21: $i] :
          ( ( ( sK1_SY0 @ ( sK5_SY22 @ SY21 ) )
            & ( SY21
             != ( sK5_SY22 @ SY21 ) ) )
          | ~ ( sK1_SY0 @ SY21 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(62,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( sK2_SY18 @ SX0 )
                      | ( sK6_SY29 = SX0 ) )
                | ~ ( sK2_SY18 @ sK6_SY29 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
                    | ~ ( ( SX0
                         != ( sK5_SY22 @ SX0 ) ) ) )
                | ~ ( sK1_SY0 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[61,exu]) ).

thf(63,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ~ ( sK1_SY0 @ SX0 )
                | ( sK2_SY18 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ~ ( sK2_SY18 @ SX1 )
                | ( sK1_SY0 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[60,exu]) ).

thf(64,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK2_SY18 @ SX0 )
                  | ( sK6_SY29 = SX0 ) )
            | ~ ( sK2_SY18 @ sK6_SY29 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
                | ~ ( ( SX0
                     != ( sK5_SY22 @ SX0 ) ) ) )
            | ~ ( sK1_SY0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(65,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK1_SY0 @ SX0 )
            | ( sK2_SY18 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK2_SY18 @ SX1 )
            | ( sK1_SY0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(66,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( sK2_SY18 @ SX0 )
                  | ( sK6_SY29 = SX0 ) )
            | ~ ( sK2_SY18 @ sK6_SY29 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[64]) ).

thf(67,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
                | ~ ( ( SX0
                     != ( sK5_SY22 @ SX0 ) ) ) )
            | ~ ( sK1_SY0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[64]) ).

thf(68,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK1_SY0 @ SX0 )
            | ( sK2_SY18 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(69,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ~ ( sK2_SY18 @ SX1 )
            | ( sK1_SY0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(70,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( sK2_SY18 @ SX0 )
                | ( sK6_SY29 = SX0 ) )
          | ~ ( sK2_SY18 @ sK6_SY29 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[66]) ).

thf(71,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SX0 ) )
              | ~ ( ( SX0
                   != ( sK5_SY22 @ SX0 ) ) ) )
          | ~ ( sK1_SY0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[67]) ).

thf(72,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( sK1_SY0 @ SX0 )
          | ( sK2_SY18 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(73,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( sK2_SY18 @ SX1 )
          | ( sK1_SY0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(74,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK2_SY18 @ SX0 )
            | ( sK6_SY29 = SX0 ) )
      | ~ ( sK2_SY18 @ sK6_SY29 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(75,plain,
    ! [SV7: $i] :
      ( ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
            | ~ ( ( SV7
                 != ( sK5_SY22 @ SV7 ) ) ) )
        | ~ ( sK1_SY0 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV8: $i] :
      ( ( ! [SY35: $i] :
            ( ( SV8 != SY35 )
            | ~ ( sK1_SY0 @ SV8 )
            | ( sK2_SY18 @ SY35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV9: $i] :
      ( ( ! [SY36: $i] :
            ( ( SV9 != SY36 )
            | ~ ( sK2_SY18 @ SY36 )
            | ( sK1_SY0 @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(78,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( sK2_SY18 @ SX0 )
            | ( sK6_SY29 = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[74]) ).

thf(79,plain,
    ( ( ~ ( sK2_SY18 @ sK6_SY29 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[74]) ).

thf(80,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
              | ~ ( ( SV7
                   != ( sK5_SY22 @ SV7 ) ) ) ) )
        = $true )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(81,plain,
    ! [SV10: $i,SV8: $i] :
      ( ( ( SV8 != SV10 )
        | ~ ( sK1_SY0 @ SV8 )
        | ( sK2_SY18 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(82,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( SV9 != SV11 )
        | ~ ( sK2_SY18 @ SV11 )
        | ( sK1_SY0 @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(83,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( sK2_SY18 @ SX0 )
          | ( sK6_SY29 = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(84,plain,
    ( ( sK2_SY18 @ sK6_SY29 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(85,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
          | ~ ( ( SV7
               != ( sK5_SY22 @ SV7 ) ) ) )
        = $false )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(86,plain,
    ! [SV10: $i,SV8: $i] :
      ( ( ( ( SV8 != SV10 ) )
        = $true )
      | ( ( ~ ( sK1_SY0 @ SV8 )
          | ( sK2_SY18 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(87,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( ( SV9 != SV11 ) )
        = $true )
      | ( ( ~ ( sK2_SY18 @ SV11 )
          | ( sK1_SY0 @ SV9 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(88,plain,
    ! [SV12: $i] :
      ( ( ~ ( sK2_SY18 @ SV12 )
        | ( sK6_SY29 = SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(89,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) ) )
        = $false )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(90,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( ( SV7
               != ( sK5_SY22 @ SV7 ) ) ) )
        = $false )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(91,plain,
    ! [SV10: $i,SV8: $i] :
      ( ( ( SV8 = SV10 )
        = $false )
      | ( ( ~ ( sK1_SY0 @ SV8 )
          | ( sK2_SY18 @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(92,plain,
    ! [SV11: $i,SV9: $i] :
      ( ( ( SV9 = SV11 )
        = $false )
      | ( ( ~ ( sK2_SY18 @ SV11 )
          | ( sK1_SY0 @ SV9 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[87]) ).

thf(93,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( sK2_SY18 @ SV12 ) )
        = $true )
      | ( ( sK6_SY29 = SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(94,plain,
    ! [SV7: $i] :
      ( ( ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
        = $true )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(95,plain,
    ! [SV7: $i] :
      ( ( ( ( SV7
           != ( sK5_SY22 @ SV7 ) ) )
        = $true )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[90]) ).

thf(96,plain,
    ! [SV10: $i,SV8: $i] :
      ( ( ( ~ ( sK1_SY0 @ SV8 ) )
        = $true )
      | ( ( sK2_SY18 @ SV10 )
        = $true )
      | ( ( SV8 = SV10 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(97,plain,
    ! [SV9: $i,SV11: $i] :
      ( ( ( ~ ( sK2_SY18 @ SV11 ) )
        = $true )
      | ( ( sK1_SY0 @ SV9 )
        = $true )
      | ( ( SV9 = SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(98,plain,
    ! [SV12: $i] :
      ( ( ( sK2_SY18 @ SV12 )
        = $false )
      | ( ( sK6_SY29 = SV12 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[93]) ).

thf(99,plain,
    ! [SV7: $i] :
      ( ( ( sK1_SY0 @ SV7 )
        = $false )
      | ( ( sK1_SY0 @ ( sK5_SY22 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(100,plain,
    ! [SV7: $i] :
      ( ( ( SV7
          = ( sK5_SY22 @ SV7 ) )
        = $false )
      | ( ( ~ ( sK1_SY0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(101,plain,
    ! [SV10: $i,SV8: $i] :
      ( ( ( sK1_SY0 @ SV8 )
        = $false )
      | ( ( sK2_SY18 @ SV10 )
        = $true )
      | ( ( SV8 = SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(102,plain,
    ! [SV9: $i,SV11: $i] :
      ( ( ( sK2_SY18 @ SV11 )
        = $false )
      | ( ( sK1_SY0 @ SV9 )
        = $true )
      | ( ( SV9 = SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(103,plain,
    ! [SV7: $i] :
      ( ( ( sK1_SY0 @ SV7 )
        = $false )
      | ( ( SV7
          = ( sK5_SY22 @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(104,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[84,103,102,101,99,98]) ).

thf(105,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[104,59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU550^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n025.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  : 600
% 0.14/0.34  % DateTime : Sat Jun 18 23:21:13 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 175
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (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)....
% 0.20/0.42  
% 0.20/0.42  ********************************
% 0.20/0.42  *   All subproblems solved!    *
% 0.20/0.42  ********************************
% 0.20/0.42  % SZS status Theorem for /export/starexec/sandbox2/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:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43  
% 0.20/0.43  %**** Beginning of derivation protocol ****
% 0.20/0.43  % SZS output start CNFRefutation
% See solution above
% 0.20/0.43  
% 0.20/0.43  %**** End of derivation protocol ****
% 0.20/0.43  %**** no. of clauses in derivation: 105 ****
% 0.20/0.43  %**** clause counter: 104 ****
% 0.20/0.43  
% 0.20/0.43  % SZS status Theorem for /export/starexec/sandbox2/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:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------