TSTP Solution File: SEU902^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU902^5 : 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 : n008.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 12:15:41 EDT 2022

% Result   : Theorem 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   87 (  21 unt;   4 typ;   0 def)
%            Number of atoms       :  570 ( 298 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :  928 ( 323   ~; 167   |;  10   &; 419   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  133 ( 133   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   2 con; 0-3 aty)
%            Number of variables   :  191 (   8   ^ 177   !;   6   ?; 191   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_d,type,
    d: $i > $o ).

thf(tp_sK1_Xh,type,
    sK1_Xh: ( $i > $o ) > $i ).

thf(tp_sK2_SY11,type,
    sK2_SY11: $i > $i > $o ).

thf(tp_sK3_SY11,type,
    sK3_SY11: ( $i > $o ) > $i > $i > $o ).

thf(1,conjecture,
    ! [Xh: ( $i > $o ) > $i] :
      ( ( ! [Xp: $i > $o,Xq: $i > $o] :
            ( ( ( Xh @ Xp )
              = ( Xh @ Xq ) )
           => ( Xp = Xq ) )
        & ( d
          = ( ^ [Xz: $i] :
              ? [Xt: $i > $o] :
                ( ~ ( Xt @ ( Xh @ Xt ) )
                & ( Xz
                  = ( Xh @ Xt ) ) ) ) ) )
     => ~ ( d @ ( Xh @ d ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM143_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xh: ( $i > $o ) > $i] :
          ( ( ! [Xp: $i > $o,Xq: $i > $o] :
                ( ( ( Xh @ Xp )
                  = ( Xh @ Xq ) )
               => ( Xp = Xq ) )
            & ( d
              = ( ^ [Xz: $i] :
                  ? [Xt: $i > $o] :
                    ( ~ ( Xt @ ( Xh @ Xt ) )
                    & ( Xz
                      = ( Xh @ Xt ) ) ) ) ) )
         => ~ ( d @ ( Xh @ d ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xh: ( $i > $o ) > $i] :
          ( ( ! [Xp: $i > $o,Xq: $i > $o] :
                ( ( ( Xh @ Xp )
                  = ( Xh @ Xq ) )
               => ( Xp = Xq ) )
            & ( d
              = ( ^ [Xz: $i] :
                  ? [Xt: $i > $o] :
                    ( ~ ( Xt @ ( Xh @ Xt ) )
                    & ( Xz
                      = ( Xh @ Xt ) ) ) ) ) )
         => ~ ( d @ ( Xh @ d ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ! [SY5: $i > $o,SY6: $i > $o] :
            ( ( ( sK1_Xh @ SY5 )
              = ( sK1_Xh @ SY6 ) )
           => ( SY5 = SY6 ) )
        & ( d
          = ( ^ [SY7: $i] :
              ? [SY8: $i > $o] :
                ( ~ ( SY8 @ ( sK1_Xh @ SY8 ) )
                & ( SY7
                  = ( sK1_Xh @ SY8 ) ) ) ) ) )
     => ~ ( d @ ( sK1_Xh @ d ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY5: $i > $o,SY6: $i > $o] :
          ( ( ( sK1_Xh @ SY5 )
            = ( sK1_Xh @ SY6 ) )
         => ( SY5 = SY6 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( d
      = ( ^ [SY7: $i] :
          ? [SY8: $i > $o] :
            ( ~ ( SY8 @ ( sK1_Xh @ SY8 ) )
            & ( SY7
              = ( sK1_Xh @ SY8 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ~ ( d @ ( sK1_Xh @ d ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(8,plain,
    ( ( d @ ( sK1_Xh @ d ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SY5: $i > $o,SY6: $i > $o] :
          ( ( ( sK1_Xh @ SY5 )
           != ( sK1_Xh @ SY6 ) )
          | ( SY5 = SY6 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(10,plain,
    ( ( d
      = ( ^ [SY7: $i] :
          ? [SY8: $i > $o] :
            ( ~ ( SY8 @ ( sK1_Xh @ SY8 ) )
            & ( SY7
              = ( sK1_Xh @ SY8 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ! [SY5: $i > $o,SY6: $i > $o] :
          ( ( ( sK1_Xh @ SY5 )
           != ( sK1_Xh @ SY6 ) )
          | ( SY5 = SY6 ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( d @ ( sK1_Xh @ d ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(13,plain,
    ( ( d
      = ( ^ [SX0: $i] :
            ~ ! [SX1: $i > $o] :
                ~ ~ ( ~ ~ ( SX1 @ ( sK1_Xh @ SX1 ) )
                    | ( SX0
                     != ( sK1_Xh @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(14,plain,
    ! [SV1: $i > $o] :
      ( ( ! [SY9: $i > $o] :
            ( ( ( sK1_Xh @ SV1 )
             != ( sK1_Xh @ SY9 ) )
            | ( SV1 = SY9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ! [SV2: $i] :
          ( ( d @ SV2 )
          = ( ~ ! [SY10: $i > $o] :
                  ~ ~ ( ~ ~ ( SY10 @ ( sK1_Xh @ SY10 ) )
                      | ( SV2
                       != ( sK1_Xh @ SY10 ) ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( d
      = ( ^ [SX0: $i] :
            ~ ! [SX1: $i > $o] :
                ~ ~ ( ~ ~ ( SX1 @ ( sK1_Xh @ SX1 ) )
                    | ( SX0
                     != ( sK1_Xh @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV3: $i > $o,SV1: $i > $o] :
      ( ( ( ( sK1_Xh @ SV1 )
         != ( sK1_Xh @ SV3 ) )
        | ( SV1 = SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV4: $i] :
      ( ( ( d @ SV4 )
        = ( ~ ! [SY11: $i > $o] :
                ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                    | ( SV4
                     != ( sK1_Xh @ SY11 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV3: $i > $o,SV1: $i > $o] :
      ( ( ( ( ( sK1_Xh @ SV1 )
           != ( sK1_Xh @ SV3 ) ) )
        = $true )
      | ( ( SV1 = SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV4: $i] :
      ( ( ~ ( ( d @ SV4 )
            | ~ ! [SY11: $i > $o] :
                  ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                      | ( SV4
                       != ( sK1_Xh @ SY11 ) ) ) )
        | ~ ( ~ ( d @ SV4 )
            | ~ ~ ! [SY11: $i > $o] :
                    ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                        | ( SV4
                         != ( sK1_Xh @ SY11 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV4: $i] :
      ( ( ( d @ SV4 )
        = ( ~ ! [SY11: $i > $o] :
                ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                    | ( SV4
                     != ( sK1_Xh @ SY11 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: $i > $o,SV1: $i > $o] :
      ( ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false )
      | ( ( SV1 = SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( d @ SV4 )
              | ~ ! [SY11: $i > $o] :
                    ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                        | ( SV4
                         != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV3: $i > $o,SV1: $i > $o] :
      ( ( ( ! [SV5: $i] :
              ( ( SV1 @ SV5 )
              = ( SV3 @ SV5 ) ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV3: $i > $o,SV1: $i > $o] :
      ( ( ( SV1 = SV3 )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV4: $i] :
      ( ( ( ( d @ SV4 )
          | ~ ! [SY11: $i > $o] :
                ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                    | ( SV4
                     != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(27,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ( SV1 @ SV6 )
          = ( SV3 @ SV6 ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV4: $i] :
      ( ( ( d @ SV4 )
        = $false )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV4: $i] :
      ( ( ( ~ ! [SY11: $i > $o] :
                ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                    | ( SV4
                     != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV6 )
              | ( SV3 @ SV6 ) )
          | ~ ( ~ ( SV1 @ SV6 )
              | ~ ( SV3 @ SV6 ) ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ( SV1 @ SV6 )
          = ( SV3 @ SV6 ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( d @ SV4 )
          | ~ ~ ! [SY11: $i > $o] :
                  ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                      | ( SV4
                       != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV4: $i] :
      ( ( ( ! [SY11: $i > $o] :
              ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                  | ( SV4
                   != ( sK1_Xh @ SY11 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV6 )
              | ( SV3 @ SV6 ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV6 )
              | ~ ( SV3 @ SV6 ) ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( d @ SV4 ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ! [SY11: $i > $o] :
                  ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                      | ( SV4
                       != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ~ ( ~ ~ ( SV7 @ ( sK1_Xh @ SV7 ) )
                | ( SV4
                 != ( sK1_Xh @ SV7 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ( SV1 @ SV6 )
          | ( SV3 @ SV6 ) )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV6 )
              | ~ ( SV3 @ SV6 ) ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(39,plain,
    ! [SV4: $i] :
      ( ( ( d @ SV4 )
        = $true )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV4: $i] :
      ( ( ( ~ ! [SY11: $i > $o] :
                ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                    | ( SV4
                     != ( sK1_Xh @ SY11 ) ) ) )
        = $true )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ( ~ ~ ( SV7 @ ( sK1_Xh @ SV7 ) )
              | ( SV4
               != ( sK1_Xh @ SV7 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(42,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV6 )
              | ~ ( SV3 @ SV6 ) ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV1: $i > $o,SV6: $i,SV3: $i > $o] :
      ( ( ( SV3 @ SV6 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV6 )
              | ~ ( SV3 @ SV6 ) ) )
        = $true )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV4: $i] :
      ( ( ( ! [SY11: $i > $o] :
              ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                  | ( SV4
                   != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ~ ( SV7 @ ( sK1_Xh @ SV7 ) )
          | ( SV4
           != ( sK1_Xh @ SV7 ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 )
          | ~ ( SV3 @ SV6 ) )
        = $false )
      | ( ( SV1 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 )
          | ~ ( SV3 @ SV6 ) )
        = $false )
      | ( ( SV3 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( sK2_SY11 @ SV4 @ ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) )
                | ( SV4
                 != ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[44]) ).

thf(49,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ~ ( SV7 @ ( sK1_Xh @ SV7 ) ) )
        = $true )
      | ( ( ( SV4
           != ( sK1_Xh @ SV7 ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(50,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 ) )
        = $false )
      | ( ( SV1 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(51,plain,
    ! [SV1: $i > $o,SV6: $i,SV3: $i > $o] :
      ( ( ( ~ ( SV3 @ SV6 ) )
        = $false )
      | ( ( SV1 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ SV6 ) )
        = $false )
      | ( ( SV3 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV1: $i > $o,SV6: $i,SV3: $i > $o] :
      ( ( ( ~ ( SV3 @ SV6 ) )
        = $false )
      | ( ( SV3 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[47]) ).

thf(54,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( sK2_SY11 @ SV4 @ ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) )
              | ( SV4
               != ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) ) ) )
        = $true )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(55,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ( SV7 @ ( sK1_Xh @ SV7 ) ) )
        = $false )
      | ( ( ( SV4
           != ( sK1_Xh @ SV7 ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(56,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $true )
      | ( ( SV1 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV1: $i > $o,SV6: $i,SV3: $i > $o] :
      ( ( ( SV3 @ SV6 )
        = $true )
      | ( ( SV1 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(58,plain,
    ! [SV3: $i > $o,SV6: $i,SV1: $i > $o] :
      ( ( ( SV1 @ SV6 )
        = $true )
      | ( ( SV3 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV1: $i > $o,SV6: $i,SV3: $i > $o] :
      ( ( ( SV3 @ SV6 )
        = $true )
      | ( ( SV3 @ SV6 )
        = $false )
      | ( ( ( sK1_Xh @ SV1 )
          = ( sK1_Xh @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( sK2_SY11 @ SV4 @ ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) )
          | ( SV4
           != ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( ( SV4
           != ( sK1_Xh @ SV7 ) ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( sK2_SY11 @ SV4 @ ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV4: $i] :
      ( ( ( ( SV4
           != ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[60]) ).

thf(64,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( ~ ( ~ ( d @ SV4 )
              | ~ ~ ! [SY11: $i > $o] :
                      ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                          | ( SV4
                           != ( sK1_Xh @ SY11 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(65,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( sK2_SY11 @ SV4 @ ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) ) )
        = $true )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[62]) ).

thf(66,plain,
    ! [SV4: $i] :
      ( ( ( SV4
          = ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) )
        = $true )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[63]) ).

thf(67,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( ~ ( d @ SV4 )
          | ~ ~ ! [SY11: $i > $o] :
                  ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                      | ( SV4
                       != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(68,plain,
    ! [SV4: $i] :
      ( ( ( sK2_SY11 @ SV4 @ ( sK1_Xh @ ( sK2_SY11 @ SV4 ) ) )
        = $false )
      | ( ( d @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(69,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( ~ ( d @ SV4 ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(70,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( ~ ~ ! [SY11: $i > $o] :
                  ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                      | ( SV4
                       != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(71,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( d @ SV4 )
        = $true )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( ~ ! [SY11: $i > $o] :
                ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                    | ( SV4
                     != ( sK1_Xh @ SY11 ) ) ) )
        = $true )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(73,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( ! [SY11: $i > $o] :
              ~ ~ ( ~ ~ ( SY11 @ ( sK1_Xh @ SY11 ) )
                  | ( SV4
                   != ( sK1_Xh @ SY11 ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(74,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ~ ( ~ ~ ( sK3_SY11 @ SV7 @ SV4 @ ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) )
                | ( SV4
                 != ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[73]) ).

thf(75,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ( ~ ~ ( sK3_SY11 @ SV7 @ SV4 @ ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) )
              | ( SV4
               != ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) ) ) )
        = $true )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[74]) ).

thf(76,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ~ ( sK3_SY11 @ SV7 @ SV4 @ ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) )
          | ( SV4
           != ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(77,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ~ ( sK3_SY11 @ SV7 @ SV4 @ ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(78,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( ( SV4
           != ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(79,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( ~ ( sK3_SY11 @ SV7 @ SV4 @ ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) ) )
        = $true )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[77]) ).

thf(80,plain,
    ! [SV7: $i > $o,SV4: $i] :
      ( ( ( SV4
          = ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) )
        = $true )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(81,plain,
    ! [SV4: $i,SV7: $i > $o] :
      ( ( ( sK3_SY11 @ SV7 @ SV4 @ ( sK1_Xh @ ( sK3_SY11 @ SV7 @ SV4 ) ) )
        = $false )
      | ( ( SV7 @ ( sK1_Xh @ SV7 ) )
        = $true )
      | ( ( SV4
          = ( sK1_Xh @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(82,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[12,81,80,71,68,66,59,58,57,56,39,31,25,21,16]) ).

thf(83,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[82]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU902^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 05:46:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout: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)..
% 0.19/0.40  
% 0.19/0.40  ********************************
% 0.19/0.40  *   All subproblems solved!    *
% 0.19/0.40  ********************************
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:82,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40  
% 0.19/0.40  %**** Beginning of derivation protocol ****
% 0.19/0.40  % SZS output start CNFRefutation
% See solution above
% 0.19/0.40  
% 0.19/0.40  %**** End of derivation protocol ****
% 0.19/0.40  %**** no. of clauses in derivation: 83 ****
% 0.19/0.40  %**** clause counter: 82 ****
% 0.19/0.40  
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:82,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------