TSTP Solution File: SEU620^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU620^2 : 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 : n014.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 12:13:25 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   46 (  28 unt;  11 typ;   3 def)
%            Number of atoms       :  167 (  69 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives : 1363 (  57   ~;  29   |;  16   &;1258   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   79 (   3   ^  64   !;  12   ?;  79   :)

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

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

thf(tp_iskpair,type,
    iskpair: $i > $o ).

thf(tp_kpair,type,
    kpair: $i > $i > $i ).

thf(tp_kpairiskpair,type,
    kpairiskpair: $o ).

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

thf(tp_sK2_SY21,type,
    sK2_SY21: $i ).

thf(tp_sK3_SY7,type,
    sK3_SY7: $i > $i > $i ).

thf(tp_sK4_SY26,type,
    sK4_SY26: $i > $i > $i ).

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

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

thf(iskpair,definition,
    ( iskpair
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
          & ? [Xy: $i] :
              ( ( in @ Xy @ ( setunion @ A ) )
              & ( A
                = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).

thf(kpair,definition,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).

thf(kpairiskpair,definition,
    ( kpairiskpair
    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).

thf(1,conjecture,
    ( kpairiskpair
   => ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).

thf(2,negated_conjecture,
    ( ( kpairiskpair
     => ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY5: $i,SY6: $i] :
        ? [SY7: $i] :
          ( ( in @ SY7 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [SY8: $i] :
              ( ( in @ SY8 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ SY7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY7 @ ( setadjoin @ SY8 @ emptyset ) ) @ emptyset ) ) ) ) )
     => ! [SY0: $i,SY1: $i] :
        ? [SY3: $i] :
          ( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [SY4: $i] :
              ( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,iskpair,kpair,kpairiskpair]) ).

thf(4,plain,
    ( ( ! [SY5: $i,SY6: $i] :
        ? [SY7: $i] :
          ( ( in @ SY7 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [SY8: $i] :
              ( ( in @ SY8 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ SY7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY7 @ ( setadjoin @ SY8 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [SY0: $i,SY1: $i] :
        ? [SY3: $i] :
          ( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
          & ? [SY4: $i] :
              ( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
              & ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [SY0: $i,SY1: $i] :
          ? [SY3: $i] :
            ( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
            & ? [SY4: $i] :
                ( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
                & ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
                  = ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY24: $i] :
          ( ! [SY25: $i] :
              ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY24 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
              | ~ ( in @ SY25 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
          | ~ ( in @ SY24 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY5: $i,SY6: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setadjoin @ ( sK4_SY26 @ SY6 @ SY5 ) @ emptyset ) ) @ emptyset ) ) )
          & ( in @ ( sK4_SY26 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
          & ( in @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [SY5: $i,SY6: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setadjoin @ ( sK4_SY26 @ SY6 @ SY5 ) @ emptyset ) ) @ emptyset ) ) )
          & ( in @ ( sK4_SY26 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
          & ( in @ ( sK3_SY7 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ! [SY24: $i] :
          ( ! [SY25: $i] :
              ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SY24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY24 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
              | ~ ( in @ SY25 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
          | ~ ( in @ SY24 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
                   != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK4_SY26 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
                  | ~ ( in @ ( sK4_SY26 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
            | ~ ( in @ ( sK3_SY7 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9,iskpair,kpair,kpairiskpair]) ).

thf(12,plain,
    ! [SV1: $i] :
      ( ( ! [SY27: $i] :
            ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY27 @ emptyset ) ) @ emptyset ) ) )
            | ~ ( in @ SY27 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        | ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV2: $i] :
      ( ( ! [SY28: $i] :
            ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY28 @ emptyset ) ) @ emptyset ) )
                     != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY28 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SY28 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SY28 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
                    | ~ ( in @ ( sK4_SY26 @ SY28 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY28 @ emptyset ) ) @ emptyset ) ) ) ) )
              | ~ ( in @ ( sK3_SY7 @ SY28 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY28 @ emptyset ) ) @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV1: $i] :
      ( ( ( ! [SY27: $i] :
              ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY27 @ emptyset ) ) @ emptyset ) ) )
              | ~ ( in @ SY27 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) ) )
        = $true )
      | ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
                   != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
                  | ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
            | ~ ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
          | ~ ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true )
      | ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
              | ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
        | ~ ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) ) )
        = $true )
      | ( ( ~ ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true )
      | ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
              | ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV2: $i,SV3: $i] :
      ( ( ~ ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( ~ ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true )
      | ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ~ ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
            | ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV2: $i,SV3: $i] :
      ( ( in @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: $i,SV4: $i] :
      ( ( ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) )
        = $false )
      | ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( ~ ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
        | ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( in @ SV1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) )
        = $false )
      | ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( in @ SV4 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY21 @ emptyset ) ) @ emptyset ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV2: $i,SV3: $i] :
      ( ( ~ ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV3: $i,SV2: $i] :
      ( ( ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK3_SY7 @ SV3 @ SV2 ) @ ( setadjoin @ ( sK4_SY26 @ SV3 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV2: $i,SV3: $i] :
      ( ( in @ ( sK4_SY26 @ SV3 @ SV2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[23,30,29,26]) ).

thf(32,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU620^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 06:39:18 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 783
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.19/0.43  
% 0.19/0.43  ********************************
% 0.19/0.43  *   All subproblems solved!    *
% 0.19/0.43  ********************************
% 0.19/0.43  % 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:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.44  
% 0.19/0.44  %**** Beginning of derivation protocol ****
% 0.19/0.44  % SZS output start CNFRefutation
% See solution above
% 0.19/0.44  
% 0.19/0.44  %**** End of derivation protocol ****
% 0.19/0.44  %**** no. of clauses in derivation: 32 ****
% 0.19/0.44  %**** clause counter: 31 ****
% 0.19/0.44  
% 0.19/0.44  % 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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------