TSTP Solution File: AGT027^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : AGT027^2 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.S1a8plbRuD true

% Computer : n023.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 : Wed Aug 30 15:58:26 EDT 2023

% Result   : Theorem 38.38s 5.48s
% Output   : Refutation 38.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  153 (  54 unt;  23 typ;   0 def)
%            Number of atoms       :  532 (  30 equ;  95 cnn)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives : 1353 ( 198   ~; 188   |;   0   &; 896   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  165 ( 165   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  22 usr;   5 con; 0-3 aty)
%                                         (  71  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  342 ( 140   ^; 202   !;   0   ?; 342   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

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

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(a1_type,type,
    a1: $i > $i > $o ).

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

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

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

thf(r_type,type,
    r: mu > $i > $o ).

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

thf('#sk37_type',type,
    '#sk37': $i > ( $i > $o ) > $i ).

thf(s_type,type,
    s: mu > $i > $o ).

thf(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(q_type,type,
    q: mu > $i > $o ).

thf(a2_type,type,
    a2: $i > $i > $o ).

thf(a_type,type,
    a: mu ).

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

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

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mexists_ind_type,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

thf(mforall_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

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

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

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

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

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

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

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

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

thf('3',plain,
    ( mbox
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
        ! [X4: $i] :
          ( ( V_2 @ X4 )
          | ~ ( V_1 @ V_3 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(mexists_ind,axiom,
    ( mexists_ind
    = ( ^ [Phi: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).

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

thf('4',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] : ( Phi @ X @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

thf('5',plain,
    ( mforall_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ! [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

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

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

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

thf('8',plain,
    ( mexists_ind
    = ( ^ [Phi: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mexists_ind,'5','7']) ).

thf('9',plain,
    ( mexists_ind
    = ( ^ [V_1: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [V_2: mu] : ( mnot @ ( V_1 @ V_2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(conj,conjecture,
    ( mvalid
    @ ( mexists_ind
      @ ^ [X: mu] : ( mbox @ a1 @ ( p @ X ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ~ ! [X6: mu] :
          ~ ! [X8: $i] :
              ( ~ ( a1 @ X4 @ X8 )
              | ( p @ X6 @ X8 ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ~ ! [X6: mu] :
            ~ ! [X8: $i] :
                ( ~ ( a1 @ X4 @ X8 )
                | ( p @ X6 @ X8 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl9,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( (~)
          @ ( !!
            @ ^ [Y1: mu] :
                ( (~)
                @ ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( a1 @ Y0 @ Y2 ) )
                      | ( p @ Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl10,plain,
    ( !!
    @ ^ [Y0: mu] :
        ( (~)
        @ ( !!
          @ ^ [Y1: $i] :
              ( ( (~) @ ( a1 @ '#sk1' @ Y1 ) )
              | ( p @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl11,plain,
    ! [X2: mu] :
      ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ '#sk1' @ Y0 ) )
            | ( p @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl12,plain,
    ! [X2: mu] :
      ~ ( ( (~) @ ( a1 @ '#sk1' @ ( '#sk2' @ X2 ) ) )
        | ( p @ X2 @ ( '#sk2' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl13,plain,
    ! [X2: mu] : ( a1 @ '#sk1' @ ( '#sk2' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).

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

thf('10',plain,
    ( mforall_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
        ! [P: $i > $o] : ( Phi @ P @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_prop]) ).

thf('11',plain,
    ( mforall_prop
    = ( ^ [V_1: ( $i > $o ) > $i > $o,V_2: $i] :
        ! [X4: $i > $o] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

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

thf('13',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('14',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'13','7']) ).

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

thf(axiom_I_for_a2_a1,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ Phi ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X10: $i] :
          ( ~ ( a1 @ X4 @ X10 )
          | ( X6 @ X10 ) )
      | ~ ! [X8: $i] :
            ( ~ ( a2 @ X4 @ X8 )
            | ( X6 @ X8 ) ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( (~) @ ( a1 @ Y0 @ Y2 ) )
                  | ( Y1 @ Y2 ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( a2 @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( a1 @ X2 @ Y1 ) )
                | ( Y0 @ Y1 ) ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( a2 @ X2 @ Y1 ) )
                  | ( Y0 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a2 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a2 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( (~) @ ( a1 @ X2 @ X6 ) )
      | ( X4 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a2 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( a1 @ X2 @ X6 )
      | ( X4 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a2 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( ( (~) @ ( a2 @ X2 @ ( '#sk10' @ X2 @ X4 ) ) )
          | ( X4 @ ( '#sk10' @ X2 @ X4 ) ) )
      | ( X4 @ X6 )
      | ~ ( a1 @ X2 @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( a2 @ X2 @ ( '#sk10' @ X2 @ X4 ) )
      | ~ ( a1 @ X2 @ X6 )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl35,plain,
    ! [X0: mu,X1: $i > $o] :
      ( ( X1 @ ( '#sk2' @ X0 ) )
      | ( a2 @ '#sk1' @ ( '#sk10' @ '#sk1' @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl33]) ).

thf(zip_derived_cl13_001,plain,
    ! [X2: mu] : ( a1 @ '#sk1' @ ( '#sk2' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl34,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( X4 @ ( '#sk10' @ X2 @ X4 ) )
      | ~ ( a1 @ X2 @ X6 )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl118,plain,
    ! [X0: mu,X1: $i > $o] :
      ( ( X1 @ ( '#sk2' @ X0 ) )
      | ~ ( X1 @ ( '#sk10' @ '#sk1' @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl34]) ).

thf(zip_derived_cl346,plain,
    ! [X0: mu,X1: mu] :
      ( ( a2 @ '#sk1' @ ( '#sk2' @ X1 ) )
      | ( a2 @ '#sk1' @ ( '#sk2' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl118]) ).

thf(zip_derived_cl466,plain,
    ! [X0: mu] : ( a2 @ '#sk1' @ ( '#sk2' @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl346]) ).

thf(mdia,axiom,
    ( mdia
    = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).

thf('16',plain,
    ( mdia
    = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mdia,'3','7']) ).

thf('17',plain,
    ( mdia
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o] : ( mnot @ ( mbox @ V_1 @ ( mnot @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf(axiom_a4,axiom,
    mvalid @ ( mdia @ a1 @ ( s @ a ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i] :
      ~ ! [X6: $i] :
          ( ~ ( a1 @ X4 @ X6 )
          | ~ ( s @ a @ X6 ) ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( (~)
        @ ( !!
          @ ^ [Y1: $i] :
              ( ( (~) @ ( a1 @ Y0 @ Y1 ) )
              | ( (~) @ ( s @ a @ Y1 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i] :
      ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X2 @ Y0 ) )
            | ( (~) @ ( s @ a @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i] :
      ~ ( ( (~) @ ( a1 @ X2 @ ( '#sk3' @ X2 ) ) )
        | ( (~) @ ( s @ a @ ( '#sk3' @ X2 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i] : ( s @ a @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl17_002,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(axiom_a3,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X ) @ ( mbox @ a1 @ ( r @ X ) ) ) ) ) ) ).

thf(zf_stmt_4,axiom,
    ! [X4: $i,X6: mu,X8: $i] :
      ( ~ ( a1 @ X4 @ X8 )
      | ! [X10: $i] :
          ( ~ ( a1 @ X8 @ X10 )
          | ( r @ X6 @ X10 ) )
      | ~ ( s @ X6 @ X8 ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( (~) @ ( a1 @ Y0 @ Y2 ) )
                | ( !!
                  @ ^ [Y3: $i] :
                      ( ( (~) @ ( a1 @ Y2 @ Y3 ) )
                      | ( r @ Y1 @ Y3 ) ) )
                | ( (~) @ ( s @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl60,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y1 ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( a1 @ Y1 @ Y2 ) )
                    | ( r @ Y0 @ Y2 ) ) )
              | ( (~) @ ( s @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl61,plain,
    ! [X2: $i,X4: mu] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( a1 @ X2 @ Y0 ) )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( a1 @ Y0 @ Y1 ) )
                | ( r @ X4 @ Y1 ) ) )
          | ( (~) @ ( s @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl62,plain,
    ! [X2: $i,X4: mu,X6: $i] :
      ( ( (~) @ ( a1 @ X2 @ X6 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X6 @ Y0 ) )
            | ( r @ X4 @ Y0 ) ) )
      | ( (~) @ ( s @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl63,plain,
    ! [X2: $i,X4: mu,X6: $i] :
      ( ~ ( a1 @ X2 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X6 @ Y0 ) )
            | ( r @ X4 @ Y0 ) ) )
      | ~ ( s @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl64,plain,
    ! [X2: $i,X4: mu,X6: $i,X8: $i] :
      ( ( (~) @ ( a1 @ X6 @ X8 ) )
      | ( r @ X4 @ X8 )
      | ~ ( s @ X4 @ X6 )
      | ~ ( a1 @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl65,plain,
    ! [X2: $i,X4: mu,X6: $i,X8: $i] :
      ( ~ ( a1 @ X6 @ X8 )
      | ( r @ X4 @ X8 )
      | ~ ( a1 @ X2 @ X6 )
      | ~ ( s @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl67,plain,
    ! [X0: $i,X1: mu,X2: $i] :
      ( ~ ( s @ X1 @ X0 )
      | ~ ( a1 @ X2 @ X0 )
      | ( r @ X1 @ ( '#sk3' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl65]) ).

thf(zip_derived_cl513,plain,
    ! [X0: $i,X1: mu] :
      ( ( r @ X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ~ ( s @ X1 @ ( '#sk3' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl67]) ).

thf(zip_derived_cl17_003,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

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

thf('18',plain,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand,'13','7']) ).

thf('19',plain,
    ( mand
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf(axiom_a2,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( mand @ ( r @ X ) @ ( s @ X ) ) @ ( q @ X ) ) ) ) ) ).

thf(zf_stmt_5,axiom,
    ! [X4: $i,X6: mu,X8: $i] :
      ( ~ ( a1 @ X4 @ X8 )
      | ( q @ X6 @ X8 )
      | ~ ( r @ X6 @ X8 )
      | ~ ( s @ X6 @ X8 ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( (~) @ ( a1 @ Y0 @ Y2 ) )
                | ( q @ Y1 @ Y2 )
                | ( (~) @ ( r @ Y1 @ Y2 ) )
                | ( (~) @ ( s @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_5]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y1 ) )
              | ( q @ Y0 @ Y1 )
              | ( (~) @ ( r @ Y0 @ Y1 ) )
              | ( (~) @ ( s @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i,X4: mu] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( a1 @ X2 @ Y0 ) )
          | ( q @ X4 @ Y0 )
          | ( (~) @ ( r @ X4 @ Y0 ) )
          | ( (~) @ ( s @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i,X4: mu,X6: $i] :
      ( ( (~) @ ( a1 @ X2 @ X6 ) )
      | ( q @ X4 @ X6 )
      | ( (~) @ ( r @ X4 @ X6 ) )
      | ( (~) @ ( s @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i,X4: mu,X6: $i] :
      ( ~ ( a1 @ X2 @ X6 )
      | ( q @ X4 @ X6 )
      | ~ ( r @ X4 @ X6 )
      | ~ ( s @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl24,plain,
    ! [X0: $i,X1: mu] :
      ( ~ ( s @ X1 @ ( '#sk3' @ X0 ) )
      | ~ ( r @ X1 @ ( '#sk3' @ X0 ) )
      | ( q @ X1 @ ( '#sk3' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl22]) ).

thf(zip_derived_cl674,plain,
    ! [X0: $i,X1: mu] :
      ( ~ ( s @ X1 @ ( '#sk3' @ X0 ) )
      | ( q @ X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ~ ( s @ X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl513,zip_derived_cl24]) ).

thf(zip_derived_cl17_004,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl17_005,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(axiom_4s_for_a1_a1,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a1 @ Phi ) ) ) ) ) ).

thf(zf_stmt_6,axiom,
    ! [X4: $i,X6: $i > $o] :
      ( ! [X10: $i] :
          ( ~ ( a1 @ X4 @ X10 )
          | ! [X12: $i] :
              ( ~ ( a1 @ X10 @ X12 )
              | ( X6 @ X12 ) ) )
      | ~ ! [X8: $i] :
            ( ~ ( a1 @ X4 @ X8 )
            | ( X6 @ X8 ) ) ) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( (~) @ ( a1 @ Y0 @ Y2 ) )
                  | ( !!
                    @ ^ [Y3: $i] :
                        ( ( (~) @ ( a1 @ Y2 @ Y3 ) )
                        | ( Y1 @ Y3 ) ) ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( a1 @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_6]) ).

thf(zip_derived_cl72,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( a1 @ X2 @ Y1 ) )
                | ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( a1 @ Y1 @ Y2 ) )
                      | ( Y0 @ Y2 ) ) ) ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( a1 @ X2 @ Y1 ) )
                  | ( Y0 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl73,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X2 @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( a1 @ Y0 @ Y1 ) )
                  | ( X4 @ Y1 ) ) ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl74,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X2 @ Y0 ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( a1 @ Y0 @ Y1 ) )
                  | ( X4 @ Y1 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl73]) ).

thf(zip_derived_cl75,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( (~) @ ( a1 @ X2 @ X6 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X6 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl76,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( a1 @ X2 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a1 @ X6 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl75]) ).

thf(zip_derived_cl77,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( (~) @ ( a1 @ X6 @ X8 ) )
      | ( X4 @ X8 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) )
      | ~ ( a1 @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl78,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( a1 @ X6 @ X8 )
      | ( X4 @ X8 )
      | ~ ( a1 @ X2 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( a1 @ X2 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl77]) ).

thf(zip_derived_cl79,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( ( (~) @ ( a1 @ X2 @ ( '#sk37' @ X2 @ X4 ) ) )
          | ( X4 @ ( '#sk37' @ X2 @ X4 ) ) )
      | ~ ( a1 @ X2 @ X6 )
      | ( X4 @ X8 )
      | ~ ( a1 @ X6 @ X8 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl80,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( a1 @ X2 @ ( '#sk37' @ X2 @ X4 ) )
      | ~ ( a1 @ X6 @ X8 )
      | ( X4 @ X8 )
      | ~ ( a1 @ X2 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl83,plain,
    ! [X0: $i,X1: $i,X2: $i > $o] :
      ( ~ ( a1 @ X1 @ X0 )
      | ( X2 @ ( '#sk3' @ X0 ) )
      | ( a1 @ X1 @ ( '#sk37' @ X1 @ X2 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl80]) ).

thf(zip_derived_cl898,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( a1 @ X0 @ ( '#sk37' @ X0 @ X1 ) )
      | ( X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl83]) ).

thf(zip_derived_cl17_006,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl17_007,plain,
    ! [X2: $i] : ( a1 @ X2 @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl81,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( X4 @ ( '#sk37' @ X2 @ X4 ) )
      | ~ ( a1 @ X6 @ X8 )
      | ( X4 @ X8 )
      | ~ ( a1 @ X2 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl624,plain,
    ! [X0: $i,X1: $i,X2: $i > $o] :
      ( ~ ( a1 @ X1 @ X0 )
      | ( X2 @ ( '#sk3' @ X0 ) )
      | ~ ( X2 @ ( '#sk37' @ X1 @ X2 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl81]) ).

thf(zip_derived_cl1064,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( X1 @ ( '#sk37' @ X0 @ X1 ) )
      | ( X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl624]) ).

thf(zip_derived_cl1848,plain,
    ! [X0: $i] :
      ( ( a1 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ( a1 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl898,zip_derived_cl1064]) ).

thf(zip_derived_cl1886,plain,
    ! [X0: $i] : ( a1 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1848]) ).

thf(zip_derived_cl33_008,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( a2 @ X2 @ ( '#sk10' @ X2 @ X4 ) )
      | ~ ( a1 @ X2 @ X6 )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl1968,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ( a2 @ X0 @ ( '#sk10' @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1886,zip_derived_cl33]) ).

thf(zip_derived_cl1886_009,plain,
    ! [X0: $i] : ( a1 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1848]) ).

thf(zip_derived_cl34_010,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( X4 @ ( '#sk10' @ X2 @ X4 ) )
      | ~ ( a1 @ X2 @ X6 )
      | ( X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl1967,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ~ ( X1 @ ( '#sk10' @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1886,zip_derived_cl34]) ).

thf(zip_derived_cl5749,plain,
    ! [X0: $i] :
      ( ( a2 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ( a2 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1968,zip_derived_cl1967]) ).

thf(zip_derived_cl5840,plain,
    ! [X0: $i] : ( a2 @ X0 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5749]) ).

thf(axiom_a1,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X: mu] : ( mbox @ a2 @ ( mimplies @ ( mdia @ a2 @ ( q @ X ) ) @ ( p @ X ) ) ) ) ) ).

thf(zf_stmt_7,axiom,
    ! [X4: $i,X6: mu,X8: $i] :
      ( ~ ( a2 @ X4 @ X8 )
      | ( p @ X6 @ X8 )
      | ! [X10: $i] :
          ( ~ ( a2 @ X8 @ X10 )
          | ~ ( q @ X6 @ X10 ) ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( (~) @ ( a2 @ Y0 @ Y2 ) )
                | ( p @ Y1 @ Y2 )
                | ( !!
                  @ ^ [Y3: $i] :
                      ( ( (~) @ ( a2 @ Y2 @ Y3 ) )
                      | ( (~) @ ( q @ Y1 @ Y3 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( (~) @ ( a2 @ X2 @ Y1 ) )
              | ( p @ Y0 @ Y1 )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( a2 @ Y1 @ Y2 ) )
                    | ( (~) @ ( q @ Y0 @ Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl49,plain,
    ! [X2: $i,X4: mu] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( a2 @ X2 @ Y0 ) )
          | ( p @ X4 @ Y0 )
          | ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( a2 @ Y0 @ Y1 ) )
                | ( (~) @ ( q @ X4 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl50,plain,
    ! [X2: $i,X4: mu,X6: $i] :
      ( ( (~) @ ( a2 @ X2 @ X6 ) )
      | ( p @ X4 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a2 @ X6 @ Y0 ) )
            | ( (~) @ ( q @ X4 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl51,plain,
    ! [X2: $i,X4: mu,X6: $i] :
      ( ~ ( a2 @ X2 @ X6 )
      | ( p @ X4 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( a2 @ X6 @ Y0 ) )
            | ( (~) @ ( q @ X4 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl52,plain,
    ! [X2: $i,X4: mu,X6: $i,X8: $i] :
      ( ( (~) @ ( a2 @ X6 @ X8 ) )
      | ( (~) @ ( q @ X4 @ X8 ) )
      | ( p @ X4 @ X6 )
      | ~ ( a2 @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl53,plain,
    ! [X2: $i,X4: mu,X6: $i,X8: $i] :
      ( ~ ( a2 @ X6 @ X8 )
      | ~ ( q @ X4 @ X8 )
      | ~ ( a2 @ X2 @ X6 )
      | ( p @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl5867,plain,
    ! [X0: $i,X1: mu,X2: $i] :
      ( ( p @ X1 @ X0 )
      | ~ ( a2 @ X2 @ X0 )
      | ~ ( q @ X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5840,zip_derived_cl53]) ).

thf(zip_derived_cl5975,plain,
    ! [X0: $i,X1: mu,X2: $i] :
      ( ~ ( s @ X1 @ ( '#sk3' @ ( '#sk3' @ X0 ) ) )
      | ~ ( s @ X1 @ ( '#sk3' @ X0 ) )
      | ~ ( a2 @ X2 @ X0 )
      | ( p @ X1 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl674,zip_derived_cl5867]) ).

thf(zip_derived_cl6116,plain,
    ! [X0: $i,X1: $i] :
      ( ( p @ a @ X0 )
      | ~ ( a2 @ X1 @ X0 )
      | ~ ( s @ a @ ( '#sk3' @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl5975]) ).

thf(zip_derived_cl18_011,plain,
    ! [X2: $i] : ( s @ a @ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl6141,plain,
    ! [X0: $i,X1: $i] :
      ( ( p @ a @ X0 )
      | ~ ( a2 @ X1 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6116,zip_derived_cl18]) ).

thf(zip_derived_cl6167,plain,
    ! [X0: mu] : ( p @ a @ ( '#sk2' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl466,zip_derived_cl6141]) ).

thf(zip_derived_cl14,plain,
    ! [X2: mu] :
      ~ ( p @ X2 @ ( '#sk2' @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl6206,plain,
    $false,
    inference('sup-',[status(thm)],[zip_derived_cl6167,zip_derived_cl14]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : AGT027^2 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.S1a8plbRuD true
% 0.15/0.37  % Computer : n023.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sun Aug 27 17:43:26 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  % Running portfolio for 300 s
% 0.15/0.37  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37  % Number of cores: 8
% 0.15/0.37  % Python version: Python 3.6.8
% 0.15/0.37  % Running in HO mode
% 0.54/0.70  % Total configuration time : 828
% 0.54/0.70  % Estimated wc time : 1656
% 0.54/0.70  % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.76  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.78  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.78  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.78  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.79  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.80  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.82  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.85  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.60/0.86  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 38.38/5.48  % Solved by lams/35_full_unif4.sh.
% 38.38/5.48  % done 406 iterations in 4.676s
% 38.38/5.48  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 38.38/5.48  % SZS output start Refutation
% See solution above
% 38.38/5.48  
% 38.38/5.48  
% 38.38/5.48  % Terminating...
% 38.81/5.65  % Runner terminated.
% 38.81/5.66  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------