TSTP Solution File: SEU706^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU706^2 : 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 : n011.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 12:14:04 EDT 2022

% Result   : Theorem 0.18s 0.38s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   96 (  57 unt;  13 typ;   6 def)
%            Number of atoms       :  476 ( 237 equ;   0 cnn)
%            Maximal formula atoms :    8 (   5 avg)
%            Number of connectives :  595 ( 157   ~; 117   |;   5   &; 291   @)
%                                         (   1 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;  11 con; 0-2 aty)
%            Number of variables   :  158 (   1   ^ 156   !;   1   ?; 158   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
    emptyset: $i ).

thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_in__Cong,type,
    in__Cong: $o ).

thf(tp_sK1_X,type,
    sK1_X: $i ).

thf(tp_sK2_SY0,type,
    sK2_SY0: $i ).

thf(tp_sK3_SX0,type,
    sK3_SX0: $i ).

thf(tp_setadjoin,type,
    setadjoin: $i > $i > $i ).

thf(tp_setadjoin__Cong,type,
    setadjoin__Cong: $o ).

thf(tp_setunion,type,
    setunion: $i > $i ).

thf(tp_setunion__Cong,type,
    setunion__Cong: $o ).

thf(tp_setunionsingleton,type,
    setunionsingleton: $o ).

thf(tp_singleton,type,
    singleton: $i > $o ).

thf(tp_uniqinunit,type,
    uniqinunit: $o ).

thf(in__Cong,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
              <=> ( in @ Xy @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).

thf(setadjoin__Cong,definition,
    ( setadjoin__Cong
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ! [Xz: $i,Xu: $i] :
              ( ( Xz = Xu )
             => ( ( setadjoin @ Xx @ Xz )
                = ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).

thf(setunion__Cong,definition,
    ( setunion__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( setunion @ A )
            = ( setunion @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).

thf(setunionsingleton,definition,
    ( setunionsingleton
    = ( ! [Xx: $i] :
          ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
          = Xx ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).

thf(singleton,definition,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( in @ Xx @ A )
          & ( A
            = ( setadjoin @ Xx @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).

thf(uniqinunit,definition,
    ( uniqinunit
    = ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).

thf(1,conjecture,
    ( uniqinunit
   => ( in__Cong
     => ( setadjoin__Cong
       => ( setunion__Cong
         => ( setunionsingleton
           => ! [X: $i] :
                ( ( singleton @ X )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ X )
                   => ( ( setunion @ X )
                      = Xx ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).

thf(2,negated_conjecture,
    ( ( uniqinunit
     => ( in__Cong
       => ( setadjoin__Cong
         => ( setunion__Cong
           => ( setunionsingleton
             => ! [X: $i] :
                  ( ( singleton @ X )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ X )
                     => ( ( setunion @ X )
                        = Xx ) ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    uniqinunit = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(4,plain,
    in__Cong = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(5,plain,
    setadjoin__Cong = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(6,plain,
    setunion__Cong = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(7,plain,
    setunionsingleton = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(8,plain,
    ( ( ! [X: $i] :
          ( ( singleton @ X )
         => ! [Xx: $i] :
              ( ( in @ Xx @ X )
             => ( ( setunion @ X )
                = Xx ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ~ ! [X: $i] :
            ( ( singleton @ X )
           => ! [Xx: $i] :
                ( ( in @ Xx @ X )
               => ( ( setunion @ X )
                  = Xx ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( singleton @ sK1_X )
      & ( in @ sK2_SY0 @ sK1_X )
      & ( ( setunion @ sK1_X )
       != sK2_SY0 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(11,plain,
    setunionsingleton = $true,
    inference(copy,[status(thm)],[7]) ).

thf(12,plain,
    setunion__Cong = $true,
    inference(copy,[status(thm)],[6]) ).

thf(13,plain,
    setadjoin__Cong = $true,
    inference(copy,[status(thm)],[5]) ).

thf(14,plain,
    in__Cong = $true,
    inference(copy,[status(thm)],[4]) ).

thf(15,plain,
    uniqinunit = $true,
    inference(copy,[status(thm)],[3]) ).

thf(16,plain,
    ( ( ( singleton @ sK1_X )
      & ( in @ sK2_SY0 @ sK1_X )
      & ( ( setunion @ sK1_X )
       != sK2_SY0 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(17,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i,SX3: $i] :
              ( ( SX2 != SX3 )
              | ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
                      | ( in @ SX3 @ SX1 ) )
                  | ~ ( ~ ( in @ SX3 @ SX1 )
                      | ( in @ SX2 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).

thf(18,plain,
    ( ( ~ ( ~ ~ ! [SX0: $i] :
                  ~ ~ ( ~ ( in @ SX0 @ sK1_X )
                      | ( sK1_X
                       != ( setadjoin @ SX0 @ emptyset ) ) )
          | ~ ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
                | ~ ( ( ( setunion @ sK1_X )
                     != sK2_SY0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).

thf(19,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i,SX3: $i] :
              ( ( SX2 != SX3 )
              | ( ( setadjoin @ SX0 @ SX2 )
                = ( setadjoin @ SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).

thf(20,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( setunion @ SX0 )
            = ( setunion @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).

thf(21,plain,
    ( ( ! [SX0: $i] :
          ( ( setunion @ ( setadjoin @ SX0 @ emptyset ) )
          = SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).

thf(22,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ! [SY1: $i] :
            ( ( SV1 != SY1 )
            | ! [SY2: $i,SY3: $i] :
                ( ( SY2 != SY3 )
                | ~ ( ~ ( ~ ( in @ SY2 @ SV1 )
                        | ( in @ SY3 @ SY1 ) )
                    | ~ ( ~ ( in @ SY3 @ SY1 )
                        | ( in @ SY2 @ SV1 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(24,plain,
    ( ( ~ ~ ! [SX0: $i] :
              ~ ~ ( ~ ( in @ SX0 @ sK1_X )
                  | ( sK1_X
                   != ( setadjoin @ SX0 @ emptyset ) ) )
      | ~ ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
            | ~ ( ( ( setunion @ sK1_X )
                 != sK2_SY0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV2: $i] :
      ( ( ! [SY4: $i] :
            ( ( SV2 != SY4 )
            | ! [SY5: $i,SY6: $i] :
                ( ( SY5 != SY6 )
                | ( ( setadjoin @ SV2 @ SY5 )
                  = ( setadjoin @ SY4 @ SY6 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(26,plain,
    ! [SV3: $i] :
      ( ( ! [SY7: $i] :
            ( ( SV3 != SY7 )
            | ( ( setunion @ SV3 )
              = ( setunion @ SY7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(27,plain,
    ! [SV4: $i] :
      ( ( ( setunion @ ( setadjoin @ SV4 @ emptyset ) )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(28,plain,
    ! [SV5: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( in @ SV5 @ ( setadjoin @ SY8 @ emptyset ) )
            | ( SV5 = SY8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(29,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( SV1 != SV6 )
        | ! [SY9: $i,SY10: $i] :
            ( ( SY9 != SY10 )
            | ~ ( ~ ( ~ ( in @ SY9 @ SV1 )
                    | ( in @ SY10 @ SV6 ) )
                | ~ ( ~ ( in @ SY10 @ SV6 )
                    | ( in @ SY9 @ SV1 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(30,plain,
    ( ( ~ ~ ! [SX0: $i] :
              ~ ~ ( ~ ( in @ SX0 @ sK1_X )
                  | ( sK1_X
                   != ( setadjoin @ SX0 @ emptyset ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(31,plain,
    ( ( ~ ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
            | ~ ( ( ( setunion @ sK1_X )
                 != sK2_SY0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(32,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( SV2 != SV7 )
        | ! [SY11: $i,SY12: $i] :
            ( ( SY11 != SY12 )
            | ( ( setadjoin @ SV2 @ SY11 )
              = ( setadjoin @ SV7 @ SY12 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(33,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( SV3 != SV8 )
        | ( ( setunion @ SV3 )
          = ( setunion @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(34,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ~ ( in @ SV5 @ ( setadjoin @ SV9 @ emptyset ) )
        | ( SV5 = SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( ( SV1 != SV6 ) )
        = $true )
      | ( ( ! [SY9: $i,SY10: $i] :
              ( ( SY9 != SY10 )
              | ~ ( ~ ( ~ ( in @ SY9 @ SV1 )
                      | ( in @ SY10 @ SV6 ) )
                  | ~ ( ~ ( in @ SY10 @ SV6 )
                      | ( in @ SY9 @ SV1 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(36,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ~ ( ~ ( in @ SX0 @ sK1_X )
                | ( sK1_X
                 != ( setadjoin @ SX0 @ emptyset ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(37,plain,
    ( ( ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
          | ~ ( ( ( setunion @ sK1_X )
               != sK2_SY0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[31]) ).

thf(38,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( ( SV2 != SV7 ) )
        = $true )
      | ( ( ! [SY11: $i,SY12: $i] :
              ( ( SY11 != SY12 )
              | ( ( setadjoin @ SV2 @ SY11 )
                = ( setadjoin @ SV7 @ SY12 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( ( SV3 != SV8 ) )
        = $true )
      | ( ( ( setunion @ SV3 )
          = ( setunion @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ( ~ ( in @ SV5 @ ( setadjoin @ SV9 @ emptyset ) ) )
        = $true )
      | ( ( SV5 = SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ( SV1 = SV6 )
        = $false )
      | ( ( ! [SY9: $i,SY10: $i] :
              ( ( SY9 != SY10 )
              | ~ ( ~ ( ~ ( in @ SY9 @ SV1 )
                      | ( in @ SY10 @ SV6 ) )
                  | ~ ( ~ ( in @ SY10 @ SV6 )
                      | ( in @ SY9 @ SV1 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(42,plain,
    ( ( ! [SX0: $i] :
          ~ ~ ( ~ ( in @ SX0 @ sK1_X )
              | ( sK1_X
               != ( setadjoin @ SX0 @ emptyset ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(43,plain,
    ( ( ~ ( in @ sK2_SY0 @ sK1_X )
      | ~ ( ( ( setunion @ sK1_X )
           != sK2_SY0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( SV2 = SV7 )
        = $false )
      | ( ( ! [SY11: $i,SY12: $i] :
              ( ( SY11 != SY12 )
              | ( ( setadjoin @ SV2 @ SY11 )
                = ( setadjoin @ SV7 @ SY12 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( SV3 = SV8 )
        = $false )
      | ( ( ( setunion @ SV3 )
          = ( setunion @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ( in @ SV5 @ ( setadjoin @ SV9 @ emptyset ) )
        = $false )
      | ( ( SV5 = SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(47,plain,
    ! [SV6: $i,SV1: $i,SV10: $i] :
      ( ( ( ! [SY13: $i] :
              ( ( SV10 != SY13 )
              | ~ ( ~ ( ~ ( in @ SV10 @ SV1 )
                      | ( in @ SY13 @ SV6 ) )
                  | ~ ( ~ ( in @ SY13 @ SV6 )
                      | ( in @ SV10 @ SV1 ) ) ) ) )
        = $true )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(48,plain,
    ( ( ~ ~ ( ~ ( in @ sK3_SX0 @ sK1_X )
            | ( sK1_X
             != ( setadjoin @ sK3_SX0 @ emptyset ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[42]) ).

thf(49,plain,
    ( ( ~ ( in @ sK2_SY0 @ sK1_X ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(50,plain,
    ( ( ~ ( ( ( setunion @ sK1_X )
           != sK2_SY0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(51,plain,
    ! [SV7: $i,SV2: $i,SV11: $i] :
      ( ( ( ! [SY14: $i] :
              ( ( SV11 != SY14 )
              | ( ( setadjoin @ SV2 @ SV11 )
                = ( setadjoin @ SV7 @ SY14 ) ) ) )
        = $true )
      | ( ( SV2 = SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(52,plain,
    ! [SV6: $i,SV1: $i,SV12: $i,SV10: $i] :
      ( ( ( ( SV10 != SV12 )
          | ~ ( ~ ( ~ ( in @ SV10 @ SV1 )
                  | ( in @ SV12 @ SV6 ) )
              | ~ ( ~ ( in @ SV12 @ SV6 )
                  | ( in @ SV10 @ SV1 ) ) ) )
        = $true )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(53,plain,
    ( ( ~ ( ~ ( in @ sK3_SX0 @ sK1_X )
          | ( sK1_X
           != ( setadjoin @ sK3_SX0 @ emptyset ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(54,plain,
    ( ( in @ sK2_SY0 @ sK1_X )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(55,plain,
    ( ( ( ( setunion @ sK1_X )
       != sK2_SY0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV7: $i,SV2: $i,SV13: $i,SV11: $i] :
      ( ( ( ( SV11 != SV13 )
          | ( ( setadjoin @ SV2 @ SV11 )
            = ( setadjoin @ SV7 @ SV13 ) ) )
        = $true )
      | ( ( SV2 = SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV6: $i,SV1: $i,SV12: $i,SV10: $i] :
      ( ( ( ( SV10 != SV12 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( in @ SV10 @ SV1 )
                  | ( in @ SV12 @ SV6 ) )
              | ~ ( ~ ( in @ SV12 @ SV6 )
                  | ( in @ SV10 @ SV1 ) ) ) )
        = $true )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(58,plain,
    ( ( ~ ( in @ sK3_SX0 @ sK1_X )
      | ( sK1_X
       != ( setadjoin @ sK3_SX0 @ emptyset ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(59,plain,
    ( ( ( setunion @ sK1_X )
      = sK2_SY0 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(60,plain,
    ! [SV7: $i,SV2: $i,SV13: $i,SV11: $i] :
      ( ( ( ( SV11 != SV13 ) )
        = $true )
      | ( ( ( setadjoin @ SV2 @ SV11 )
          = ( setadjoin @ SV7 @ SV13 ) )
        = $true )
      | ( ( SV2 = SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(61,plain,
    ! [SV6: $i,SV1: $i,SV12: $i,SV10: $i] :
      ( ( ( SV10 = SV12 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( in @ SV10 @ SV1 )
                  | ( in @ SV12 @ SV6 ) )
              | ~ ( ~ ( in @ SV12 @ SV6 )
                  | ( in @ SV10 @ SV1 ) ) ) )
        = $true )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(62,plain,
    ( ( ~ ( in @ sK3_SX0 @ sK1_X ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(63,plain,
    ( ( ( sK1_X
       != ( setadjoin @ sK3_SX0 @ emptyset ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(64,plain,
    ! [SV7: $i,SV2: $i,SV13: $i,SV11: $i] :
      ( ( ( SV11 = SV13 )
        = $false )
      | ( ( ( setadjoin @ SV2 @ SV11 )
          = ( setadjoin @ SV7 @ SV13 ) )
        = $true )
      | ( ( SV2 = SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(65,plain,
    ! [SV6: $i,SV12: $i,SV1: $i,SV10: $i] :
      ( ( ( ~ ( ~ ( in @ SV10 @ SV1 )
              | ( in @ SV12 @ SV6 ) )
          | ~ ( ~ ( in @ SV12 @ SV6 )
              | ( in @ SV10 @ SV1 ) ) )
        = $false )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(66,plain,
    ( ( in @ sK3_SX0 @ sK1_X )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[62]) ).

thf(67,plain,
    ( ( sK1_X
      = ( setadjoin @ sK3_SX0 @ emptyset ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV6: $i,SV12: $i,SV1: $i,SV10: $i] :
      ( ( ( ~ ( ~ ( in @ SV10 @ SV1 )
              | ( in @ SV12 @ SV6 ) ) )
        = $false )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(69,plain,
    ! [SV1: $i,SV10: $i,SV6: $i,SV12: $i] :
      ( ( ( ~ ( ~ ( in @ SV12 @ SV6 )
              | ( in @ SV10 @ SV1 ) ) )
        = $false )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV6: $i,SV12: $i,SV1: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV1 )
          | ( in @ SV12 @ SV6 ) )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(71,plain,
    ! [SV1: $i,SV10: $i,SV6: $i,SV12: $i] :
      ( ( ( ~ ( in @ SV12 @ SV6 )
          | ( in @ SV10 @ SV1 ) )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV6: $i,SV12: $i,SV1: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV1 ) )
        = $true )
      | ( ( in @ SV12 @ SV6 )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(73,plain,
    ! [SV1: $i,SV10: $i,SV6: $i,SV12: $i] :
      ( ( ( ~ ( in @ SV12 @ SV6 ) )
        = $true )
      | ( ( in @ SV10 @ SV1 )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(74,plain,
    ! [SV6: $i,SV12: $i,SV1: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV1 )
        = $false )
      | ( ( in @ SV12 @ SV6 )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(75,plain,
    ! [SV1: $i,SV10: $i,SV6: $i,SV12: $i] :
      ( ( ( in @ SV12 @ SV6 )
        = $false )
      | ( ( in @ SV10 @ SV1 )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV1 = SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(76,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[27,75,74,67,66,64,59,54,46,45]) ).

thf(77,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[76]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU706^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n011.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 : Mon Jun 20 03:16:54 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 1174
% 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:false,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:5,ps:3,u:6,ude:false,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:76,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: 77 ****
% 0.18/0.38  %**** clause counter: 76 ****
% 0.18/0.38  
% 0.18/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:false,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:76,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------