TSTP Solution File: SYO449^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYO449^1 : 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.dZrzf3rCSj true

% Computer : n012.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 05:51:14 EDT 2023

% Result   : Theorem 3.02s 1.04s
% Output   : Refutation 3.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   50
% Syntax   : Number of formulae    :  157 (  46 unt;  20 typ;   0 def)
%            Number of atoms       :  927 (  30 equ; 202 cnn)
%            Maximal formula atoms :   45 (   6 avg)
%            Number of connectives : 2030 ( 392   ~; 377   |;   9   &;1118   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   89 (  89   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  20 usr;  11 con; 0-3 aty)
%                                         ( 119  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  280 ( 170   ^; 110   !;   0   ?; 280   :)

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

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

thf('#sk1_type',type,
    '#sk1': $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('#sk5_type',type,
    '#sk5': $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(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

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

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

thf('#sk7_type',type,
    '#sk7': $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 @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i,X6: $i] :
      ( ~ ( rel_s5 @ X4 @ X6 )
      | ~ ( ~ ( ! [X20: $i] :
                  ( ~ ( rel_s5 @ X6 @ X20 )
                  | ( q @ X20 )
                  | ! [X22: $i] :
                      ( ~ ( rel_s5 @ X20 @ X22 )
                      | ~ ( p @ X22 ) ) )
              | ~ ! [X16: $i] :
                    ( ~ ( rel_s5 @ X6 @ X16 )
                    | ! [X18: $i] :
                        ( ~ ( rel_s5 @ X16 @ X18 )
                        | ( q @ X18 ) )
                    | ~ ( p @ X16 ) ) )
          | ~ ( ! [X12: $i] :
                  ( ~ ( rel_s5 @ X6 @ X12 )
                  | ! [X14: $i] :
                      ( ~ ( rel_s5 @ X12 @ X14 )
                      | ( q @ X14 ) )
                  | ~ ( p @ X12 ) )
              | ~ ! [X8: $i] :
                    ( ~ ( rel_s5 @ X6 @ X8 )
                    | ( q @ X8 )
                    | ! [X10: $i] :
                        ( ~ ( rel_s5 @ X8 @ X10 )
                        | ~ ( p @ X10 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i,X6: $i] :
        ( ~ ( rel_s5 @ X4 @ X6 )
        | ~ ( ~ ( ! [X20: $i] :
                    ( ~ ( rel_s5 @ X6 @ X20 )
                    | ( q @ X20 )
                    | ! [X22: $i] :
                        ( ~ ( rel_s5 @ X20 @ X22 )
                        | ~ ( p @ X22 ) ) )
                | ~ ! [X16: $i] :
                      ( ~ ( rel_s5 @ X6 @ X16 )
                      | ! [X18: $i] :
                          ( ~ ( rel_s5 @ X16 @ X18 )
                          | ( q @ X18 ) )
                      | ~ ( p @ X16 ) ) )
            | ~ ( ! [X12: $i] :
                    ( ~ ( rel_s5 @ X6 @ X12 )
                    | ! [X14: $i] :
                        ( ~ ( rel_s5 @ X12 @ X14 )
                        | ( q @ X14 ) )
                    | ~ ( p @ X12 ) )
                | ~ ! [X8: $i] :
                      ( ~ ( rel_s5 @ X6 @ X8 )
                      | ( q @ X8 )
                      | ! [X10: $i] :
                          ( ~ ( rel_s5 @ X8 @ X10 )
                          | ~ ( p @ X10 ) ) ) ) ) ),
    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 )
                            | ( !!
                              @ ^ [Y3: $i] :
                                  ( ( (~) @ ( rel_s5 @ Y2 @ Y3 ) )
                                  | ( (~) @ ( p @ Y3 ) ) ) ) ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y2: $i] :
                              ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                              | ( !!
                                @ ^ [Y3: $i] :
                                    ( ( (~) @ ( rel_s5 @ Y2 @ Y3 ) )
                                    | ( q @ Y3 ) ) )
                              | ( (~) @ ( p @ Y2 ) ) ) ) ) ) )
                  | ( (~)
                    @ ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                            | ( !!
                              @ ^ [Y3: $i] :
                                  ( ( (~) @ ( rel_s5 @ Y2 @ Y3 ) )
                                  | ( q @ Y3 ) ) )
                            | ( (~) @ ( p @ Y2 ) ) ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y2: $i] :
                              ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                              | ( q @ Y2 )
                              | ( !!
                                @ ^ [Y3: $i] :
                                    ( ( (~) @ ( rel_s5 @ Y2 @ Y3 ) )
                                    | ( (~) @ ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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 )
                        | ( !!
                          @ ^ [Y2: $i] :
                              ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                              | ( (~) @ ( p @ Y2 ) ) ) ) ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y1: $i] :
                          ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                          | ( !!
                            @ ^ [Y2: $i] :
                                ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                                | ( q @ Y2 ) ) )
                          | ( (~) @ ( p @ Y1 ) ) ) ) ) ) )
              | ( (~)
                @ ( ( !!
                    @ ^ [Y1: $i] :
                        ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                        | ( !!
                          @ ^ [Y2: $i] :
                              ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                              | ( q @ Y2 ) ) )
                        | ( (~) @ ( p @ Y1 ) ) ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y1: $i] :
                          ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                          | ( q @ Y1 )
                          | ( !!
                            @ ^ [Y2: $i] :
                                ( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
                                | ( (~) @ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl26,plain,
    ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
      | ( (~)
        @ ( ( (~)
            @ ( ( !!
                @ ^ [Y0: $i] :
                    ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                    | ( q @ Y0 )
                    | ( !!
                      @ ^ [Y1: $i] :
                          ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                          | ( (~) @ ( p @ Y1 ) ) ) ) ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y0: $i] :
                      ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                      | ( !!
                        @ ^ [Y1: $i] :
                            ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                            | ( q @ Y1 ) ) )
                      | ( (~) @ ( p @ Y0 ) ) ) ) ) ) )
          | ( (~)
            @ ( ( !!
                @ ^ [Y0: $i] :
                    ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                    | ( !!
                      @ ^ [Y1: $i] :
                          ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                          | ( q @ Y1 ) ) )
                    | ( (~) @ ( p @ Y0 ) ) ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y0: $i] :
                      ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                      | ( q @ Y0 )
                      | ( !!
                        @ ^ [Y1: $i] :
                            ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                            | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl28,plain,
    ( ( (~)
      @ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( q @ Y0 )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( (~) @ ( p @ Y1 ) ) ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( q @ Y1 ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) ) )
    | ( (~)
      @ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( q @ Y1 ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( q @ Y0 )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl29,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( q @ Y0 )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( (~) @ ( p @ Y1 ) ) ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( q @ Y1 ) ) )
                | ( (~) @ ( p @ Y0 ) ) ) ) ) )
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( q @ Y1 ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( q @ Y0 )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl30,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) )
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( q @ Y1 ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( q @ Y0 )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl32,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) )
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( q @ Y1 ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~) @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl33,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl34,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk2' @ '#sk3' ) )
        | ( q @ '#sk3' )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
              | ( (~) @ ( p @ Y0 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl39,plain,
    ( ( rel_s5 @ '#sk2' @ '#sk3' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl43,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl44,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk2' @ '#sk5' ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk5' @ Y0 ) )
              | ( q @ Y0 ) ) )
        | ( (~) @ ( p @ '#sk5' ) ) )
    | '#form4' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl50,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk5' @ Y0 ) )
            | ( q @ Y0 ) ) )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl54,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk5' @ '#sk7' ) )
        | ( q @ '#sk7' ) )
    | '#form4' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl59,plain,
    ( ~ ( q @ '#sk7' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl41,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl43_001,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl47,plain,
    ( ~ '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl41,zip_derived_cl43]) ).

thf(zip_derived_cl52,plain,
    ( ~ ( ( (~) @ ( rel_s5 @ '#sk3' @ '#sk6' ) )
        | ( (~) @ ( p @ '#sk6' ) ) )
    | ~ '#form4' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl55,plain,
    ( ( rel_s5 @ '#sk3' @ '#sk6' )
    | ~ '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).

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_cl76,plain,
    ( ~ '#form4'
    | ( rel_s5 @ '#sk6' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl7]) ).

thf(zip_derived_cl55_002,plain,
    ( ( rel_s5 @ '#sk3' @ '#sk6' )
    | ~ '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl31,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                | ( q @ Y1 ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( q @ Y1 ) ) )
              | ( (~) @ ( p @ Y0 ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( q @ Y0 )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl35,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                | ( q @ Y1 ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( $false
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
                | ( q @ Y0 )
                | ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                      | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl36,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                | ( q @ Y1 ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ~ ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
              | ( q @ Y0 )
              | ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                    | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl37,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                | ( q @ Y1 ) ) )
          | ( (~) @ ( p @ Y0 ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
          | ( q @ Y0 )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
            | ( q @ Y0 ) ) )
      | ( (~) @ ( p @ X2 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
            | ( q @ Y0 ) ) )
      | ~ ( p @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i,X4: $i] :
      ( ( (~) @ ( rel_s5 @ X2 @ X4 ) )
      | ( q @ X4 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) )
      | ~ ( p @ X2 )
      | ~ ( rel_s5 @ '#sk2' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl53,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel_s5 @ X2 @ X4 )
      | ( q @ X4 )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ~ ( p @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( q @ Y0 )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( (~) @ ( p @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl57,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( (~) @ ( rel_s5 @ '#sk2' @ X6 ) )
      | ( q @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ X6 @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
      | ~ ( p @ X2 )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ( q @ X4 )
      | ~ ( rel_s5 @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl60,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( rel_s5 @ '#sk2' @ X6 )
      | ( q @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ X6 @ Y0 ) )
            | ( (~) @ ( p @ Y0 ) ) ) )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( q @ X4 )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ~ ( p @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl61,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ( (~) @ ( rel_s5 @ X6 @ X8 ) )
      | ( (~) @ ( p @ X8 ) )
      | ~ ( p @ X2 )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ( q @ X4 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( q @ X6 )
      | ~ ( rel_s5 @ '#sk2' @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl62,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( rel_s5 @ X6 @ X8 )
      | ~ ( p @ X8 )
      | ~ ( rel_s5 @ '#sk2' @ X6 )
      | ( q @ X6 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( q @ X4 )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ~ ( p @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl97,plain,
    ! [X0: $i,X1: $i] :
      ( ~ '#form4'
      | ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ '#sk3' )
      | ~ ( rel_s5 @ '#sk2' @ '#sk3' )
      | ~ ( p @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl62]) ).

thf(zip_derived_cl40,plain,
    ( ~ ( q @ '#sk3' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl43_003,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl46,plain,
    ( ~ '#form4'
    | ~ ( q @ '#sk3' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl40,zip_derived_cl43]) ).

thf(zip_derived_cl565,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( p @ '#sk6' )
      | ~ ( rel_s5 @ '#sk2' @ '#sk3' )
      | ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( p @ X0 )
      | ~ '#form4' ),
    inference(clc,[status(thm)],[zip_derived_cl97,zip_derived_cl46]) ).

thf(zip_derived_cl56,plain,
    ( ( p @ '#sk6' )
    | ~ '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl566,plain,
    ! [X0: $i,X1: $i] :
      ( ~ '#form4'
      | ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ X0 @ X1 )
      | ~ ( rel_s5 @ '#sk2' @ '#sk3' ) ),
    inference(clc,[status(thm)],[zip_derived_cl565,zip_derived_cl56]) ).

thf(zip_derived_cl39_004,plain,
    ( ( rel_s5 @ '#sk2' @ '#sk3' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl43_005,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
                  | ( q @ Y1 ) ) )
            | ( (~) @ ( p @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl45,plain,
    ( ~ '#form4'
    | ( rel_s5 @ '#sk2' @ '#sk3' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl43]) ).

thf(zip_derived_cl567,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( p @ X0 )
      | ~ '#form4' ),
    inference(clc,[status(thm)],[zip_derived_cl566,zip_derived_cl45]) ).

thf(zip_derived_cl571,plain,
    ( ~ '#form4'
    | ~ '#form4'
    | ~ ( p @ '#sk6' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk6' )
    | ( q @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl76,zip_derived_cl567]) ).

thf(zip_derived_cl614,plain,
    ( ( q @ '#sk3' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk6' )
    | ~ ( p @ '#sk6' )
    | ~ '#form4' ),
    inference(simplify,[status(thm)],[zip_derived_cl571]) ).

thf(zip_derived_cl46_006,plain,
    ( ~ '#form4'
    | ~ ( q @ '#sk3' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl40,zip_derived_cl43]) ).

thf(zip_derived_cl670,plain,
    ( ~ '#form4'
    | ~ ( p @ '#sk6' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk6' ) ),
    inference(clc,[status(thm)],[zip_derived_cl614,zip_derived_cl46]) ).

thf(zip_derived_cl56_007,plain,
    ( ( p @ '#sk6' )
    | ~ '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl671,plain,
    ( ~ ( rel_s5 @ '#sk2' @ '#sk6' )
    | ~ '#form4' ),
    inference(clc,[status(thm)],[zip_derived_cl670,zip_derived_cl56]) ).

thf(zip_derived_cl45_008,plain,
    ( ~ '#form4'
    | ( rel_s5 @ '#sk2' @ '#sk3' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl43]) ).

thf(zip_derived_cl55_009,plain,
    ( ( rel_s5 @ '#sk3' @ '#sk6' )
    | ~ '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).

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_cl75,plain,
    ! [X0: $i] :
      ( ~ '#form4'
      | ( rel_s5 @ X0 @ '#sk6' )
      | ~ ( rel_s5 @ X0 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl16]) ).

thf(zip_derived_cl194,plain,
    ( ~ '#form4'
    | ( rel_s5 @ '#sk2' @ '#sk6' )
    | ~ '#form4' ),
    inference('sup-',[status(thm)],[zip_derived_cl45,zip_derived_cl75]) ).

thf(zip_derived_cl202,plain,
    ( ( rel_s5 @ '#sk2' @ '#sk6' )
    | ~ '#form4' ),
    inference(simplify,[status(thm)],[zip_derived_cl194]) ).

thf(zip_derived_cl672,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl671,zip_derived_cl202]) ).

thf(zip_derived_cl676,plain,
    ~ ( q @ '#sk7' ),
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl672]) ).

thf(zip_derived_cl58,plain,
    ( ( rel_s5 @ '#sk5' @ '#sk7' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl672_010,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl671,zip_derived_cl202]) ).

thf(zip_derived_cl675,plain,
    rel_s5 @ '#sk5' @ '#sk7',
    inference(demod,[status(thm)],[zip_derived_cl58,zip_derived_cl672]) ).

thf(zip_derived_cl58_011,plain,
    ( ( rel_s5 @ '#sk5' @ '#sk7' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl7_012,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_cl84,plain,
    ( '#form4'
    | ( rel_s5 @ '#sk7' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl58,zip_derived_cl7]) ).

thf(zip_derived_cl672_013,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl671,zip_derived_cl202]) ).

thf(zip_derived_cl680,plain,
    rel_s5 @ '#sk7' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl84,zip_derived_cl672]) ).

thf(zip_derived_cl62_014,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( rel_s5 @ X6 @ X8 )
      | ~ ( p @ X8 )
      | ~ ( rel_s5 @ '#sk2' @ X6 )
      | ( q @ X6 )
      | ~ ( rel_s5 @ X2 @ X4 )
      | ( q @ X4 )
      | ~ ( rel_s5 @ '#sk2' @ X2 )
      | ~ ( p @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl715,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ '#sk7' )
      | ~ ( rel_s5 @ '#sk2' @ '#sk7' )
      | ~ ( p @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl680,zip_derived_cl62]) ).

thf(zip_derived_cl51,plain,
    ( ( p @ '#sk5' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl672_015,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl671,zip_derived_cl202]) ).

thf(zip_derived_cl674,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl51,zip_derived_cl672]) ).

thf(zip_derived_cl721,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ '#sk7' )
      | ~ ( rel_s5 @ '#sk2' @ '#sk7' ) ),
    inference(demod,[status(thm)],[zip_derived_cl715,zip_derived_cl674]) ).

thf(zip_derived_cl49,plain,
    ( ( rel_s5 @ '#sk2' @ '#sk5' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl58_016,plain,
    ( ( rel_s5 @ '#sk5' @ '#sk7' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl16_017,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_cl83,plain,
    ! [X0: $i] :
      ( '#form4'
      | ( rel_s5 @ X0 @ '#sk7' )
      | ~ ( rel_s5 @ X0 @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl58,zip_derived_cl16]) ).

thf(zip_derived_cl292,plain,
    ( '#form4'
    | ( rel_s5 @ '#sk2' @ '#sk7' )
    | '#form4' ),
    inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl83]) ).

thf(zip_derived_cl300,plain,
    ( ( rel_s5 @ '#sk2' @ '#sk7' )
    | '#form4' ),
    inference(simplify,[status(thm)],[zip_derived_cl292]) ).

thf(zip_derived_cl672_018,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl671,zip_derived_cl202]) ).

thf(zip_derived_cl684,plain,
    rel_s5 @ '#sk2' @ '#sk7',
    inference(demod,[status(thm)],[zip_derived_cl300,zip_derived_cl672]) ).

thf(zip_derived_cl1663,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( p @ X0 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ '#sk7' ) ),
    inference(demod,[status(thm)],[zip_derived_cl721,zip_derived_cl684]) ).

thf(zip_derived_cl676_019,plain,
    ~ ( q @ '#sk7' ),
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl672]) ).

thf(zip_derived_cl1664,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( rel_s5 @ X0 @ X1 )
      | ( q @ X1 )
      | ~ ( rel_s5 @ '#sk2' @ X0 )
      | ~ ( p @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1663,zip_derived_cl676]) ).

thf(zip_derived_cl1668,plain,
    ( ~ ( p @ '#sk5' )
    | ~ ( rel_s5 @ '#sk2' @ '#sk5' )
    | ( q @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl675,zip_derived_cl1664]) ).

thf(zip_derived_cl674_020,plain,
    p @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl51,zip_derived_cl672]) ).

thf(zip_derived_cl49_021,plain,
    ( ( rel_s5 @ '#sk2' @ '#sk5' )
    | '#form4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl672_022,plain,
    ~ '#form4',
    inference(clc,[status(thm)],[zip_derived_cl671,zip_derived_cl202]) ).

thf(zip_derived_cl673,plain,
    rel_s5 @ '#sk2' @ '#sk5',
    inference(demod,[status(thm)],[zip_derived_cl49,zip_derived_cl672]) ).

thf(zip_derived_cl1694,plain,
    q @ '#sk7',
    inference(demod,[status(thm)],[zip_derived_cl1668,zip_derived_cl674,zip_derived_cl673]) ).

thf(zip_derived_cl1715,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl676,zip_derived_cl1694]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO449^1 : 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.dZrzf3rCSj true
% 0.17/0.35  % Computer : n012.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Sat Aug 26 00:32:56 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.17/0.35  % Running portfolio for 300 s
% 0.17/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.35  % Number of cores: 8
% 0.17/0.35  % Python version: Python 3.6.8
% 0.17/0.36  % Running in HO mode
% 0.21/0.67  % Total configuration time : 828
% 0.21/0.67  % Estimated wc time : 1656
% 0.21/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.81  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 2.45/0.93  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 3.02/1.04  % Solved by lams/35_full_unif4.sh.
% 3.02/1.04  % done 546 iterations in 0.235s
% 3.02/1.04  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.02/1.04  % SZS output start Refutation
% See solution above
% 3.02/1.04  
% 3.02/1.04  
% 3.02/1.04  % Terminating...
% 3.44/1.12  % Runner terminated.
% 3.44/1.13  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------