TSTP Solution File: SEU675^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU675^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.GFSeCjnYmh true

% 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  : 300s
% DateTime : Thu Aug 31 19:16:02 EDT 2023

% Result   : Theorem 1.16s 0.91s
% Output   : Refutation 1.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   93 (  31 unt;  19 typ;   0 def)
%            Number of atoms       :  404 (  63 equ;   0 cnn)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives : 1521 (  57   ~;  37   |;  60   &;1236   @)
%                                         (   0 <=>;  57  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  44   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  19 usr;   9 con; 0-3 aty)
%                                         (  48  !!;  26  ??;   0 @@+;   0 @@-)
%            Number of variables   :  313 ( 204   ^; 103   !;   6   ?; 313   :)

% Comments : 
%------------------------------------------------------------------------------
thf(singleton_type,type,
    singleton: $i > $o ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

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

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

thf(ex1_type,type,
    ex1: $i > ( $i > $o ) > $o ).

thf('#sk2_type',type,
    '#sk2': $i ).

thf(func_type,type,
    func: $i > $i > $i > $o ).

thf('#sk18_type',type,
    '#sk18': $i > $i > $i > $i ).

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

thf(funcSet_type,type,
    funcSet: $i > $i > $i ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf('#sk1_type',type,
    '#sk1': $i ).

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

thf('#sk5_type',type,
    '#sk5': $i ).

thf(emptyset_type,type,
    emptyset: $i ).

thf('#sk8_type',type,
    '#sk8': $i ).

thf(breln_type,type,
    breln: $i > $i > $i > $o ).

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

thf(func,axiom,
    ( func
    = ( ^ [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
          & ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ex1 @ B
                @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).

thf(breln,axiom,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).

thf('0',plain,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[breln]) ).

thf('1',plain,
    ( breln
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ) ).

thf('2',plain,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[singleton]) ).

thf('3',plain,
    ( singleton
    = ( ^ [V_1: $i] :
        ? [X4: $i] :
          ( ( V_1
            = ( setadjoin @ X4 @ emptyset ) )
          & ( in @ X4 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ex1,'3']) ).

thf('5',plain,
    ( ex1
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( singleton
          @ ( dsetconstr @ V_1
            @ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( func
    = ( ^ [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
          & ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ex1 @ B
                @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[func,'1','5','3']) ).

thf('7',plain,
    ( func
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] :
          ( ( breln @ V_1 @ V_2 @ V_3 )
          & ! [X4: $i] :
              ( ( in @ X4 @ V_1 )
             => ( ex1 @ V_2
                @ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(funcSet,axiom,
    ( funcSet
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
          @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ( funcSet
    = ( ^ [V_1: $i,V_2: $i] :
          ( dsetconstr @ ( powerset @ ( cartprod @ V_1 @ V_2 ) )
          @ ^ [V_3: $i] :
              ( ! [X4: $i] :
                  ( ( in @ X4 @ V_1 )
                 => ? [X6: $i] :
                      ( ( in @ X6
                        @ ( dsetconstr @ V_2
                          @ ^ [V_5: $i] : ( in @ ( kpair @ X4 @ V_5 ) @ V_3 ) ) )
                      & ( ( dsetconstr @ V_2
                          @ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) )
                        = ( setadjoin @ X6 @ emptyset ) ) ) )
              & ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ) ) ) ).

thf(zip_derived_cl0,plain,
    ( funcSet
    = ( ^ [Y0: $i,Y1: $i] :
          ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
          @ ^ [Y2: $i] :
              ( ( !!
                @ ^ [Y3: $i] :
                    ( ( in @ Y3 @ Y0 )
                   => ( ??
                      @ ^ [Y4: $i] :
                          ( ( in @ Y4
                            @ ( dsetconstr @ Y1
                              @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                          & ( ( dsetconstr @ Y1
                              @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                            = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
              & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ! [X1: $i,X2: $i] :
      ( ( funcSet @ X1 @ X2 )
      = ( ^ [Y0: $i,Y1: $i] :
            ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
            @ ^ [Y2: $i] :
                ( ( !!
                  @ ^ [Y3: $i] :
                      ( ( in @ Y3 @ Y0 )
                     => ( ??
                        @ ^ [Y4: $i] :
                            ( ( in @ Y4
                              @ ( dsetconstr @ Y1
                                @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                            & ( ( dsetconstr @ Y1
                                @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                              = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) )
        @ X1
        @ X2 ) ),
    inference(ho_complete_eq,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl5,plain,
    ! [X1: $i,X2: $i] :
      ( ( funcSet @ X1 @ X2 )
      = ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X2 ) )
        @ ^ [Y0: $i] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X1 )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ X2
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ X2
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).

thf(dsetconstrER,axiom,
    ( dsetconstrER
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( Xphi @ Xx ) ) ) ) ).

thf('8',plain,
    ( dsetconstrER
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(infuncsetfunc,conjecture,
    ( dsetconstrER
   => ! [A: $i,B: $i,Xf: $i] :
        ( ( in @ Xf @ ( funcSet @ A @ B ) )
       => ( func @ A @ B @ Xf ) ) ) ).

thf(zf_stmt_1,conjecture,
    ( ! [X4: $i,X6: $i > $o,X8: $i] :
        ( ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
       => ( X6 @ X8 ) )
   => ! [X10: $i,X12: $i,X14: $i] :
        ( ( in @ X14 @ ( funcSet @ X10 @ X12 ) )
       => ( ! [X16: $i] :
              ( ( in @ X16 @ X10 )
             => ? [X18: $i] :
                  ( ( in @ X18
                    @ ( dsetconstr @ X12
                      @ ^ [V_3: $i] : ( in @ ( kpair @ X16 @ V_3 ) @ X14 ) ) )
                  & ( ( dsetconstr @ X12
                      @ ^ [V_2: $i] : ( in @ ( kpair @ X16 @ V_2 ) @ X14 ) )
                    = ( setadjoin @ X18 @ emptyset ) ) ) )
          & ( subset @ X14 @ ( cartprod @ X10 @ X12 ) ) ) ) ) ).

thf(zf_stmt_2,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) )
     => ! [X10: $i,X12: $i,X14: $i] :
          ( ( in @ X14 @ ( funcSet @ X10 @ X12 ) )
         => ( ! [X16: $i] :
                ( ( in @ X16 @ X10 )
               => ? [X18: $i] :
                    ( ( in @ X18
                      @ ( dsetconstr @ X12
                        @ ^ [V_3: $i] : ( in @ ( kpair @ X16 @ V_3 ) @ X14 ) ) )
                    & ( ( dsetconstr @ X12
                        @ ^ [V_2: $i] : ( in @ ( kpair @ X16 @ V_2 ) @ X14 ) )
                      = ( setadjoin @ X18 @ emptyset ) ) ) )
            & ( subset @ X14 @ ( cartprod @ X10 @ X12 ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2
                      @ ( dsetconstr @ Y0
                        @ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
                   => ( Y1 @ Y2 ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ ( funcSet @ Y0 @ Y1 ) )
                   => ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ??
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4
                                    @ ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                  & ( ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                    = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                      & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl8,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
                   => ( Y1 @ Y2 ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ ( funcSet @ Y0 @ Y1 ) )
                   => ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ??
                              @ ^ [Y4: $i] :
                                  ( ( in @ Y4
                                    @ ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                  & ( ( dsetconstr @ Y1
                                      @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                    = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                      & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl9,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $o] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
               => ( Y1 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
             => ( Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i > $o] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
         => ( X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl14,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0
            @ ( dsetconstr @ X2
              @ ^ [Y1: $i] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ X1 )
                       => ( ??
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3
                                @ ( dsetconstr @ X0
                                  @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
                              & ( ( dsetconstr @ X0
                                  @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
                                = ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
                  & ( subset @ Y1 @ ( cartprod @ X1 @ X0 ) ) ) ) )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X1 )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ X0
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ X0
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ X1 @ X0 ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl57,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( in @ X4
        @ ( dsetconstr @ X2
          @ ^ [Y0: $i] :
              ( ( !!
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ X1 )
                   => ( ??
                      @ ^ [Y2: $i] :
                          ( ( in @ Y2
                            @ ( dsetconstr @ X0
                              @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                          & ( ( dsetconstr @ X0
                              @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                            = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
              & ( subset @ Y0 @ ( cartprod @ X1 @ X0 ) ) ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X1 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X0
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X4 ) ) )
                    & ( ( dsetconstr @ X0
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X4 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ X4 @ ( cartprod @ X1 @ X0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl58,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ~ ( in @ X4
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] :
                ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ X1 )
                     => ( ??
                        @ ^ [Y2: $i] :
                            ( ( in @ Y2
                              @ ( dsetconstr @ X0
                                @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                            & ( ( dsetconstr @ X0
                                @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                              = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
                & ( subset @ Y0 @ ( cartprod @ X1 @ X0 ) ) ) ) )
      | ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X1 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X0
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X4 ) ) )
                    & ( ( dsetconstr @ X0
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X4 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ X4 @ ( cartprod @ X1 @ X0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl60,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( subset @ X4 @ ( cartprod @ X1 @ X0 ) )
      | ~ ( in @ X4
          @ ( dsetconstr @ X2
            @ ^ [Y0: $i] :
                ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ X1 )
                     => ( ??
                        @ ^ [Y2: $i] :
                            ( ( in @ Y2
                              @ ( dsetconstr @ X0
                                @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                            & ( ( dsetconstr @ X0
                                @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                              = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
                & ( subset @ Y0 @ ( cartprod @ X1 @ X0 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl67,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
      | ( subset @ X2 @ ( cartprod @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl60]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ ( funcSet @ Y0 @ Y1 ) )
                 => ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( ??
                            @ ^ [Y4: $i] :
                                ( ( in @ Y4
                                  @ ( dsetconstr @ Y1
                                    @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
                                & ( ( dsetconstr @ Y1
                                    @ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
                                  = ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
                    & ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl12,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( in @ Y1 @ ( funcSet @ '#sk1' @ Y0 ) )
             => ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ '#sk1' )
                     => ( ??
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3
                              @ ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
                            & ( ( dsetconstr @ Y0
                                @ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
                              = ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
                & ( subset @ Y1 @ ( cartprod @ '#sk1' @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl15,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ ( funcSet @ '#sk1' @ '#sk2' ) )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ '#sk1' )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ '#sk2'
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ '#sk2'
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl17,plain,
    ~ ( ( in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ '#sk1' )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ '#sk2'
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
                    & ( ( dsetconstr @ '#sk2'
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl19,plain,
    in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl5_001,plain,
    ! [X1: $i,X2: $i] :
      ( ( funcSet @ X1 @ X2 )
      = ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X2 ) )
        @ ^ [Y0: $i] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X1 )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ X2
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ X2
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl13_002,plain,
    ! [X2: $i,X4: $i > $o] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
         => ( X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
     => ( X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl28,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
      | ( ^ [Y0: $i] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ X1 )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2
                          @ ( dsetconstr @ X0
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
                        & ( ( dsetconstr @ X0
                            @ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
            & ( subset @ Y0 @ ( cartprod @ X1 @ X0 ) ) )
        @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl18]) ).

thf(zip_derived_cl37,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
      | ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X1 )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1
                      @ ( dsetconstr @ X0
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
                    & ( ( dsetconstr @ X0
                        @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) )
                      = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
        & ( subset @ X2 @ ( cartprod @ X1 @ X0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl76,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X1 )
           => ( ??
              @ ^ [Y1: $i] :
                  ( ( in @ Y1
                    @ ( dsetconstr @ X0
                      @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
                  & ( ( dsetconstr @ X0
                      @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) )
                    = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl78,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( ( in @ X4 @ X1 )
       => ( ??
          @ ^ [Y0: $i] :
              ( ( in @ Y0
                @ ( dsetconstr @ X0
                  @ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) )
              & ( ( dsetconstr @ X0
                  @ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) )
                = ( setadjoin @ Y0 @ emptyset ) ) ) ) )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl79,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ X1 )
      | ( ??
        @ ^ [Y0: $i] :
            ( ( in @ Y0
              @ ( dsetconstr @ X0
                @ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) )
            & ( ( dsetconstr @ X0
                @ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) )
              = ( setadjoin @ Y0 @ emptyset ) ) ) )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl80,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( ( in @ ( '#sk18' @ X0 @ X2 @ X4 )
          @ ( dsetconstr @ X0
            @ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) )
        & ( ( dsetconstr @ X0
            @ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) )
          = ( setadjoin @ ( '#sk18' @ X0 @ X2 @ X4 ) @ emptyset ) ) )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
      | ~ ( in @ X4 @ X1 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl82,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( ( dsetconstr @ X0
          @ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) )
        = ( setadjoin @ ( '#sk18' @ X0 @ X2 @ X4 ) @ emptyset ) )
      | ~ ( in @ X4 @ X1 )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl83,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( ( dsetconstr @ X0
          @ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) )
        = ( setadjoin @ ( '#sk18' @ X0 @ X2 @ X4 ) @ emptyset ) )
      | ~ ( in @ X4 @ X1 )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl82]) ).

thf(zip_derived_cl92,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ '#sk1' )
      | ( ( dsetconstr @ '#sk2'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk5' ) )
        = ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ X0 ) @ emptyset ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl83]) ).

thf(zip_derived_cl20,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ '#sk1' )
           => ( ??
              @ ^ [Y1: $i] :
                  ( ( in @ Y1
                    @ ( dsetconstr @ '#sk2'
                      @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
                  & ( ( dsetconstr @ '#sk2'
                      @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
                    = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
      & ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl21,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ '#sk1' )
           => ( ??
              @ ^ [Y1: $i] :
                  ( ( in @ Y1
                    @ ( dsetconstr @ '#sk2'
                      @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
                  & ( ( dsetconstr @ '#sk2'
                      @ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
                    = ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
    | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl22,plain,
    ( ~ ( ( in @ '#sk8' @ '#sk1' )
       => ( ??
          @ ^ [Y0: $i] :
              ( ( in @ Y0
                @ ( dsetconstr @ '#sk2'
                  @ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) ) )
              & ( ( dsetconstr @ '#sk2'
                  @ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) )
                = ( setadjoin @ Y0 @ emptyset ) ) ) ) )
    | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl24,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( ( in @ Y0
              @ ( dsetconstr @ '#sk2'
                @ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) ) )
            & ( ( dsetconstr @ '#sk2'
                @ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) )
              = ( setadjoin @ Y0 @ emptyset ) ) ) )
    | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i] :
      ( ~ ( ( in @ X2
            @ ( dsetconstr @ '#sk2'
              @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
          & ( ( dsetconstr @ '#sk2'
              @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
            = ( setadjoin @ X2 @ emptyset ) ) )
      | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2
          @ ( dsetconstr @ '#sk2'
            @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
      | ( ( dsetconstr @ '#sk2'
          @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
       != ( setadjoin @ X2 @ emptyset ) )
      | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2
          @ ( dsetconstr @ '#sk2'
            @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
      | ( ( dsetconstr @ '#sk2'
          @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
       != ( setadjoin @ X2 @ emptyset ) )
      | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl19_003,plain,
    in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl81,plain,
    ! [X0: $i,X1: $i,X2: $i,X4: $i] :
      ( ( in @ ( '#sk18' @ X0 @ X2 @ X4 )
        @ ( dsetconstr @ X0
          @ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) )
      | ~ ( in @ X4 @ X1 )
      | ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl84,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ '#sk1' )
      | ( in @ ( '#sk18' @ '#sk2' @ '#sk5' @ X0 )
        @ ( dsetconstr @ '#sk2'
          @ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk5' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl81]) ).

thf(zip_derived_cl88,plain,
    ( ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) )
    | ( ( dsetconstr @ '#sk2'
        @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
     != ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ '#sk8' ) @ emptyset ) )
    | ~ ( in @ '#sk8' @ '#sk1' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl27,zip_derived_cl84]) ).

thf(zip_derived_cl23,plain,
    ( ( in @ '#sk8' @ '#sk1' )
    | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl67_004,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
      | ( subset @ X2 @ ( cartprod @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl60]) ).

thf(zip_derived_cl69,plain,
    ( ( in @ '#sk8' @ '#sk1' )
    | ~ ( in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl23,zip_derived_cl67]) ).

thf(zip_derived_cl19_005,plain,
    in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl72,plain,
    in @ '#sk8' @ '#sk1',
    inference(demod,[status(thm)],[zip_derived_cl69,zip_derived_cl19]) ).

thf(zip_derived_cl89,plain,
    ( ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) )
    | ( ( dsetconstr @ '#sk2'
        @ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
     != ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ '#sk8' ) @ emptyset ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl88,zip_derived_cl72]) ).

thf(zip_derived_cl95,plain,
    ( ( ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ '#sk8' ) @ emptyset )
     != ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ '#sk8' ) @ emptyset ) )
    | ~ ( in @ '#sk8' @ '#sk1' )
    | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl92,zip_derived_cl89]) ).

thf(zip_derived_cl72_006,plain,
    in @ '#sk8' @ '#sk1',
    inference(demod,[status(thm)],[zip_derived_cl69,zip_derived_cl19]) ).

thf(zip_derived_cl99,plain,
    ( ( ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ '#sk8' ) @ emptyset )
     != ( setadjoin @ ( '#sk18' @ '#sk2' @ '#sk5' @ '#sk8' ) @ emptyset ) )
    | ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl95,zip_derived_cl72]) ).

thf(zip_derived_cl100,plain,
    ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl99]) ).

thf(zip_derived_cl105,plain,
    ~ ( in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl67,zip_derived_cl100]) ).

thf(zip_derived_cl19_007,plain,
    in @ '#sk5' @ ( funcSet @ '#sk1' @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl108,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl19]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU675^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.GFSeCjnYmh true
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Wed Aug 23 14:19:36 EDT 2023
% 0.16/0.38  % CPUTime  : 
% 0.16/0.38  % Running portfolio for 300 s
% 0.16/0.38  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.38  % Number of cores: 8
% 0.16/0.38  % Python version: Python 3.6.8
% 0.16/0.38  % Running in HO mode
% 0.24/0.70  % Total configuration time : 828
% 0.24/0.70  % Estimated wc time : 1656
% 0.24/0.70  % Estimated cpu time (8 cpus) : 207.0
% 0.24/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.24/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.24/0.78  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.24/0.79  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.24/0.79  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.24/0.79  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.24/0.82  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.24/0.82  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.16/0.91  % Solved by lams/35_full_unif4.sh.
% 1.16/0.91  % done 26 iterations in 0.071s
% 1.16/0.91  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.16/0.91  % SZS output start Refutation
% See solution above
% 1.16/0.91  
% 1.16/0.91  
% 1.16/0.91  % Terminating...
% 1.52/1.00  % Runner terminated.
% 1.52/1.00  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------