TSTP Solution File: SYO066^4.002 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYO066^4.002 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.j7Z7qml0oV true

% Computer : n028.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 : Fri Sep  1 05:49:31 EDT 2023

% Result   : Theorem 2.69s 1.22s
% Output   : Refutation 2.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   48
% Syntax   : Number of formulae    :  236 (  65 unt;  25 typ;   0 def)
%            Number of atoms       :  874 (  21 equ;   0 cnn)
%            Maximal formula atoms :   36 (   4 avg)
%            Number of connectives : 1927 ( 177   ~; 205   |;  93   &;1164   @)
%                                         (   0 <=>; 164  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   69 (  69   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  25 usr;  13 con; 0-3 aty)
%                                         ( 124  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  307 ( 166   ^; 141   !;   0   ?; 307   :)

% Comments : 
%------------------------------------------------------------------------------
thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf('#sk11_type',type,
    '#sk11': $i ).

thf(o21_type,type,
    o21: $i > $o ).

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

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(o12_type,type,
    o12: $i > $o ).

thf(irel_type,type,
    irel: $i > $i > $o ).

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk7_type',type,
    '#sk7': $i ).

thf('#sk10_type',type,
    '#sk10': $i ).

thf('#sk4_type',type,
    '#sk4': $i ).

thf(ior_type,type,
    ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

thf(mbox_s4_type,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf('#sk3_type',type,
    '#sk3': $i ).

thf(o31_type,type,
    o31: $i > $o ).

thf(o11_type,type,
    o11: $i > $o ).

thf(iand_type,type,
    iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk9_type',type,
    '#sk9': $i ).

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

thf(o32_type,type,
    o32: $i > $o ).

thf('#sk6_type',type,
    '#sk6': $i ).

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

thf(o22_type,type,
    o22: $i > $o ).

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(ivalid,axiom,
    ( ivalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ) ).

thf('0',plain,
    ( ivalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ivalid]) ).

thf('1',plain,
    ( ivalid
    = ( ^ [V_1: $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 ) ) ),
    define([status(thm)]) ).

thf(ior,axiom,
    ( ior
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( irel @ X @ Y )
         => ( P @ Y ) ) ) ) ).

thf('2',plain,
    ( mbox_s4
    = ( ^ [P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( irel @ X @ Y )
         => ( P @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).

thf('3',plain,
    ( mbox_s4
    = ( ^ [V_1: $i > $o,V_2: $i] :
        ! [X4: $i] :
          ( ( irel @ V_2 @ X4 )
         => ( V_1 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ) ).

thf('4',plain,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

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

thf('6',plain,
    ( ior
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ior,'3','5']) ).

thf('7',plain,
    ( ior
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(iand,axiom,
    ( iand
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).

thf(mand,axiom,
    ( mand
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ) ).

thf('8',plain,
    ( mand
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand]) ).

thf('9',plain,
    ( mand
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf('10',plain,
    ( iand
    = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
    inference(simplify_rw_rule,[status(thm)],[iand,'9']) ).

thf('11',plain,
    ( iand
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(iatom,axiom,
    ( iatom
    = ( ^ [P: $i > $o] : P ) ) ).

thf('12',plain,
    ( iatom
    = ( ^ [P: $i > $o] : P ) ),
    inference(simplify_rw_rule,[status(thm)],[iatom]) ).

thf('13',plain,
    ( iatom
    = ( ^ [V_1: $i > $o] : V_1 ) ),
    define([status(thm)]) ).

thf(con,conjecture,
    ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ! [X8: $i] :
          ( ( irel @ X4 @ X8 )
         => ( ! [X12: $i] :
                ( ( irel @ X8 @ X12 )
               => ( ! [X16: $i] :
                      ( ( irel @ X12 @ X16 )
                     => ( ! [X20: $i] :
                            ( ( irel @ X16 @ X20 )
                           => ( ! [X24: $i] :
                                  ( ( irel @ X20 @ X24 )
                                 => ( ( o32 @ X24 )
                                    & ( o22 @ X24 ) ) )
                              | ! [X22: $i] :
                                  ( ( irel @ X20 @ X22 )
                                 => ( ( o32 @ X22 )
                                    & ( o12 @ X22 ) ) ) ) )
                        | ! [X18: $i] :
                            ( ( irel @ X16 @ X18 )
                           => ( ( o22 @ X18 )
                              & ( o12 @ X18 ) ) ) ) )
                  | ! [X14: $i] :
                      ( ( irel @ X12 @ X14 )
                     => ( ( o31 @ X14 )
                        & ( o21 @ X14 ) ) ) ) )
            | ! [X10: $i] :
                ( ( irel @ X8 @ X10 )
               => ( ( o31 @ X10 )
                  & ( o11 @ X10 ) ) ) ) )
      | ! [X6: $i] :
          ( ( irel @ X4 @ X6 )
         => ( ( o21 @ X6 )
            & ( o11 @ X6 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ! [X8: $i] :
            ( ( irel @ X4 @ X8 )
           => ( ! [X12: $i] :
                  ( ( irel @ X8 @ X12 )
                 => ( ! [X16: $i] :
                        ( ( irel @ X12 @ X16 )
                       => ( ! [X20: $i] :
                              ( ( irel @ X16 @ X20 )
                             => ( ! [X24: $i] :
                                    ( ( irel @ X20 @ X24 )
                                   => ( ( o32 @ X24 )
                                      & ( o22 @ X24 ) ) )
                                | ! [X22: $i] :
                                    ( ( irel @ X20 @ X22 )
                                   => ( ( o32 @ X22 )
                                      & ( o12 @ X22 ) ) ) ) )
                          | ! [X18: $i] :
                              ( ( irel @ X16 @ X18 )
                             => ( ( o22 @ X18 )
                                & ( o12 @ X18 ) ) ) ) )
                    | ! [X14: $i] :
                        ( ( irel @ X12 @ X14 )
                       => ( ( o31 @ X14 )
                          & ( o21 @ X14 ) ) ) ) )
              | ! [X10: $i] :
                  ( ( irel @ X8 @ X10 )
                 => ( ( o31 @ X10 )
                    & ( o11 @ X10 ) ) ) ) )
        | ! [X6: $i] :
            ( ( irel @ X4 @ X6 )
           => ( ( o21 @ X6 )
              & ( o11 @ X6 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( irel @ Y0 @ Y1 )
               => ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( irel @ Y1 @ Y2 )
                       => ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( irel @ Y2 @ Y3 )
                               => ( ( !!
                                    @ ^ [Y4: $i] :
                                        ( ( irel @ Y3 @ Y4 )
                                       => ( ( !!
                                            @ ^ [Y5: $i] :
                                                ( ( irel @ Y4 @ Y5 )
                                               => ( ( o32 @ Y5 )
                                                  & ( o22 @ Y5 ) ) ) )
                                          | ( !!
                                            @ ^ [Y5: $i] :
                                                ( ( irel @ Y4 @ Y5 )
                                               => ( ( o32 @ Y5 )
                                                  & ( o12 @ Y5 ) ) ) ) ) ) )
                                  | ( !!
                                    @ ^ [Y4: $i] :
                                        ( ( irel @ Y3 @ Y4 )
                                       => ( ( o22 @ Y4 )
                                          & ( o12 @ Y4 ) ) ) ) ) ) )
                          | ( !!
                            @ ^ [Y3: $i] :
                                ( ( irel @ Y2 @ Y3 )
                               => ( ( o31 @ Y3 )
                                  & ( o21 @ Y3 ) ) ) ) ) ) )
                  | ( !!
                    @ ^ [Y2: $i] :
                        ( ( irel @ Y1 @ Y2 )
                       => ( ( o31 @ Y2 )
                          & ( o11 @ Y2 ) ) ) ) ) ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( irel @ Y0 @ Y1 )
               => ( ( o21 @ Y1 )
                  & ( o11 @ Y1 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl50,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk1' @ Y0 )
           => ( ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( irel @ Y1 @ Y2 )
                           => ( ( !!
                                @ ^ [Y3: $i] :
                                    ( ( irel @ Y2 @ Y3 )
                                   => ( ( !!
                                        @ ^ [Y4: $i] :
                                            ( ( irel @ Y3 @ Y4 )
                                           => ( ( o32 @ Y4 )
                                              & ( o22 @ Y4 ) ) ) )
                                      | ( !!
                                        @ ^ [Y4: $i] :
                                            ( ( irel @ Y3 @ Y4 )
                                           => ( ( o32 @ Y4 )
                                              & ( o12 @ Y4 ) ) ) ) ) ) )
                              | ( !!
                                @ ^ [Y3: $i] :
                                    ( ( irel @ Y2 @ Y3 )
                                   => ( ( o22 @ Y3 )
                                      & ( o12 @ Y3 ) ) ) ) ) ) )
                      | ( !!
                        @ ^ [Y2: $i] :
                            ( ( irel @ Y1 @ Y2 )
                           => ( ( o31 @ Y2 )
                              & ( o21 @ Y2 ) ) ) ) ) ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( o31 @ Y1 )
                      & ( o11 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk1' @ Y0 )
           => ( ( o21 @ Y0 )
              & ( o11 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl51,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk1' @ Y0 )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( irel @ Y1 @ Y2 )
                         => ( ( !!
                              @ ^ [Y3: $i] :
                                  ( ( irel @ Y2 @ Y3 )
                                 => ( ( !!
                                      @ ^ [Y4: $i] :
                                          ( ( irel @ Y3 @ Y4 )
                                         => ( ( o32 @ Y4 )
                                            & ( o22 @ Y4 ) ) ) )
                                    | ( !!
                                      @ ^ [Y4: $i] :
                                          ( ( irel @ Y3 @ Y4 )
                                         => ( ( o32 @ Y4 )
                                            & ( o12 @ Y4 ) ) ) ) ) ) )
                            | ( !!
                              @ ^ [Y3: $i] :
                                  ( ( irel @ Y2 @ Y3 )
                                 => ( ( o22 @ Y3 )
                                    & ( o12 @ Y3 ) ) ) ) ) ) )
                    | ( !!
                      @ ^ [Y2: $i] :
                          ( ( irel @ Y1 @ Y2 )
                         => ( ( o31 @ Y2 )
                            & ( o21 @ Y2 ) ) ) ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( o31 @ Y1 )
                    & ( o11 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl53,plain,
    ~ ( ( irel @ '#sk1' @ '#sk2' )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk2' @ Y0 )
             => ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( irel @ Y0 @ Y1 )
                     => ( ( !!
                          @ ^ [Y2: $i] :
                              ( ( irel @ Y1 @ Y2 )
                             => ( ( !!
                                  @ ^ [Y3: $i] :
                                      ( ( irel @ Y2 @ Y3 )
                                     => ( ( o32 @ Y3 )
                                        & ( o22 @ Y3 ) ) ) )
                                | ( !!
                                  @ ^ [Y3: $i] :
                                      ( ( irel @ Y2 @ Y3 )
                                     => ( ( o32 @ Y3 )
                                        & ( o12 @ Y3 ) ) ) ) ) ) )
                        | ( !!
                          @ ^ [Y2: $i] :
                              ( ( irel @ Y1 @ Y2 )
                             => ( ( o22 @ Y2 )
                                & ( o12 @ Y2 ) ) ) ) ) ) )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( irel @ Y0 @ Y1 )
                     => ( ( o31 @ Y1 )
                        & ( o21 @ Y1 ) ) ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk2' @ Y0 )
             => ( ( o31 @ Y0 )
                & ( o11 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl56,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk2' @ Y0 )
           => ( ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( irel @ Y1 @ Y2 )
                           => ( ( !!
                                @ ^ [Y3: $i] :
                                    ( ( irel @ Y2 @ Y3 )
                                   => ( ( o32 @ Y3 )
                                      & ( o22 @ Y3 ) ) ) )
                              | ( !!
                                @ ^ [Y3: $i] :
                                    ( ( irel @ Y2 @ Y3 )
                                   => ( ( o32 @ Y3 )
                                      & ( o12 @ Y3 ) ) ) ) ) ) )
                      | ( !!
                        @ ^ [Y2: $i] :
                            ( ( irel @ Y1 @ Y2 )
                           => ( ( o22 @ Y2 )
                              & ( o12 @ Y2 ) ) ) ) ) ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( o31 @ Y1 )
                      & ( o21 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk2' @ Y0 )
           => ( ( o31 @ Y0 )
              & ( o11 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl60,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk2' @ Y0 )
         => ( ( o31 @ Y0 )
            & ( o11 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl63,plain,
    ~ ( ( irel @ '#sk2' @ '#sk5' )
     => ( ( o31 @ '#sk5' )
        & ( o11 @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl66,plain,
    irel @ '#sk2' @ '#sk5',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl63]) ).

thf(axiom1,axiom,
    ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i] :
      ( ! [X8: $i] :
          ( ( irel @ X4 @ X8 )
         => ( o12 @ X8 ) )
      | ! [X6: $i] :
          ( ( irel @ X4 @ X6 )
         => ( o11 @ X6 ) ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( !!
          @ ^ [Y1: $i] :
              ( ( irel @ Y0 @ Y1 )
             => ( o12 @ Y1 ) ) )
        | ( !!
          @ ^ [Y1: $i] :
              ( ( irel @ Y0 @ Y1 )
             => ( o11 @ Y1 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o12 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o11 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o12 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o11 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( irel @ X2 @ X4 )
       => ( o12 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o11 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( irel @ X2 @ X4 )
      | ( o12 @ X4 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o11 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( irel @ X2 @ X6 )
       => ( o11 @ X6 ) )
      | ( o12 @ X4 )
      | ~ ( irel @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X2 @ X6 )
      | ( o11 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( o12 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl123,plain,
    ! [X0: $i] :
      ( ( o12 @ X0 )
      | ~ ( irel @ '#sk2' @ X0 )
      | ( o11 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl25]) ).

thf(zip_derived_cl66_001,plain,
    irel @ '#sk2' @ '#sk5',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl63]) ).

thf(axiom3,axiom,
    ivalid @ ( ior @ ( iatom @ o31 ) @ ( iatom @ o32 ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i] :
      ( ! [X8: $i] :
          ( ( irel @ X4 @ X8 )
         => ( o32 @ X8 ) )
      | ! [X6: $i] :
          ( ( irel @ X4 @ X6 )
         => ( o31 @ X6 ) ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( !!
          @ ^ [Y1: $i] :
              ( ( irel @ Y0 @ Y1 )
             => ( o32 @ Y1 ) ) )
        | ( !!
          @ ^ [Y1: $i] :
              ( ( irel @ Y0 @ Y1 )
             => ( o31 @ Y1 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl40,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o32 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o31 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl41,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o32 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o31 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( irel @ X2 @ X4 )
       => ( o32 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o31 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( irel @ X2 @ X4 )
      | ( o32 @ X4 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o31 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( irel @ X2 @ X6 )
       => ( o31 @ X6 ) )
      | ( o32 @ X4 )
      | ~ ( irel @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl45,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X2 @ X6 )
      | ( o31 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( o32 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl121,plain,
    ! [X0: $i] :
      ( ( o32 @ X0 )
      | ~ ( irel @ '#sk2' @ X0 )
      | ( o31 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl45]) ).

thf(zip_derived_cl59,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk2' @ Y0 )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( irel @ Y1 @ Y2 )
                         => ( ( !!
                              @ ^ [Y3: $i] :
                                  ( ( irel @ Y2 @ Y3 )
                                 => ( ( o32 @ Y3 )
                                    & ( o22 @ Y3 ) ) ) )
                            | ( !!
                              @ ^ [Y3: $i] :
                                  ( ( irel @ Y2 @ Y3 )
                                 => ( ( o32 @ Y3 )
                                    & ( o12 @ Y3 ) ) ) ) ) ) )
                    | ( !!
                      @ ^ [Y2: $i] :
                          ( ( irel @ Y1 @ Y2 )
                         => ( ( o22 @ Y2 )
                            & ( o12 @ Y2 ) ) ) ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( o31 @ Y1 )
                    & ( o21 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl62,plain,
    ~ ( ( irel @ '#sk2' @ '#sk4' )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk4' @ Y0 )
             => ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( irel @ Y0 @ Y1 )
                     => ( ( !!
                          @ ^ [Y2: $i] :
                              ( ( irel @ Y1 @ Y2 )
                             => ( ( o32 @ Y2 )
                                & ( o22 @ Y2 ) ) ) )
                        | ( !!
                          @ ^ [Y2: $i] :
                              ( ( irel @ Y1 @ Y2 )
                             => ( ( o32 @ Y2 )
                                & ( o12 @ Y2 ) ) ) ) ) ) )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( irel @ Y0 @ Y1 )
                     => ( ( o22 @ Y1 )
                        & ( o12 @ Y1 ) ) ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk4' @ Y0 )
             => ( ( o31 @ Y0 )
                & ( o21 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl65,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk4' @ Y0 )
           => ( ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( irel @ Y1 @ Y2 )
                           => ( ( o32 @ Y2 )
                              & ( o22 @ Y2 ) ) ) )
                      | ( !!
                        @ ^ [Y2: $i] :
                            ( ( irel @ Y1 @ Y2 )
                           => ( ( o32 @ Y2 )
                              & ( o12 @ Y2 ) ) ) ) ) ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( o22 @ Y1 )
                      & ( o12 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk4' @ Y0 )
           => ( ( o31 @ Y0 )
              & ( o21 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl68,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk4' @ Y0 )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( irel @ Y1 @ Y2 )
                         => ( ( o32 @ Y2 )
                            & ( o22 @ Y2 ) ) ) )
                    | ( !!
                      @ ^ [Y2: $i] :
                          ( ( irel @ Y1 @ Y2 )
                         => ( ( o32 @ Y2 )
                            & ( o12 @ Y2 ) ) ) ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( o22 @ Y1 )
                    & ( o12 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl71,plain,
    ~ ( ( irel @ '#sk4' @ '#sk6' )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk6' @ Y0 )
             => ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( irel @ Y0 @ Y1 )
                     => ( ( o32 @ Y1 )
                        & ( o22 @ Y1 ) ) ) )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( irel @ Y0 @ Y1 )
                     => ( ( o32 @ Y1 )
                        & ( o12 @ Y1 ) ) ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk6' @ Y0 )
             => ( ( o22 @ Y0 )
                & ( o12 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl74,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk6' @ Y0 )
           => ( ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( o32 @ Y1 )
                      & ( o22 @ Y1 ) ) ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( irel @ Y0 @ Y1 )
                   => ( ( o32 @ Y1 )
                      & ( o12 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk6' @ Y0 )
           => ( ( o22 @ Y0 )
              & ( o12 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl77,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk6' @ Y0 )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( o32 @ Y1 )
                    & ( o22 @ Y1 ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( irel @ Y0 @ Y1 )
                 => ( ( o32 @ Y1 )
                    & ( o12 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl80,plain,
    ~ ( ( irel @ '#sk6' @ '#sk8' )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk8' @ Y0 )
             => ( ( o32 @ Y0 )
                & ( o22 @ Y0 ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( irel @ '#sk8' @ Y0 )
             => ( ( o32 @ Y0 )
                & ( o12 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl77]) ).

thf(zip_derived_cl83,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk8' @ Y0 )
           => ( ( o32 @ Y0 )
              & ( o22 @ Y0 ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ '#sk8' @ Y0 )
           => ( ( o32 @ Y0 )
              & ( o12 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl87,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk8' @ Y0 )
         => ( ( o32 @ Y0 )
            & ( o12 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl83]) ).

thf(zip_derived_cl90,plain,
    ~ ( ( irel @ '#sk8' @ '#sk11' )
     => ( ( o32 @ '#sk11' )
        & ( o12 @ '#sk11' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl94,plain,
    ~ ( ( o32 @ '#sk11' )
      & ( o12 @ '#sk11' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl96,plain,
    ( ~ ( o32 @ '#sk11' )
    | ~ ( o12 @ '#sk11' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl435,plain,
    ( ( o31 @ '#sk5' )
    | ~ ( irel @ '#sk2' @ '#sk11' )
    | ~ ( o12 @ '#sk11' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl121,zip_derived_cl96]) ).

thf(zip_derived_cl67,plain,
    ~ ( ( o31 @ '#sk5' )
      & ( o11 @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl70,plain,
    ( ~ ( o31 @ '#sk5' )
    | ~ ( o11 @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl447,plain,
    ( ~ ( o12 @ '#sk11' )
    | ~ ( irel @ '#sk2' @ '#sk11' )
    | ~ ( o11 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl435,zip_derived_cl70]) ).

thf(zip_derived_cl64,plain,
    irel @ '#sk2' @ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl73,plain,
    irel @ '#sk4' @ '#sk6',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).

thf(trans_axiom,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( ( irel @ Y @ Z )
        & ( irel @ X @ Y ) )
     => ( irel @ X @ Z ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( irel @ Y1 @ Y2 )
                  & ( irel @ Y0 @ Y1 ) )
               => ( irel @ Y0 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[trans_axiom]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( irel @ Y0 @ Y1 )
                & ( irel @ X2 @ Y0 ) )
             => ( irel @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl8,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( irel @ X4 @ Y0 )
            & ( irel @ X2 @ X4 ) )
         => ( irel @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( irel @ X4 @ X6 )
        & ( irel @ X2 @ X4 ) )
     => ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl10,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( irel @ X4 @ X6 )
          & ( irel @ X2 @ X4 ) )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X4 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl132,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk6' )
      | ~ ( irel @ X0 @ '#sk4' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl11]) ).

thf(zip_derived_cl565,plain,
    irel @ '#sk2' @ '#sk6',
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl132]) ).

thf(zip_derived_cl82,plain,
    irel @ '#sk6' @ '#sk8',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl11_002,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X4 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl163,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk8' )
      | ~ ( irel @ X0 @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl11]) ).

thf(zip_derived_cl694,plain,
    irel @ '#sk2' @ '#sk8',
    inference('sup-',[status(thm)],[zip_derived_cl565,zip_derived_cl163]) ).

thf(zip_derived_cl93,plain,
    irel @ '#sk8' @ '#sk11',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl11_003,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X4 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl193,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk11' )
      | ~ ( irel @ X0 @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl11]) ).

thf(zip_derived_cl1290,plain,
    irel @ '#sk2' @ '#sk11',
    inference('sup-',[status(thm)],[zip_derived_cl694,zip_derived_cl193]) ).

thf(zip_derived_cl1343,plain,
    ( ~ ( o12 @ '#sk11' )
    | ~ ( o11 @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl447,zip_derived_cl1290]) ).

thf(zip_derived_cl52,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk1' @ Y0 )
         => ( ( o21 @ Y0 )
            & ( o11 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl54,plain,
    ~ ( ( irel @ '#sk1' @ '#sk3' )
     => ( ( o21 @ '#sk3' )
        & ( o11 @ '#sk3' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl57,plain,
    irel @ '#sk1' @ '#sk3',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl25_004,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X2 @ X6 )
      | ( o11 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( o12 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl107,plain,
    ! [X0: $i] :
      ( ( o12 @ X0 )
      | ~ ( irel @ '#sk1' @ X0 )
      | ( o11 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl25]) ).

thf(zip_derived_cl69,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk4' @ Y0 )
         => ( ( o31 @ Y0 )
            & ( o21 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl72,plain,
    ~ ( ( irel @ '#sk4' @ '#sk7' )
     => ( ( o31 @ '#sk7' )
        & ( o21 @ '#sk7' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl75,plain,
    irel @ '#sk4' @ '#sk7',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).

thf(axiom2,axiom,
    ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ) ).

thf(zf_stmt_4,axiom,
    ! [X4: $i] :
      ( ! [X8: $i] :
          ( ( irel @ X4 @ X8 )
         => ( o22 @ X8 ) )
      | ! [X6: $i] :
          ( ( irel @ X4 @ X6 )
         => ( o21 @ X6 ) ) ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( !!
          @ ^ [Y1: $i] :
              ( ( irel @ Y0 @ Y1 )
             => ( o22 @ Y1 ) ) )
        | ( !!
          @ ^ [Y1: $i] :
              ( ( irel @ Y0 @ Y1 )
             => ( o21 @ Y1 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o22 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o21 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o22 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o21 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( irel @ X2 @ X4 )
       => ( o22 @ X4 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o21 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( irel @ X2 @ X4 )
      | ( o22 @ X4 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( irel @ X2 @ Y0 )
           => ( o21 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl34,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( irel @ X2 @ X6 )
       => ( o21 @ X6 ) )
      | ( o22 @ X4 )
      | ~ ( irel @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl35,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X2 @ X6 )
      | ( o21 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( o22 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl151,plain,
    ! [X0: $i] :
      ( ( o22 @ X0 )
      | ~ ( irel @ '#sk4' @ X0 )
      | ( o21 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl35]) ).

thf(zip_derived_cl121_005,plain,
    ! [X0: $i] :
      ( ( o32 @ X0 )
      | ~ ( irel @ '#sk2' @ X0 )
      | ( o31 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl45]) ).

thf(zip_derived_cl86,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk8' @ Y0 )
         => ( ( o32 @ Y0 )
            & ( o22 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl83]) ).

thf(zip_derived_cl89,plain,
    ~ ( ( irel @ '#sk8' @ '#sk10' )
     => ( ( o32 @ '#sk10' )
        & ( o22 @ '#sk10' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl92,plain,
    ~ ( ( o32 @ '#sk10' )
      & ( o22 @ '#sk10' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl95,plain,
    ( ~ ( o32 @ '#sk10' )
    | ~ ( o22 @ '#sk10' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl436,plain,
    ( ( o31 @ '#sk5' )
    | ~ ( irel @ '#sk2' @ '#sk10' )
    | ~ ( o22 @ '#sk10' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl121,zip_derived_cl95]) ).

thf(zip_derived_cl70_006,plain,
    ( ~ ( o31 @ '#sk5' )
    | ~ ( o11 @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl487,plain,
    ( ~ ( o22 @ '#sk10' )
    | ~ ( irel @ '#sk2' @ '#sk10' )
    | ~ ( o11 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl436,zip_derived_cl70]) ).

thf(zip_derived_cl694_007,plain,
    irel @ '#sk2' @ '#sk8',
    inference('sup-',[status(thm)],[zip_derived_cl565,zip_derived_cl163]) ).

thf(zip_derived_cl91,plain,
    irel @ '#sk8' @ '#sk10',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl11_008,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X4 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl183,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk10' )
      | ~ ( irel @ X0 @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl11]) ).

thf(zip_derived_cl1004,plain,
    irel @ '#sk2' @ '#sk10',
    inference('sup-',[status(thm)],[zip_derived_cl694,zip_derived_cl183]) ).

thf(zip_derived_cl1053,plain,
    ( ~ ( o22 @ '#sk10' )
    | ~ ( o11 @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl487,zip_derived_cl1004]) ).

thf(zip_derived_cl1144,plain,
    ( ( o21 @ '#sk7' )
    | ~ ( irel @ '#sk4' @ '#sk10' )
    | ~ ( o11 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl151,zip_derived_cl1053]) ).

thf(zip_derived_cl73_009,plain,
    irel @ '#sk4' @ '#sk6',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl163_010,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk8' )
      | ~ ( irel @ X0 @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl11]) ).

thf(zip_derived_cl693,plain,
    irel @ '#sk4' @ '#sk8',
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl163]) ).

thf(zip_derived_cl183_011,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk10' )
      | ~ ( irel @ X0 @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl11]) ).

thf(zip_derived_cl1003,plain,
    irel @ '#sk4' @ '#sk10',
    inference('sup-',[status(thm)],[zip_derived_cl693,zip_derived_cl183]) ).

thf(zip_derived_cl1165,plain,
    ( ( o21 @ '#sk7' )
    | ~ ( o11 @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl1144,zip_derived_cl1003]) ).

thf(zip_derived_cl75_012,plain,
    irel @ '#sk4' @ '#sk7',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl45_013,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X2 @ X6 )
      | ( o31 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( o32 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl150,plain,
    ! [X0: $i] :
      ( ( o32 @ X0 )
      | ~ ( irel @ '#sk4' @ X0 )
      | ( o31 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl45]) ).

thf(zip_derived_cl95_014,plain,
    ( ~ ( o32 @ '#sk10' )
    | ~ ( o22 @ '#sk10' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl600,plain,
    ( ( o31 @ '#sk7' )
    | ~ ( irel @ '#sk4' @ '#sk10' )
    | ~ ( o22 @ '#sk10' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl150,zip_derived_cl95]) ).

thf(zip_derived_cl76,plain,
    ~ ( ( o31 @ '#sk7' )
      & ( o21 @ '#sk7' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl79,plain,
    ( ~ ( o31 @ '#sk7' )
    | ~ ( o21 @ '#sk7' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl779,plain,
    ( ~ ( o22 @ '#sk10' )
    | ~ ( irel @ '#sk4' @ '#sk10' )
    | ~ ( o21 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl600,zip_derived_cl79]) ).

thf(zip_derived_cl1003_015,plain,
    irel @ '#sk4' @ '#sk10',
    inference('sup-',[status(thm)],[zip_derived_cl693,zip_derived_cl183]) ).

thf(zip_derived_cl1036,plain,
    ( ~ ( o22 @ '#sk10' )
    | ~ ( o21 @ '#sk7' ) ),
    inference(demod,[status(thm)],[zip_derived_cl779,zip_derived_cl1003]) ).

thf(zip_derived_cl57_016,plain,
    irel @ '#sk1' @ '#sk3',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl35_017,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X2 @ X6 )
      | ( o21 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( o22 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl106,plain,
    ! [X0: $i] :
      ( ( o22 @ X0 )
      | ~ ( irel @ '#sk1' @ X0 )
      | ( o21 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl35]) ).

thf(zip_derived_cl1081,plain,
    ( ~ ( o21 @ '#sk7' )
    | ( o21 @ '#sk3' )
    | ~ ( irel @ '#sk1' @ '#sk10' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1036,zip_derived_cl106]) ).

thf(zip_derived_cl55,plain,
    irel @ '#sk1' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl64_018,plain,
    irel @ '#sk2' @ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl11_019,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X4 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl116,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk4' )
      | ~ ( irel @ X0 @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl11]) ).

thf(zip_derived_cl417,plain,
    irel @ '#sk1' @ '#sk4',
    inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl116]) ).

thf(zip_derived_cl132_020,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk6' )
      | ~ ( irel @ X0 @ '#sk4' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl11]) ).

thf(zip_derived_cl566,plain,
    irel @ '#sk1' @ '#sk6',
    inference('sup-',[status(thm)],[zip_derived_cl417,zip_derived_cl132]) ).

thf(zip_derived_cl163_021,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk8' )
      | ~ ( irel @ X0 @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl11]) ).

thf(zip_derived_cl695,plain,
    irel @ '#sk1' @ '#sk8',
    inference('sup-',[status(thm)],[zip_derived_cl566,zip_derived_cl163]) ).

thf(zip_derived_cl183_022,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk10' )
      | ~ ( irel @ X0 @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl11]) ).

thf(zip_derived_cl1005,plain,
    irel @ '#sk1' @ '#sk10',
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl183]) ).

thf(zip_derived_cl1691,plain,
    ( ~ ( o21 @ '#sk7' )
    | ( o21 @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl1081,zip_derived_cl1005]) ).

thf(zip_derived_cl1692,plain,
    ( ~ ( o11 @ '#sk5' )
    | ( o21 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1165,zip_derived_cl1691]) ).

thf(zip_derived_cl58,plain,
    ~ ( ( o21 @ '#sk3' )
      & ( o11 @ '#sk3' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl61,plain,
    ( ~ ( o21 @ '#sk3' )
    | ~ ( o11 @ '#sk3' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl1694,plain,
    ( ~ ( o11 @ '#sk5' )
    | ~ ( o11 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1692,zip_derived_cl61]) ).

thf(zip_derived_cl123_023,plain,
    ! [X0: $i] :
      ( ( o12 @ X0 )
      | ~ ( irel @ '#sk2' @ X0 )
      | ( o11 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl25]) ).

thf(zip_derived_cl106_024,plain,
    ! [X0: $i] :
      ( ( o22 @ X0 )
      | ~ ( irel @ '#sk1' @ X0 )
      | ( o21 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl35]) ).

thf(zip_derived_cl78,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( irel @ '#sk6' @ Y0 )
         => ( ( o22 @ Y0 )
            & ( o12 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl81,plain,
    ~ ( ( irel @ '#sk6' @ '#sk9' )
     => ( ( o22 @ '#sk9' )
        & ( o12 @ '#sk9' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl85,plain,
    ~ ( ( o22 @ '#sk9' )
      & ( o12 @ '#sk9' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl88,plain,
    ( ~ ( o22 @ '#sk9' )
    | ~ ( o12 @ '#sk9' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl367,plain,
    ( ( o21 @ '#sk3' )
    | ~ ( irel @ '#sk1' @ '#sk9' )
    | ~ ( o12 @ '#sk9' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl88]) ).

thf(zip_derived_cl61_025,plain,
    ( ~ ( o21 @ '#sk3' )
    | ~ ( o11 @ '#sk3' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl371,plain,
    ( ~ ( o12 @ '#sk9' )
    | ~ ( irel @ '#sk1' @ '#sk9' )
    | ~ ( o11 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl367,zip_derived_cl61]) ).

thf(zip_derived_cl566_026,plain,
    irel @ '#sk1' @ '#sk6',
    inference('sup-',[status(thm)],[zip_derived_cl417,zip_derived_cl132]) ).

thf(zip_derived_cl84,plain,
    irel @ '#sk6' @ '#sk9',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl11_027,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( irel @ X4 @ X6 )
      | ~ ( irel @ X2 @ X4 )
      | ( irel @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl173,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk9' )
      | ~ ( irel @ X0 @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl84,zip_derived_cl11]) ).

thf(zip_derived_cl825,plain,
    irel @ '#sk1' @ '#sk9',
    inference('sup-',[status(thm)],[zip_derived_cl566,zip_derived_cl173]) ).

thf(zip_derived_cl863,plain,
    ( ~ ( o12 @ '#sk9' )
    | ~ ( o11 @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl371,zip_derived_cl825]) ).

thf(zip_derived_cl898,plain,
    ( ( o11 @ '#sk5' )
    | ~ ( irel @ '#sk2' @ '#sk9' )
    | ~ ( o11 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl863]) ).

thf(zip_derived_cl565_028,plain,
    irel @ '#sk2' @ '#sk6',
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl132]) ).

thf(zip_derived_cl173_029,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk9' )
      | ~ ( irel @ X0 @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl84,zip_derived_cl11]) ).

thf(zip_derived_cl824,plain,
    irel @ '#sk2' @ '#sk9',
    inference('sup-',[status(thm)],[zip_derived_cl565,zip_derived_cl173]) ).

thf(zip_derived_cl918,plain,
    ( ( o11 @ '#sk5' )
    | ~ ( o11 @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl898,zip_derived_cl824]) ).

thf(zip_derived_cl1698,plain,
    ~ ( o11 @ '#sk3' ),
    inference(clc,[status(thm)],[zip_derived_cl1694,zip_derived_cl918]) ).

thf(zip_derived_cl1699,plain,
    ! [X0: $i] :
      ( ( o12 @ X0 )
      | ~ ( irel @ '#sk1' @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl107,zip_derived_cl1698]) ).

thf(zip_derived_cl1701,plain,
    ( ~ ( o11 @ '#sk5' )
    | ~ ( irel @ '#sk1' @ '#sk11' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1343,zip_derived_cl1699]) ).

thf(zip_derived_cl695_030,plain,
    irel @ '#sk1' @ '#sk8',
    inference('sup-',[status(thm)],[zip_derived_cl566,zip_derived_cl163]) ).

thf(zip_derived_cl193_031,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk11' )
      | ~ ( irel @ X0 @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl11]) ).

thf(zip_derived_cl1291,plain,
    irel @ '#sk1' @ '#sk11',
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl193]) ).

thf(zip_derived_cl1702,plain,
    ~ ( o11 @ '#sk5' ),
    inference(demod,[status(thm)],[zip_derived_cl1701,zip_derived_cl1291]) ).

thf(zip_derived_cl1704,plain,
    ! [X0: $i] :
      ( ( o12 @ X0 )
      | ~ ( irel @ '#sk2' @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl1702]) ).

thf(zip_derived_cl1704_032,plain,
    ! [X0: $i] :
      ( ( o12 @ X0 )
      | ~ ( irel @ '#sk2' @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl1702]) ).

thf(zip_derived_cl151_033,plain,
    ! [X0: $i] :
      ( ( o22 @ X0 )
      | ~ ( irel @ '#sk4' @ X0 )
      | ( o21 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl35]) ).

thf(zip_derived_cl88_034,plain,
    ( ~ ( o22 @ '#sk9' )
    | ~ ( o12 @ '#sk9' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl608,plain,
    ( ( o21 @ '#sk7' )
    | ~ ( irel @ '#sk4' @ '#sk9' )
    | ~ ( o12 @ '#sk9' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl151,zip_derived_cl88]) ).

thf(zip_derived_cl73_035,plain,
    irel @ '#sk4' @ '#sk6',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl173_036,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk9' )
      | ~ ( irel @ X0 @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl84,zip_derived_cl11]) ).

thf(zip_derived_cl823,plain,
    irel @ '#sk4' @ '#sk9',
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl173]) ).

thf(zip_derived_cl1714,plain,
    ( ( o21 @ '#sk7' )
    | ~ ( o12 @ '#sk9' ) ),
    inference(demod,[status(thm)],[zip_derived_cl608,zip_derived_cl823]) ).

thf(zip_derived_cl150_037,plain,
    ! [X0: $i] :
      ( ( o32 @ X0 )
      | ~ ( irel @ '#sk4' @ X0 )
      | ( o31 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl45]) ).

thf(zip_derived_cl96_038,plain,
    ( ~ ( o32 @ '#sk11' )
    | ~ ( o12 @ '#sk11' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl599,plain,
    ( ( o31 @ '#sk7' )
    | ~ ( irel @ '#sk4' @ '#sk11' )
    | ~ ( o12 @ '#sk11' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl150,zip_derived_cl96]) ).

thf(zip_derived_cl79_039,plain,
    ( ~ ( o31 @ '#sk7' )
    | ~ ( o21 @ '#sk7' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl743,plain,
    ( ~ ( o12 @ '#sk11' )
    | ~ ( irel @ '#sk4' @ '#sk11' )
    | ~ ( o21 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl599,zip_derived_cl79]) ).

thf(zip_derived_cl693_040,plain,
    irel @ '#sk4' @ '#sk8',
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl163]) ).

thf(zip_derived_cl193_041,plain,
    ! [X0: $i] :
      ( ( irel @ X0 @ '#sk11' )
      | ~ ( irel @ X0 @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl11]) ).

thf(zip_derived_cl1289,plain,
    irel @ '#sk4' @ '#sk11',
    inference('sup-',[status(thm)],[zip_derived_cl693,zip_derived_cl193]) ).

thf(zip_derived_cl1326,plain,
    ( ~ ( o12 @ '#sk11' )
    | ~ ( o21 @ '#sk7' ) ),
    inference(demod,[status(thm)],[zip_derived_cl743,zip_derived_cl1289]) ).

thf(zip_derived_cl1716,plain,
    ( ~ ( o12 @ '#sk9' )
    | ~ ( o12 @ '#sk11' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1714,zip_derived_cl1326]) ).

thf(zip_derived_cl1743,plain,
    ( ~ ( irel @ '#sk2' @ '#sk9' )
    | ~ ( o12 @ '#sk11' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1704,zip_derived_cl1716]) ).

thf(zip_derived_cl824_042,plain,
    irel @ '#sk2' @ '#sk9',
    inference('sup-',[status(thm)],[zip_derived_cl565,zip_derived_cl173]) ).

thf(zip_derived_cl1761,plain,
    ~ ( o12 @ '#sk11' ),
    inference(demod,[status(thm)],[zip_derived_cl1743,zip_derived_cl824]) ).

thf(zip_derived_cl1789,plain,
    ~ ( irel @ '#sk2' @ '#sk11' ),
    inference('sup-',[status(thm)],[zip_derived_cl1704,zip_derived_cl1761]) ).

thf(zip_derived_cl1290_043,plain,
    irel @ '#sk2' @ '#sk11',
    inference('sup-',[status(thm)],[zip_derived_cl694,zip_derived_cl193]) ).

thf(zip_derived_cl1818,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl1789,zip_derived_cl1290]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SYO066^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.j7Z7qml0oV true
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sat Aug 26 03:30:52 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.15/0.35  % Running portfolio for 300 s
% 0.15/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35  % Number of cores: 8
% 0.22/0.36  % Python version: Python 3.6.8
% 0.22/0.36  % Running in HO mode
% 0.22/0.67  % Total configuration time : 828
% 0.22/0.67  % Estimated wc time : 1656
% 0.22/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.99/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.99/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.99/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.99/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.99/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.36/0.82  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.42/0.87  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.76/1.16  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 2.69/1.22  % Solved by lams/35_full_unif4.sh.
% 2.69/1.22  % done 1073 iterations in 0.420s
% 2.69/1.22  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.69/1.22  % SZS output start Refutation
% See solution above
% 2.69/1.22  
% 2.69/1.22  
% 2.69/1.22  % Terminating...
% 2.69/1.30  % Runner terminated.
% 2.69/1.32  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------