TSTP Solution File: SYO444^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYO444^1 : 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.EoiW5mAFZe true

% Computer : n020.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 05:51:12 EDT 2023

% Result   : Theorem 1.47s 1.01s
% Output   : Refutation 1.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  235 (  63 unt;  19 typ;   0 def)
%            Number of atoms       : 1178 (  30 equ; 300 cnn)
%            Maximal formula atoms :   50 (   5 avg)
%            Number of connectives : 2747 ( 552   ~; 450   |;   9   &;1602   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   90 (  90   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  19 usr;   9 con; 0-3 aty)
%                                         ( 119  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  302 ( 170   ^; 132   !;   0   ?; 302   :)

% Comments : 
%------------------------------------------------------------------------------
thf(q_type,type,
    q: $i > $o ).

thf(rel_s5_type,type,
    rel_s5: $i > $i > $o ).

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

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

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

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(p_type,type,
    p: $i > $o ).

thf(mdia_s5_type,type,
    mdia_s5: ( $i > $o ) > $i > $o ).

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

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(mbox_s5_type,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

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

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#form4_type',type,
    '#form4': $o ).

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

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

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

thf(mdia_s5,axiom,
    ( mdia_s5
    = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ) ).

thf(mbox_s5,axiom,
    ( mbox_s5
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( rel_s5 @ W @ V ) ) ) ) ).

thf('0',plain,
    ( mbox_s5
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( rel_s5 @ W @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox_s5]) ).

thf('1',plain,
    ( mbox_s5
    = ( ^ [V_1: $i > $o,V_2: $i] :
        ! [X4: $i] :
          ( ( V_1 @ X4 )
          | ~ ( rel_s5 @ V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

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

thf('2',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

thf('3',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( mdia_s5
    = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mdia_s5,'1','3']) ).

thf('5',plain,
    ( mdia_s5
    = ( ^ [V_1: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('6',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

thf('7',plain,
    ( mvalid
    = ( ^ [V_1: $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 ) ) ),
    define([status(thm)]) ).

thf(mequiv,axiom,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).

thf(mor,axiom,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ) ).

thf('8',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('9',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('10',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'9','3']) ).

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

thf(mand,axiom,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).

thf('12',plain,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand,'9','3']) ).

thf('13',plain,
    ( mand
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf('14',plain,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv,'11','13','9','3']) ).

thf('15',plain,
    ( mequiv
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(prove,conjecture,
    mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ~ ( ~ ( ! [X18: $i] :
                ( ~ ( rel_s5 @ X4 @ X18 )
                | ~ ! [X20: $i] :
                      ( ~ ( rel_s5 @ X18 @ X20 )
                      | ~ ( q @ X20 ) )
                | ~ ( p @ X18 ) )
            | ~ ( ~ ! [X16: $i] :
                      ( ~ ( rel_s5 @ X4 @ X16 )
                      | ~ ( q @ X16 ) )
                | ! [X14: $i] :
                    ( ~ ( rel_s5 @ X4 @ X14 )
                    | ~ ( p @ X14 ) ) ) )
        | ~ ( ~ ! [X12: $i] :
                  ( ~ ( rel_s5 @ X4 @ X12 )
                  | ~ ( q @ X12 ) )
            | ! [X10: $i] :
                ( ~ ( rel_s5 @ X4 @ X10 )
                | ~ ( p @ X10 ) )
            | ~ ! [X6: $i] :
                  ( ~ ( rel_s5 @ X4 @ X6 )
                  | ~ ! [X8: $i] :
                        ( ~ ( rel_s5 @ X6 @ X8 )
                        | ~ ( q @ X8 ) )
                  | ~ ( p @ X6 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ~ ( ~ ( ! [X18: $i] :
                  ( ~ ( rel_s5 @ X4 @ X18 )
                  | ~ ! [X20: $i] :
                        ( ~ ( rel_s5 @ X18 @ X20 )
                        | ~ ( q @ X20 ) )
                  | ~ ( p @ X18 ) )
              | ~ ( ~ ! [X16: $i] :
                        ( ~ ( rel_s5 @ X4 @ X16 )
                        | ~ ( q @ X16 ) )
                  | ! [X14: $i] :
                      ( ~ ( rel_s5 @ X4 @ X14 )
                      | ~ ( p @ X14 ) ) ) )
          | ~ ( ~ ! [X12: $i] :
                    ( ~ ( rel_s5 @ X4 @ X12 )
                    | ~ ( q @ X12 ) )
              | ! [X10: $i] :
                  ( ~ ( rel_s5 @ X4 @ X10 )
                  | ~ ( p @ X10 ) )
              | ~ ! [X6: $i] :
                    ( ~ ( rel_s5 @ X4 @ X6 )
                    | ~ ! [X8: $i] :
                          ( ~ ( rel_s5 @ X6 @ X8 )
                          | ~ ( q @ X8 ) )
                    | ~ ( p @ X6 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( (~)
          @ ( ( (~)
              @ ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y2: $i] :
                              ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                              | ( (~) @ ( q @ Y2 ) ) ) ) )
                      | ( (~) @ ( p @ Y1 ) ) ) )
                | ( (~)
                  @ ( ( (~)
                      @ ( !!
                        @ ^ [Y1: $i] :
                            ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                            | ( (~) @ ( q @ Y1 ) ) ) ) )
                    | ( !!
                      @ ^ [Y1: $i] :
                          ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                          | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) )
            | ( (~)
              @ ( ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( p @ Y1 ) ) ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~)
                          @ ( !!
                            @ ^ [Y2: $i] :
                                ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                                | ( (~) @ ( q @ Y2 ) ) ) ) )
                        | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl25,plain,
    ( ( (~)
      @ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( q @ Y1 ) ) ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( ( (~)
              @ ( !!
                @ ^ [Y0: $i] :
                    ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                    | ( (~) @ ( q @ Y0 ) ) ) ) )
            | ( !!
              @ ^ [Y0: $i] :
                  ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                  | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ) )
    | ( (~)
      @ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl26,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( q @ Y1 ) ) ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( ( (~)
              @ ( !!
                @ ^ [Y0: $i] :
                    ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                    | ( (~) @ ( q @ Y0 ) ) ) ) )
            | ( !!
              @ ^ [Y0: $i] :
                  ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                  | ( (~) @ ( p @ Y0 ) ) ) ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl27,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( (~) @ ( q @ Y1 ) ) ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl29,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( (~) @ ( q @ Y1 ) ) ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~) @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl30,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( (~) @ ( q @ Y1 ) ) ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl31,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( (~) @ ( p @ '#sk2' ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl34,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
          | ( (~) @ ( q @ Y0 ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
      | ( (~) @ ( q @ X2 ) )
      | ~ ( ( (~)
            @ ( !!
              @ ^ [Y0: $i] :
                  ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                  | ( (~) @ ( q @ Y0 ) ) ) ) )
          | ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl51,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X2 )
      | ~ ( q @ X2 )
      | ~ ( ( (~)
            @ ( !!
              @ ^ [Y0: $i] :
                  ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                  | ( (~) @ ( q @ Y0 ) ) ) ) )
          | ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl61,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( q @ Y0 ) ) ) )
      | ~ ( q @ X2 )
      | ~ ( rel_s5 @ '#sk2' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl67,plain,
    ! [X2: $i,X4: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk1' @ X4 ) )
      | ( (~) @ ( q @ X4 ) )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ~ ( q @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl71,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X4 )
      | ~ ( q @ X4 )
      | ~ ( q @ X2 )
      | ~ ( rel_s5 @ '#sk2' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl121,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( q @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl33,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl41,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl48,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl49,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk5' ) )
        | ( (~) @ ( p @ '#sk5' ) ) )
    | '#form4' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl60,plain,
    ( ( p @ '#sk5' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl35,plain,
    ( ( p @ '#sk2' )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl44,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ( p @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl48_001,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl53,plain,
    ( ~ '#form4'
    | ( p @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl48]) ).

thf(zip_derived_cl28,plain,
    ( ( (~)
      @ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( q @ Y0 ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl32,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( q @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~) @ ( q @ Y0 ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl36,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( q @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( (~) @ $true )
        | $false
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( (~) @ ( q @ Y1 ) ) ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl37,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( q @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( q @ Y1 ) ) ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl38,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( q @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl39,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk3' ) )
        | ( (~) @ ( q @ '#sk3' ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl45,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl54,plain,
    ( ~ '#form4'
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl55,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
      | ( (~) @ ( p @ X2 ) )
      | ~ '#form4' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl65,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ~ '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl89,plain,
    ( ~ '#form4'
    | ~ '#form4'
    | ~ ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl65]) ).

thf(zip_derived_cl94,plain,
    ( ~ ( rel_s5 @ '#sk1' @ '#sk2' )
    | ~ '#form4' ),
    inference(simplify,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl41_002,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl48_003,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl50,plain,
    ( ~ '#form4'
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl41,zip_derived_cl48]) ).

thf(zip_derived_cl98,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl94,zip_derived_cl50]) ).

thf(zip_derived_cl99,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl98]) ).

thf(zip_derived_cl46,plain,
    ( ( q @ '#sk3' )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl54_004,plain,
    ( ~ '#form4'
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl48_005,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl57,plain,
    ( '#form4'
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( q @ '#sk3' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl46,zip_derived_cl54,zip_derived_cl48]) ).

thf(zip_derived_cl66,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
              | ( (~) @ ( q @ Y0 ) ) ) ) )
      | ( (~) @ ( p @ X2 ) )
      | ( q @ '#sk3' )
      | '#form4' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl70,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
              | ( (~) @ ( q @ Y0 ) ) ) )
      | ~ ( p @ X2 )
      | '#form4'
      | ( q @ '#sk3' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl73,plain,
    ! [X2: $i] :
      ( ~ ( ( (~) @ ( rel_s5 @ X2 @ ( '#sk6' @ X2 ) ) )
          | ( (~) @ ( q @ ( '#sk6' @ X2 ) ) ) )
      | ( q @ '#sk3' )
      | '#form4'
      | ~ ( p @ X2 )
      | ~ ( rel_s5 @ '#sk1' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl77,plain,
    ! [X2: $i] :
      ( ( q @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | '#form4'
      | ( q @ '#sk3' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl73]) ).

thf(zip_derived_cl98_006,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl94,zip_derived_cl50]) ).

thf(zip_derived_cl229,plain,
    ! [X2: $i] :
      ( ( q @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ( q @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl77,zip_derived_cl98]) ).

thf(zip_derived_cl121_007,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( q @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl230,plain,
    ! [X0: $i] :
      ( ( q @ '#sk3' )
      | ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ X0 ) )
      | ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl229,zip_derived_cl121]) ).

thf(zip_derived_cl728,plain,
    ( ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ '#sk5' )
    | ( q @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl230]) ).

thf(zip_derived_cl59,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk5' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl98_008,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl94,zip_derived_cl50]) ).

thf(zip_derived_cl102,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl734,plain,
    ( ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ( q @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl728,zip_derived_cl102]) ).

thf(zip_derived_cl742,plain,
    ( ~ ( rel_s5 @ '#sk1' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl121,zip_derived_cl734]) ).

thf(zip_derived_cl99_009,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl98]) ).

thf(zip_derived_cl45_010,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl54_011,plain,
    ( ~ '#form4'
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl48_012,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl56,plain,
    ( '#form4'
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( q @ Y1 ) ) ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl45,zip_derived_cl54,zip_derived_cl48]) ).

thf(zip_derived_cl64,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
              | ( (~) @ ( q @ Y0 ) ) ) ) )
      | ( (~) @ ( p @ X2 ) )
      | ( rel_s5 @ '#sk1' @ '#sk3' )
      | '#form4' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl69,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
              | ( (~) @ ( q @ Y0 ) ) ) )
      | ~ ( p @ X2 )
      | '#form4'
      | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl72,plain,
    ! [X2: $i] :
      ( ~ ( ( (~) @ ( rel_s5 @ X2 @ ( '#sk6' @ X2 ) ) )
          | ( (~) @ ( q @ ( '#sk6' @ X2 ) ) ) )
      | ( rel_s5 @ '#sk1' @ '#sk3' )
      | '#form4'
      | ~ ( p @ X2 )
      | ~ ( rel_s5 @ '#sk1' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl75,plain,
    ! [X2: $i] :
      ( ( q @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | '#form4'
      | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl98_013,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl94,zip_derived_cl50]) ).

thf(zip_derived_cl148,plain,
    ! [X2: $i] :
      ( ( q @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl98]) ).

thf(zip_derived_cl40,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
          | ( (~) @ ( q @ Y0 ) ) ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl47,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
      | ( (~) @ ( q @ X2 ) )
      | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl58,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( q @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl152,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ '#sk1' @ '#sk3' )
      | ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 )
      | ( rel_s5 @ '#sk1' @ '#sk2' )
      | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl148,zip_derived_cl58]) ).

thf(zip_derived_cl590,plain,
    ( ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' )
    | ~ ( rel_s5 @ '#sk1' @ '#sk5' )
    | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl152]) ).

thf(zip_derived_cl102_014,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl602,plain,
    ( ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl590,zip_derived_cl102]) ).

thf(zip_derived_cl99_015,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl98]) ).

thf(zip_derived_cl76,plain,
    ! [X2: $i] :
      ( ( rel_s5 @ X2 @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | '#form4'
      | ( q @ '#sk3' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl73]) ).

thf(zip_derived_cl98_016,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl94,zip_derived_cl50]) ).

thf(zip_derived_cl198,plain,
    ! [X2: $i] :
      ( ( rel_s5 @ X2 @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ( q @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl76,zip_derived_cl98]) ).

thf(zip_derived_cl199,plain,
    ( ( q @ '#sk3' )
    | ~ ( rel_s5 @ '#sk1' @ '#sk5' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl198]) ).

thf(zip_derived_cl102_017,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl201,plain,
    ( ( q @ '#sk3' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl199,zip_derived_cl102]) ).

thf(zip_derived_cl58_018,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( q @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl206,plain,
    ( ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' )
    | ~ ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl201,zip_derived_cl58]) ).

thf(zip_derived_cl99_019,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl98]) ).

thf(zip_derived_cl74,plain,
    ! [X2: $i] :
      ( ( rel_s5 @ X2 @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | '#form4'
      | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl98_020,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl94,zip_derived_cl50]) ).

thf(zip_derived_cl123,plain,
    ! [X2: $i] :
      ( ( rel_s5 @ X2 @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl74,zip_derived_cl98]) ).

thf(zip_derived_cl124,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk1' @ '#sk5' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl123]) ).

thf(zip_derived_cl102_021,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl126,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl102]) ).

thf(zip_derived_cl269,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl206,zip_derived_cl126]) ).

thf(msymmetric,axiom,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ) ).

thf('16',plain,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).

thf('17',plain,
    ( msymmetric
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i] :
          ( ( V_1 @ X4 @ X6 )
         => ( V_1 @ X6 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(a3,axiom,
    msymmetric @ rel_s5 ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i] :
      ( ( rel_s5 @ X4 @ X6 )
     => ( rel_s5 @ X6 @ X4 ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( rel_s5 @ Y0 @ Y1 )
           => ( rel_s5 @ Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl5,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( rel_s5 @ X2 @ Y0 )
         => ( rel_s5 @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl6,plain,
    ! [X2: $i,X4: $i] :
      ( ( rel_s5 @ X2 @ X4 )
     => ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl272,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl269,zip_derived_cl7]) ).

thf(zip_derived_cl102_022,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl7_023,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl104,plain,
    rel_s5 @ '#sk5' @ '#sk1',
    inference('sup-',[status(thm)],[zip_derived_cl102,zip_derived_cl7]) ).

thf(mtransitive,axiom,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ) ).

thf('18',plain,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).

thf('19',plain,
    ( mtransitive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X6 @ X8 ) )
         => ( V_1 @ X4 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(a2,axiom,
    mtransitive @ rel_s5 ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( ( rel_s5 @ X6 @ X8 )
        & ( rel_s5 @ X4 @ X6 ) )
     => ( rel_s5 @ X4 @ X8 ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( rel_s5 @ Y1 @ Y2 )
                  & ( rel_s5 @ Y0 @ Y1 ) )
               => ( rel_s5 @ Y0 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( rel_s5 @ Y0 @ Y1 )
                & ( rel_s5 @ X2 @ Y0 ) )
             => ( rel_s5 @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( rel_s5 @ X4 @ Y0 )
            & ( rel_s5 @ X2 @ X4 ) )
         => ( rel_s5 @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( rel_s5 @ X4 @ X6 )
        & ( rel_s5 @ X2 @ X4 ) )
     => ( rel_s5 @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( rel_s5 @ X4 @ X6 )
          & ( rel_s5 @ X2 @ X4 ) )
      | ( rel_s5 @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rel_s5 @ X4 @ X6 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl107,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ X0 @ '#sk1' )
      | ~ ( rel_s5 @ X0 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl16]) ).

thf(zip_derived_cl278,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl272,zip_derived_cl107]) ).

thf(zip_derived_cl7_024,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl286,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl278,zip_derived_cl7]) ).

thf(zip_derived_cl620,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(clc,[status(thm)],[zip_derived_cl602,zip_derived_cl286]) ).

thf(zip_derived_cl7_025,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl622,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk2' @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl620,zip_derived_cl7]) ).

thf(zip_derived_cl126_026,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl102]) ).

thf(zip_derived_cl7_027,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl129,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl126,zip_derived_cl7]) ).

thf(zip_derived_cl107_028,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ X0 @ '#sk1' )
      | ~ ( rel_s5 @ X0 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl16]) ).

thf(zip_derived_cl132,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl107]) ).

thf(zip_derived_cl7_029,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl140,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl132,zip_derived_cl7]) ).

thf(zip_derived_cl16_030,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rel_s5 @ X4 @ X6 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl144,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ '#sk1' @ '#sk3' )
      | ( rel_s5 @ X0 @ ( '#sk6' @ '#sk5' ) )
      | ~ ( rel_s5 @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl140,zip_derived_cl16]) ).

thf(zip_derived_cl99_031,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl98]) ).

thf(zip_derived_cl148_032,plain,
    ! [X2: $i] :
      ( ( q @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl98]) ).

thf(zip_derived_cl121_033,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( q @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl149,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ '#sk1' @ '#sk3' )
      | ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ X0 ) )
      | ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl148,zip_derived_cl121]) ).

thf(zip_derived_cl469,plain,
    ( ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ '#sk5' )
    | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl149]) ).

thf(zip_derived_cl102_034,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl478,plain,
    ( ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl469,zip_derived_cl102]) ).

thf(zip_derived_cl140_035,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl132,zip_derived_cl7]) ).

thf(zip_derived_cl500,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl478,zip_derived_cl140]) ).

thf(zip_derived_cl503,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk1' )
    | ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl144,zip_derived_cl500]) ).

thf(zip_derived_cl509,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk1' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl503]) ).

thf(zip_derived_cl629,plain,
    rel_s5 @ '#sk1' @ '#sk3',
    inference(clc,[status(thm)],[zip_derived_cl622,zip_derived_cl509]) ).

thf(zip_derived_cl754,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl742,zip_derived_cl629]) ).

thf(zip_derived_cl201_036,plain,
    ( ( q @ '#sk3' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl199,zip_derived_cl102]) ).

thf(zip_derived_cl121_037,plain,
    ! [X0: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( q @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl203,plain,
    ( ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk1' @ '#sk3' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl201,zip_derived_cl121]) ).

thf(zip_derived_cl126_038,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl102]) ).

thf(zip_derived_cl365,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ( rel_s5 @ '#sk5' @ ( '#sk6' @ '#sk5' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl203,zip_derived_cl126]) ).

thf(zip_derived_cl7_039,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl369,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl365,zip_derived_cl7]) ).

thf(zip_derived_cl107_040,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ X0 @ '#sk1' )
      | ~ ( rel_s5 @ X0 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl16]) ).

thf(zip_derived_cl378,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl369,zip_derived_cl107]) ).

thf(zip_derived_cl7_041,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl406,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl378,zip_derived_cl7]) ).

thf(zip_derived_cl796,plain,
    ( ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) )
    | ~ ( rel_s5 @ '#sk2' @ '#sk3' ) ),
    inference(clc,[status(thm)],[zip_derived_cl754,zip_derived_cl406]) ).

thf(zip_derived_cl58_042,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( q @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl99_043,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl98]) ).

thf(zip_derived_cl229_044,plain,
    ! [X2: $i] :
      ( ( q @ ( '#sk6' @ X2 ) )
      | ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( p @ X2 )
      | ( q @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl77,zip_derived_cl98]) ).

thf(zip_derived_cl58_045,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk1' @ X2 )
      | ~ ( q @ X2 )
      | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl233,plain,
    ! [X0: $i] :
      ( ( q @ '#sk3' )
      | ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk1' @ X0 )
      | ( rel_s5 @ '#sk1' @ '#sk2' )
      | ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl229,zip_derived_cl58]) ).

thf(zip_derived_cl800,plain,
    ( ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' )
    | ~ ( rel_s5 @ '#sk1' @ '#sk5' )
    | ( q @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl233]) ).

thf(zip_derived_cl102_046,plain,
    rel_s5 @ '#sk1' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl98]) ).

thf(zip_derived_cl806,plain,
    ( ~ ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) )
    | ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( q @ '#sk3' ) ),
    inference(demod,[status(thm)],[zip_derived_cl800,zip_derived_cl102]) ).

thf(zip_derived_cl286_047,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl278,zip_derived_cl7]) ).

thf(zip_derived_cl808,plain,
    ( ( q @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(clc,[status(thm)],[zip_derived_cl806,zip_derived_cl286]) ).

thf(zip_derived_cl818,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ~ ( rel_s5 @ '#sk1' @ '#sk3' )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl58,zip_derived_cl808]) ).

thf(zip_derived_cl629_048,plain,
    rel_s5 @ '#sk1' @ '#sk3',
    inference(clc,[status(thm)],[zip_derived_cl622,zip_derived_cl509]) ).

thf(zip_derived_cl831,plain,
    ( ( rel_s5 @ '#sk1' @ '#sk2' )
    | ( rel_s5 @ '#sk1' @ '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl818,zip_derived_cl629]) ).

thf(zip_derived_cl832,plain,
    rel_s5 @ '#sk1' @ '#sk2',
    inference(simplify,[status(thm)],[zip_derived_cl831]) ).

thf(zip_derived_cl7_049,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl848,plain,
    rel_s5 @ '#sk2' @ '#sk1',
    inference('sup-',[status(thm)],[zip_derived_cl832,zip_derived_cl7]) ).

thf(zip_derived_cl629_050,plain,
    rel_s5 @ '#sk1' @ '#sk3',
    inference(clc,[status(thm)],[zip_derived_cl622,zip_derived_cl509]) ).

thf(zip_derived_cl16_051,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rel_s5 @ X4 @ X6 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl631,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ X0 @ '#sk3' )
      | ~ ( rel_s5 @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl629,zip_derived_cl16]) ).

thf(zip_derived_cl851,plain,
    rel_s5 @ '#sk2' @ '#sk3',
    inference('sup-',[status(thm)],[zip_derived_cl848,zip_derived_cl631]) ).

thf(zip_derived_cl873,plain,
    ~ ( rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl796,zip_derived_cl851]) ).

thf(zip_derived_cl378_052,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk3' )
    | ( rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl369,zip_derived_cl107]) ).

thf(zip_derived_cl851_053,plain,
    rel_s5 @ '#sk2' @ '#sk3',
    inference('sup-',[status(thm)],[zip_derived_cl848,zip_derived_cl631]) ).

thf(zip_derived_cl869,plain,
    rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk1',
    inference(demod,[status(thm)],[zip_derived_cl378,zip_derived_cl851]) ).

thf(zip_derived_cl832_054,plain,
    rel_s5 @ '#sk1' @ '#sk2',
    inference(simplify,[status(thm)],[zip_derived_cl831]) ).

thf(zip_derived_cl16_055,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rel_s5 @ X4 @ X6 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl847,plain,
    ! [X0: $i] :
      ( ( rel_s5 @ X0 @ '#sk2' )
      | ~ ( rel_s5 @ X0 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl832,zip_derived_cl16]) ).

thf(zip_derived_cl1017,plain,
    rel_s5 @ ( '#sk6' @ '#sk5' ) @ '#sk2',
    inference('sup-',[status(thm)],[zip_derived_cl869,zip_derived_cl847]) ).

thf(zip_derived_cl7_056,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( rel_s5 @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl1028,plain,
    rel_s5 @ '#sk2' @ ( '#sk6' @ '#sk5' ),
    inference('sup-',[status(thm)],[zip_derived_cl1017,zip_derived_cl7]) ).

thf(zip_derived_cl1031,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl873,zip_derived_cl1028]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO444^1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EoiW5mAFZe true
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 02:05:30 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.68  % Total configuration time : 828
% 0.22/0.68  % Estimated wc time : 1656
% 0.22/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.91/0.88  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 1.47/1.01  % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s
% 1.47/1.01  % Solved by lams/35_full_unif4.sh.
% 1.47/1.01  % done 414 iterations in 0.216s
% 1.47/1.01  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.47/1.01  % SZS output start Refutation
% See solution above
% 1.47/1.02  
% 1.47/1.02  
% 1.47/1.02  % Terminating...
% 2.16/1.11  % Runner terminated.
% 2.16/1.13  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------