TSTP Solution File: SEU781^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU781^2 : 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 : n029.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 12:14:42 EDT 2022

% Result   : Theorem 0.20s 0.48s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   95 (  50 unt;  15 typ;   3 def)
%            Number of atoms       :  825 ( 176 equ;   0 cnn)
%            Maximal formula atoms :    9 (  10 avg)
%            Number of connectives : 2701 ( 446   ~; 318   |;  22   &;1852   @)
%                                         (   0 <=>;  63  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   9 con; 0-5 aty)
%            Number of variables   :  226 (   5   ^ 218   !;   3   ?; 226   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_breln,type,
    breln: $i > $i > $i > $o ).

thf(tp_breln1,type,
    breln1: $i > $i > $o ).

thf(tp_breln1compE,type,
    breln1compE: $o ).

thf(tp_breln1compset,type,
    breln1compset: $i > $i > $i > $i ).

thf(tp_cartprod,type,
    cartprod: $i > $i > $i ).

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

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

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

thf(tp_sK2_SY49,type,
    sK2_SY49: $i ).

thf(tp_sK3_SY55,type,
    sK3_SY55: $i ).

thf(tp_sK4_SY60,type,
    sK4_SY60: $i ).

thf(tp_sK5_SY64,type,
    sK5_SY64: $i ).

thf(tp_sK6_SY67,type,
    sK6_SY67: $o ).

thf(tp_sK7_Xz,type,
    sK7_Xz: $i > $i > $i > $i > $i > $i ).

thf(tp_subset,type,
    subset: $i > $i > $o ).

thf(breln,definition,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).

thf(breln1,definition,
    ( breln1
    = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).

thf(breln1compE,definition,
    ( breln1compE
    = ( ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ! [S: $i] :
              ( ( breln1 @ A @ S )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ A )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
                       => ? [Xz: $i] :
                            ( ( in @ Xz @ A )
                            & ( in @ ( kpair @ Xx @ Xz ) @ R )
                            & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compE) ).

thf(1,conjecture,
    ( breln1compE
   => ! [A: $i,R: $i] :
        ( ( breln1 @ A @ R )
       => ! [S: $i] :
            ( ( breln1 @ A @ S )
           => ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ! [Xy: $i] :
                    ( ( in @ Xy @ A )
                   => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
                     => ! [Xphi: $o] :
                          ( ! [Xz: $i] :
                              ( ( in @ Xz @ A )
                             => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
                               => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
                                 => Xphi ) ) )
                         => Xphi ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).

thf(2,negated_conjecture,
    ( ( breln1compE
     => ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ! [S: $i] :
              ( ( breln1 @ A @ S )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ A )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
                       => ! [Xphi: $o] :
                            ( ! [Xz: $i] :
                                ( ( in @ Xz @ A )
                               => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
                                 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
                                   => Xphi ) ) )
                           => Xphi ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY15: $i,SY16: $i] :
          ( ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
         => ! [SY21: $i] :
              ( ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY15 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY15 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
                       => ? [Xz: $i] :
                            ( ( in @ Xz @ SY15 )
                            & ( in @ ( kpair @ Xx @ Xz ) @ SY16 )
                            & ( in @ ( kpair @ Xz @ Xy ) @ SY21 ) ) ) ) ) ) )
     => ! [SY0: $i,SY1: $i] :
          ( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
         => ! [SY6: $i] :
              ( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY0 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY0 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY0 @ SY1 @ SY6 ) )
                       => ! [Xphi: $o] :
                            ( ! [Xz: $i] :
                                ( ( in @ Xz @ SY0 )
                               => ( ( in @ ( kpair @ Xx @ Xz ) @ SY1 )
                                 => ( ( in @ ( kpair @ Xz @ Xy ) @ SY6 )
                                   => Xphi ) ) )
                           => Xphi ) ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,breln,breln1,breln1compE]) ).

thf(4,plain,
    ( ( ! [SY15: $i,SY16: $i] :
          ( ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
         => ! [SY21: $i] :
              ( ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY15 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY15 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
                       => ? [Xz: $i] :
                            ( ( in @ Xz @ SY15 )
                            & ( in @ ( kpair @ Xx @ Xz ) @ SY16 )
                            & ( in @ ( kpair @ Xz @ Xy ) @ SY21 ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [SY0: $i,SY1: $i] :
          ( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
         => ! [SY6: $i] :
              ( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY0 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY0 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY0 @ SY1 @ SY6 ) )
                       => ! [Xphi: $o] :
                            ( ! [Xz: $i] :
                                ( ( in @ Xz @ SY0 )
                               => ( ( in @ ( kpair @ Xx @ Xz ) @ SY1 )
                                 => ( ( in @ ( kpair @ Xz @ Xy ) @ SY6 )
                                   => Xphi ) ) )
                           => Xphi ) ) ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [SY0: $i,SY1: $i] :
            ( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
           => ! [SY6: $i] :
                ( ( subset @ SY6 @ ( cartprod @ SY0 @ SY0 ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ SY0 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY0 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY0 @ SY1 @ SY6 ) )
                         => ! [Xphi: $o] :
                              ( ! [Xz: $i] :
                                  ( ( in @ Xz @ SY0 )
                                 => ( ( in @ ( kpair @ Xx @ Xz ) @ SY1 )
                                   => ( ( in @ ( kpair @ Xz @ Xy ) @ SY6 )
                                     => Xphi ) ) )
                             => Xphi ) ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
      & ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
      & ( in @ sK4_SY60 @ sK1_SY0 )
      & ( in @ sK5_SY64 @ sK1_SY0 )
      & ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
      & ! [SY69: $i] :
          ( ~ ( in @ SY69 @ sK1_SY0 )
          | ~ ( in @ ( kpair @ sK4_SY60 @ SY69 ) @ sK2_SY49 )
          | ~ ( in @ ( kpair @ SY69 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 )
      & ~ sK6_SY67 )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY15: $i,SY16: $i] :
          ( ~ ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
          | ! [SY21: $i] :
              ( ~ ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY15 )
                  | ! [Xy: $i] :
                      ( ~ ( in @ Xy @ SY15 )
                      | ~ ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
                      | ( ( in @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ SY15 )
                        & ( in @ ( kpair @ Xx @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) ) @ SY16 )
                        & ( in @ ( kpair @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ Xy ) @ SY21 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [SY15: $i,SY16: $i] :
          ( ~ ( subset @ SY16 @ ( cartprod @ SY15 @ SY15 ) )
          | ! [SY21: $i] :
              ( ~ ( subset @ SY21 @ ( cartprod @ SY15 @ SY15 ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY15 )
                  | ! [Xy: $i] :
                      ( ~ ( in @ Xy @ SY15 )
                      | ~ ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ SY15 @ SY16 @ SY21 ) )
                      | ( ( in @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ SY15 )
                        & ( in @ ( kpair @ Xx @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) ) @ SY16 )
                        & ( in @ ( kpair @ ( sK7_Xz @ Xy @ Xx @ SY21 @ SY16 @ SY15 ) @ Xy ) @ SY21 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
      & ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
      & ( in @ sK4_SY60 @ sK1_SY0 )
      & ( in @ sK5_SY64 @ sK1_SY0 )
      & ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
      & ! [SY69: $i] :
          ( ~ ( in @ SY69 @ sK1_SY0 )
          | ~ ( in @ ( kpair @ sK4_SY60 @ SY69 ) @ sK2_SY49 )
          | ~ ( in @ ( kpair @ SY69 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 )
      & ~ sK6_SY67 )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ! [SX4: $i] :
                      ( ~ ( in @ SX4 @ SX0 )
                      | ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
                      | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                                | ~ ( in @ ( kpair @ SX3 @ ( sK7_Xz @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
                          | ~ ( in @ ( kpair @ ( sK7_Xz @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9,breln,breln1,breln1compE]) ).

thf(12,plain,
    ( ( ~ ( ~ ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
          | ~ ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
                | ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
                      | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                            | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( in @ SX0 @ sK1_SY0 )
                                              | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                              | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                              | sK6_SY67 )
                                        | ~ ~ sK6_SY67 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,breln,breln1,breln1compE]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( ! [SY70: $i] :
            ( ~ ( subset @ SY70 @ ( cartprod @ SV1 @ SV1 ) )
            | ! [SY71: $i] :
                ( ~ ( subset @ SY71 @ ( cartprod @ SV1 @ SV1 ) )
                | ! [SY72: $i] :
                    ( ~ ( in @ SY72 @ SV1 )
                    | ! [SY73: $i] :
                        ( ~ ( in @ SY73 @ SV1 )
                        | ~ ( in @ ( kpair @ SY72 @ SY73 ) @ ( breln1compset @ SV1 @ SY70 @ SY71 ) )
                        | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY73 @ SY72 @ SY71 @ SY70 @ SV1 ) @ SV1 )
                                  | ~ ( in @ ( kpair @ SY72 @ ( sK7_Xz @ SY73 @ SY72 @ SY71 @ SY70 @ SV1 ) ) @ SY70 ) )
                            | ~ ( in @ ( kpair @ ( sK7_Xz @ SY73 @ SY72 @ SY71 @ SY70 @ SV1 ) @ SY73 ) @ SY71 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
      | ~ ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
            | ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
                  | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                        | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( in @ SX0 @ sK1_SY0 )
                                          | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                          | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                          | sK6_SY67 )
                                    | ~ ~ sK6_SY67 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        | ! [SY74: $i] :
            ( ~ ( subset @ SY74 @ ( cartprod @ SV1 @ SV1 ) )
            | ! [SY75: $i] :
                ( ~ ( in @ SY75 @ SV1 )
                | ! [SY76: $i] :
                    ( ~ ( in @ SY76 @ SV1 )
                    | ~ ( in @ ( kpair @ SY75 @ SY76 ) @ ( breln1compset @ SV1 @ SV2 @ SY74 ) )
                    | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SV1 )
                              | ~ ( in @ ( kpair @ SY75 @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) ) @ SV2 ) )
                        | ~ ( in @ ( kpair @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SY76 ) @ SY74 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
            | ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
                  | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                        | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( in @ SX0 @ sK1_SY0 )
                                          | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                          | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                          | sK6_SY67 )
                                    | ~ ~ sK6_SY67 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) ) )
        = $true )
      | ( ( ! [SY74: $i] :
              ( ~ ( subset @ SY74 @ ( cartprod @ SV1 @ SV1 ) )
              | ! [SY75: $i] :
                  ( ~ ( in @ SY75 @ SV1 )
                  | ! [SY76: $i] :
                      ( ~ ( in @ SY76 @ SV1 )
                      | ~ ( in @ ( kpair @ SY75 @ SY76 ) @ ( breln1compset @ SV1 @ SV2 @ SY74 ) )
                      | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SV1 )
                                | ~ ( in @ ( kpair @ SY75 @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) ) @ SV2 ) )
                          | ~ ( in @ ( kpair @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SY76 ) @ SY74 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( subset @ sK2_SY49 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
          | ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
                | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                      | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( in @ SX0 @ sK1_SY0 )
                                        | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                        | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                        | sK6_SY67 )
                                  | ~ ~ sK6_SY67 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( ! [SY74: $i] :
              ( ~ ( subset @ SY74 @ ( cartprod @ SV1 @ SV1 ) )
              | ! [SY75: $i] :
                  ( ~ ( in @ SY75 @ SV1 )
                  | ! [SY76: $i] :
                      ( ~ ( in @ SY76 @ SV1 )
                      | ~ ( in @ ( kpair @ SY75 @ SY76 ) @ ( breln1compset @ SV1 @ SV2 @ SY74 ) )
                      | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SV1 )
                                | ~ ( in @ ( kpair @ SY75 @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) ) @ SV2 ) )
                          | ~ ( in @ ( kpair @ ( sK7_Xz @ SY76 @ SY75 @ SY74 @ SV2 @ SV1 ) @ SY76 ) @ SY74 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
      | ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
            | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                  | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( in @ SX0 @ sK1_SY0 )
                                    | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                    | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                    | sK6_SY67 )
                              | ~ ~ sK6_SY67 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV2: $i,SV1: $i,SV3: $i] :
      ( ( ( ~ ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
          | ! [SY77: $i] :
              ( ~ ( in @ SY77 @ SV1 )
              | ! [SY78: $i] :
                  ( ~ ( in @ SY78 @ SV1 )
                  | ~ ( in @ ( kpair @ SY77 @ SY78 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
                  | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                            | ~ ( in @ ( kpair @ SY77 @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
                      | ~ ( in @ ( kpair @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SY78 ) @ SV3 ) ) ) ) )
        = $true )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(24,plain,
    ( ( ~ ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(25,plain,
    ( ( ~ ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
            | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                  | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( in @ SX0 @ sK1_SY0 )
                                    | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                    | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                    | sK6_SY67 )
                              | ~ ~ sK6_SY67 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV2: $i,SV1: $i,SV3: $i] :
      ( ( ( ~ ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) ) )
        = $true )
      | ( ( ! [SY77: $i] :
              ( ~ ( in @ SY77 @ SV1 )
              | ! [SY78: $i] :
                  ( ~ ( in @ SY78 @ SV1 )
                  | ~ ( in @ ( kpair @ SY77 @ SY78 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
                  | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                            | ~ ( in @ ( kpair @ SY77 @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
                      | ~ ( in @ ( kpair @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SY78 ) @ SV3 ) ) ) ) )
        = $true )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(27,plain,
    ( ( subset @ sK3_SY55 @ ( cartprod @ sK1_SY0 @ sK1_SY0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ~ ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
          | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
                | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( in @ SX0 @ sK1_SY0 )
                                  | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                                  | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                                  | sK6_SY67 )
                            | ~ ~ sK6_SY67 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV2: $i,SV1: $i,SV3: $i] :
      ( ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( ! [SY77: $i] :
              ( ~ ( in @ SY77 @ SV1 )
              | ! [SY78: $i] :
                  ( ~ ( in @ SY78 @ SV1 )
                  | ~ ( in @ ( kpair @ SY77 @ SY78 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
                  | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                            | ~ ( in @ ( kpair @ SY77 @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
                      | ~ ( in @ ( kpair @ ( sK7_Xz @ SY78 @ SY77 @ SV3 @ SV2 @ SV1 ) @ SY78 ) @ SV3 ) ) ) ) )
        = $true )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(30,plain,
    ( ( ~ ( in @ sK4_SY60 @ sK1_SY0 )
      | ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
            | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( in @ SX0 @ sK1_SY0 )
                              | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                              | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                              | sK6_SY67 )
                        | ~ ~ sK6_SY67 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV3: $i,SV2: $i,SV1: $i,SV4: $i] :
      ( ( ( ~ ( in @ SV4 @ SV1 )
          | ! [SY79: $i] :
              ( ~ ( in @ SY79 @ SV1 )
              | ~ ( in @ ( kpair @ SV4 @ SY79 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
              | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                        | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
                  | ~ ( in @ ( kpair @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SY79 ) @ SV3 ) ) ) )
        = $true )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(32,plain,
    ( ( ~ ( in @ sK4_SY60 @ sK1_SY0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(33,plain,
    ( ( ~ ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
            | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( in @ SX0 @ sK1_SY0 )
                              | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                              | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                              | sK6_SY67 )
                        | ~ ~ sK6_SY67 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV3: $i,SV2: $i,SV1: $i,SV4: $i] :
      ( ( ( ~ ( in @ SV4 @ SV1 ) )
        = $true )
      | ( ( ! [SY79: $i] :
              ( ~ ( in @ SY79 @ SV1 )
              | ~ ( in @ ( kpair @ SV4 @ SY79 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
              | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                        | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
                  | ~ ( in @ ( kpair @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SY79 ) @ SV3 ) ) ) )
        = $true )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(35,plain,
    ( ( in @ sK4_SY60 @ sK1_SY0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(36,plain,
    ( ( ~ ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
          | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( in @ SX0 @ sK1_SY0 )
                            | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                            | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                            | sK6_SY67 )
                      | ~ ~ sK6_SY67 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV3: $i,SV2: $i,SV1: $i,SV4: $i] :
      ( ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( ! [SY79: $i] :
              ( ~ ( in @ SY79 @ SV1 )
              | ~ ( in @ ( kpair @ SV4 @ SY79 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
              | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                        | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
                  | ~ ( in @ ( kpair @ ( sK7_Xz @ SY79 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SY79 ) @ SV3 ) ) ) )
        = $true )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(38,plain,
    ( ( ~ ( in @ sK5_SY64 @ sK1_SY0 )
      | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( in @ SX0 @ sK1_SY0 )
                        | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                        | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                        | sK6_SY67 )
                  | ~ ~ sK6_SY67 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV3: $i,SV2: $i,SV4: $i,SV1: $i,SV5: $i] :
      ( ( ( ~ ( in @ SV5 @ SV1 )
          | ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
          | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
              | ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
        = $true )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(40,plain,
    ( ( ~ ( in @ sK5_SY64 @ sK1_SY0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ~ ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( in @ SX0 @ sK1_SY0 )
                        | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                        | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                        | sK6_SY67 )
                  | ~ ~ sK6_SY67 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV3: $i,SV2: $i,SV4: $i,SV1: $i,SV5: $i] :
      ( ( ( ~ ( in @ SV5 @ SV1 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
          | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
              | ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
        = $true )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(43,plain,
    ( ( in @ sK5_SY64 @ sK1_SY0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(44,plain,
    ( ( ~ ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( in @ SX0 @ sK1_SY0 )
                      | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                      | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                      | sK6_SY67 )
                | ~ ~ sK6_SY67 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(45,plain,
    ! [SV3: $i,SV2: $i,SV4: $i,SV1: $i,SV5: $i] :
      ( ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
          | ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
              | ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
        = $true )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(46,plain,
    ( ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( in @ SX0 @ sK1_SY0 )
                  | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                  | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                  | sK6_SY67 )
            | ~ ~ sK6_SY67 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV3: $i,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
              | ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
        = $true )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(48,plain,
    ( ( ~ ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(49,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( in @ SX0 @ sK1_SY0 )
                  | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                  | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                  | sK6_SY67 )
            | ~ ~ sK6_SY67 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV3: $i,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
              | ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) ) )
        = $true )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(51,plain,
    ( ( in @ ( kpair @ sK4_SY60 @ sK5_SY64 ) @ ( breln1compset @ sK1_SY0 @ sK2_SY49 @ sK3_SY55 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(52,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( in @ SX0 @ sK1_SY0 )
                | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
                | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
                | sK6_SY67 )
          | ~ ~ sK6_SY67 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
          | ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(54,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( in @ SX0 @ sK1_SY0 )
            | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
            | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
            | sK6_SY67 )
      | ~ ~ sK6_SY67 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
                | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) ) )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[53]) ).

thf(56,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 ) )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[53]) ).

thf(57,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( in @ SX0 @ sK1_SY0 )
            | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
            | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
            | sK6_SY67 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[54]) ).

thf(58,plain,
    ( ( ~ ~ sK6_SY67 )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
              | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) ) )
        = $true )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(60,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( in @ ( kpair @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV5 ) @ SV3 )
        = $true )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(61,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ sK1_SY0 )
          | ~ ( in @ ( kpair @ sK4_SY60 @ SX0 ) @ sK2_SY49 )
          | ~ ( in @ ( kpair @ SX0 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[57]) ).

thf(62,plain,
    ( ( ~ sK6_SY67 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(63,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
          | ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV6: $i] :
      ( ( ~ ( in @ SV6 @ sK1_SY0 )
        | ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
        | ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
        | sK6_SY67 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(65,plain,
    sK6_SY67 = $false,
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(66,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( ~ ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 ) )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[63]) ).

thf(67,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV5: $i,SV4: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 ) )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( in @ SV6 @ sK1_SY0 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
          | ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV4: $i,SV5: $i] :
      ( ( ( in @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) @ SV1 )
        = $true )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[66]) ).

thf(70,plain,
    ! [SV1: $i,SV2: $i,SV3: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ ( sK7_Xz @ SV5 @ SV4 @ SV3 @ SV2 @ SV1 ) ) @ SV2 )
        = $true )
      | ( ( in @ ( kpair @ SV4 @ SV5 ) @ ( breln1compset @ SV1 @ SV2 @ SV3 ) )
        = $false )
      | ( ( in @ SV5 @ SV1 )
        = $false )
      | ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( subset @ SV3 @ ( cartprod @ SV1 @ SV1 ) )
        = $false )
      | ( ( subset @ SV2 @ ( cartprod @ SV1 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[67]) ).

thf(71,plain,
    ! [SV6: $i] :
      ( ( ( in @ SV6 @ sK1_SY0 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
          | ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(72,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 )
        = $true )
      | ( ( in @ SV6 @ sK1_SY0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(73,plain,
    ! [SV6: $i] :
      ( ( ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
          | sK6_SY67 )
        = $true )
      | ( ( in @ SV6 @ sK1_SY0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(74,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 ) )
        = $true )
      | ( sK6_SY67 = $true )
      | ( ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
        = $false )
      | ( ( in @ SV6 @ sK1_SY0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(75,plain,
    ! [SV6: $i] :
      ( ( ( in @ ( kpair @ SV6 @ sK5_SY64 ) @ sK3_SY55 )
        = $false )
      | ( sK6_SY67 = $true )
      | ( ( in @ ( kpair @ sK4_SY60 @ SV6 ) @ sK2_SY49 )
        = $false )
      | ( ( in @ SV6 @ sK1_SY0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(76,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,75,70,69,65,60,51,43,35,27]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU781^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 20 13:52:15 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 664
% 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).......
% 0.20/0.48  
% 0.20/0.48  ********************************
% 0.20/0.48  *   All subproblems solved!    *
% 0.20/0.48  ********************************
% 0.20/0.48  % 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:76,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.48  
% 0.20/0.48  %**** Beginning of derivation protocol ****
% 0.20/0.48  % SZS output start CNFRefutation
% See solution above
% 0.20/0.48  
% 0.20/0.48  %**** End of derivation protocol ****
% 0.20/0.48  %**** no. of clauses in derivation: 77 ****
% 0.20/0.48  %**** clause counter: 76 ****
% 0.20/0.48  
% 0.20/0.48  % 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:76,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------