TSTP Solution File: LCL872^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : LCL872^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TcpTz20unw true

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 09:02:29 EDT 2023

% Result   : Theorem 1.53s 1.40s
% Output   : Refutation 1.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  163 (  42 unt;  23 typ;   0 def)
%            Number of atoms       :  799 (  26 equ; 144 cnn)
%            Maximal formula atoms :   25 (   5 avg)
%            Number of connectives : 2069 ( 316   ~; 291   |;  55   &;1223   @)
%                                         (   3 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  178 ( 178   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  23 usr;  11 con; 0-4 aty)
%                                         ( 135  !!;  22  ??;   0 @@+;   0 @@-)
%            Number of variables   :  382 ( 215   ^; 162   !;   5   ?; 382   :)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk114_type',type,
    '#sk114': $i ).

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

thf('#sk116_type',type,
    '#sk116': $i ).

thf('#sk117_type',type,
    '#sk117': $i ).

thf('#sk16_type',type,
    '#sk16': $i > $i > $i ).

thf(i_type,type,
    i: $i > $i > $o ).

thf(confluence_type,type,
    confluence: ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf('#sk12_type',type,
    '#sk12': ( $i > $o ) > $i > $i ).

thf('#sk118_type',type,
    '#sk118': $i ).

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

thf('#sk27_type',type,
    '#sk27': ( $i > $o ) > $i > $i ).

thf('#form3_type',type,
    '#form3': $o ).

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

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

thf('#sk112_type',type,
    '#sk112': $i ).

thf('#sk113_type',type,
    '#sk113': $i ).

thf('#sk115_type',type,
    '#sk115': $i > $o ).

thf(j_type,type,
    j: $i > $i > $o ).

thf(k_type,type,
    k: $i > $i > $o ).

thf(l_type,type,
    l: $i > $i > $o ).

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

thf(confluence,axiom,
    ( confluence
    = ( ^ [I: $i > $i > $o,J: $i > $i > $o,K: $i > $i > $o,L: $i > $i > $o] :
        ! [A: $i,B: $i,C: $i] :
          ( ( ( I @ A @ B )
            & ( K @ A @ C ) )
         => ? [D: $i] :
              ( ( L @ C @ D )
              & ( J @ B @ D ) ) ) ) ) ).

thf('0',plain,
    ( confluence
    = ( ^ [I: $i > $i > $o,J: $i > $i > $o,K: $i > $i > $o,L: $i > $i > $o] :
        ! [A: $i,B: $i,C: $i] :
          ( ( ( I @ A @ B )
            & ( K @ A @ C ) )
         => ? [D: $i] :
              ( ( L @ C @ D )
              & ( J @ B @ D ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[confluence]) ).

thf('1',plain,
    ( confluence
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $i > $o,V_3: $i > $i > $o,V_4: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_3 @ X4 @ X8 ) )
         => ? [X10: $i] :
              ( ( V_4 @ X8 @ X10 )
              & ( V_2 @ X6 @ X10 ) ) ) ) ),
    define([status(thm)]) ).

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

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

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

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

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

thf('4',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('5',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(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,
    ( mdia
    = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mdia,'5','7']) ).

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

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(conj,conjecture,
    ( ( mvalid
      @ ( mforall_prop
        @ ^ [P: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ P ) ) @ ( mbox @ k @ ( mdia @ l @ P ) ) ) ) )
  <=> ( confluence @ i @ j @ k @ l ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $o] :
        ( ! [X12: $i] :
            ( ~ ( k @ X4 @ X12 )
            | ~ ! [X14: $i] :
                  ( ~ ( l @ X12 @ X14 )
                  | ~ ( X6 @ X14 ) ) )
        | ! [X8: $i] :
            ( ~ ( i @ X4 @ X8 )
            | ~ ! [X10: $i] :
                  ( ~ ( j @ X8 @ X10 )
                  | ( X6 @ X10 ) ) ) )
  <=> ! [X16: $i,X18: $i,X20: $i] :
        ( ( ( k @ X16 @ X20 )
          & ( i @ X16 @ X18 ) )
       => ? [X22: $i] :
            ( ( j @ X18 @ X22 )
            & ( l @ X20 @ X22 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o] :
          ( ! [X12: $i] :
              ( ~ ( k @ X4 @ X12 )
              | ~ ! [X14: $i] :
                    ( ~ ( l @ X12 @ X14 )
                    | ~ ( X6 @ X14 ) ) )
          | ! [X8: $i] :
              ( ~ ( i @ X4 @ X8 )
              | ~ ! [X10: $i] :
                    ( ~ ( j @ X8 @ X10 )
                    | ( X6 @ X10 ) ) ) )
    <=> ! [X16: $i,X18: $i,X20: $i] :
          ( ( ( k @ X16 @ X20 )
            & ( i @ X16 @ X18 ) )
         => ? [X22: $i] :
              ( ( j @ X18 @ X22 )
              & ( l @ X20 @ X22 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( k @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( l @ Y2 @ Y3 ) )
                            | ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( i @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( j @ Y2 @ Y3 ) )
                            | ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
   != ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( k @ Y0 @ Y2 )
                    & ( i @ Y0 @ Y1 ) )
                 => ( ??
                    @ ^ [Y3: $i] :
                        ( ( j @ Y1 @ Y3 )
                        & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( k @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( l @ Y2 @ Y3 ) )
                              | ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
                | ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( i @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( j @ Y2 @ Y3 ) )
                              | ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl45,plain,
    ( '#form3'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl46,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( k @ '#sk112' @ Y1 )
                  & ( i @ '#sk112' @ Y0 ) )
               => ( ??
                  @ ^ [Y2: $i] :
                      ( ( j @ Y0 @ Y2 )
                      & ( l @ Y1 @ Y2 ) ) ) ) ) )
    | '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl49,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( ( k @ '#sk112' @ Y0 )
              & ( i @ '#sk112' @ '#sk114' ) )
           => ( ??
              @ ^ [Y1: $i] :
                  ( ( j @ '#sk114' @ Y1 )
                  & ( l @ Y0 @ Y1 ) ) ) ) )
    | '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl52,plain,
    ( ~ ( ( ( k @ '#sk112' @ '#sk116' )
          & ( i @ '#sk112' @ '#sk114' ) )
       => ( ??
          @ ^ [Y0: $i] :
              ( ( j @ '#sk114' @ Y0 )
              & ( l @ '#sk116' @ Y0 ) ) ) )
    | '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl55,plain,
    ( ( ( k @ '#sk112' @ '#sk116' )
      & ( i @ '#sk112' @ '#sk114' ) )
    | '#form3' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl59,plain,
    ( ( k @ '#sk112' @ '#sk116' )
    | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl2_001,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( k @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( l @ Y2 @ Y3 ) )
                              | ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
                | ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( i @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( j @ Y2 @ Y3 ) )
                              | ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl45_002,plain,
    ( '#form3'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl0_003,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( k @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( l @ Y2 @ Y3 ) )
                            | ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( i @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( j @ Y2 @ Y3 ) )
                            | ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
   != ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( k @ Y0 @ Y2 )
                    & ( i @ Y0 @ Y1 ) )
                 => ( ??
                    @ ^ [Y3: $i] :
                        ( ( j @ Y1 @ Y3 )
                        & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( k @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( l @ Y2 @ Y3 ) )
                            | ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( i @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( j @ Y2 @ Y3 ) )
                            | ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( k @ Y0 @ Y2 )
                    & ( i @ Y0 @ Y1 ) )
                 => ( ??
                    @ ^ [Y3: $i] :
                        ( ( j @ Y1 @ Y3 )
                        & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( k @ X2 @ Y1 ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: $i] :
                          ( ( (~) @ ( l @ Y1 @ Y2 ) )
                          | ( (~) @ ( Y0 @ Y2 ) ) ) ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( i @ X2 @ Y1 ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: $i] :
                          ( ( (~) @ ( j @ Y1 @ Y2 ) )
                          | ( Y0 @ Y2 ) ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl4,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( k @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( l @ Y0 @ Y1 ) )
                    | ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl7,plain,
    ( ~ '#form3'
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( k @ Y0 @ Y2 )
                    & ( i @ Y0 @ Y1 ) )
                 => ( ??
                    @ ^ [Y3: $i] :
                        ( ( j @ Y1 @ Y3 )
                        & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl47,plain,
    ( ~ '#form3'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( k @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( l @ Y2 @ Y3 ) )
                              | ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
                | ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( i @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( j @ Y2 @ Y3 ) )
                              | ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl2,zip_derived_cl45,zip_derived_cl7]) ).

thf(zip_derived_cl48,plain,
    ( ~ ( !!
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( k @ '#sk113' @ Y1 ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: $i] :
                          ( ( (~) @ ( l @ Y1 @ Y2 ) )
                          | ( (~) @ ( Y0 @ Y2 ) ) ) ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( i @ '#sk113' @ Y1 ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: $i] :
                          ( ( (~) @ ( j @ Y1 @ Y2 ) )
                          | ( Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl51,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( k @ '#sk113' @ Y0 ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( l @ Y0 @ Y1 ) )
                      | ( (~) @ ( '#sk115' @ Y1 ) ) ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( i @ '#sk113' @ Y0 ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( j @ Y0 @ Y1 ) )
                      | ( '#sk115' @ Y1 ) ) ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl54,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ '#sk113' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( '#sk115' @ Y1 ) ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl58,plain,
    ( ~ ( ( (~) @ ( i @ '#sk113' @ '#sk118' ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( j @ '#sk118' @ Y0 ) )
                | ( '#sk115' @ Y0 ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl65,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( j @ '#sk118' @ Y0 ) )
          | ( '#sk115' @ Y0 ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl68,plain,
    ! [X2: $i] :
      ( ( (~) @ ( j @ '#sk118' @ X2 ) )
      | ( '#sk115' @ X2 )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl70,plain,
    ! [X2: $i] :
      ( ~ ( j @ '#sk118' @ X2 )
      | ( '#sk115' @ X2 )
      | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl53,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( k @ '#sk113' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( l @ Y0 @ Y1 ) )
                    | ( (~) @ ( '#sk115' @ Y1 ) ) ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl57,plain,
    ( ~ ( ( (~) @ ( k @ '#sk113' @ '#sk117' ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( l @ '#sk117' @ Y0 ) )
                | ( (~) @ ( '#sk115' @ Y0 ) ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl62,plain,
    ( ( k @ '#sk113' @ '#sk117' )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl7_004,plain,
    ( ~ '#form3'
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( k @ Y0 @ Y2 )
                    & ( i @ Y0 @ Y1 ) )
                 => ( ??
                    @ ^ [Y3: $i] :
                        ( ( j @ Y1 @ Y3 )
                        & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl8,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( k @ X2 @ Y1 )
                  & ( i @ X2 @ Y0 ) )
               => ( ??
                  @ ^ [Y2: $i] :
                      ( ( j @ Y0 @ Y2 )
                      & ( l @ Y1 @ Y2 ) ) ) ) ) )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i,X4: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( ( k @ X2 @ Y0 )
              & ( i @ X2 @ X4 ) )
           => ( ??
              @ ^ [Y1: $i] :
                  ( ( j @ X4 @ Y1 )
                  & ( l @ Y0 @ Y1 ) ) ) ) )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( ( k @ X2 @ X6 )
          & ( i @ X2 @ X4 ) )
       => ( ??
          @ ^ [Y0: $i] :
              ( ( j @ X4 @ Y0 )
              & ( l @ X6 @ Y0 ) ) ) )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( k @ X2 @ X6 )
          & ( i @ X2 @ X4 ) )
      | ( ??
        @ ^ [Y0: $i] :
            ( ( j @ X4 @ Y0 )
            & ( l @ X6 @ Y0 ) ) )
      | ~ '#form3' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( k @ X2 @ X6 )
      | ~ ( i @ X2 @ X4 )
      | ~ '#form3'
      | ( ??
        @ ^ [Y0: $i] :
            ( ( j @ X4 @ Y0 )
            & ( l @ X6 @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( j @ X4 @ ( '#sk16' @ X4 @ X6 ) )
        & ( l @ X6 @ ( '#sk16' @ X4 @ X6 ) ) )
      | ~ '#form3'
      | ~ ( i @ X2 @ X4 )
      | ~ ( k @ X2 @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( j @ X4 @ ( '#sk16' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | ~ ( i @ X2 @ X4 )
      | ~ '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl76,plain,
    ! [X0: $i] :
      ( ~ '#form3'
      | ~ '#form3'
      | ~ ( i @ '#sk113' @ X0 )
      | ( j @ X0 @ ( '#sk16' @ X0 @ '#sk117' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl23]) ).

thf(zip_derived_cl80,plain,
    ! [X0: $i] :
      ( ( j @ X0 @ ( '#sk16' @ X0 @ '#sk117' ) )
      | ~ ( i @ '#sk113' @ X0 )
      | ~ '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl169,plain,
    ( ~ '#form3'
    | ( '#sk115' @ ( '#sk16' @ '#sk118' @ '#sk117' ) )
    | ~ '#form3'
    | ~ ( i @ '#sk113' @ '#sk118' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl80]) ).

thf(zip_derived_cl172,plain,
    ( ~ ( i @ '#sk113' @ '#sk118' )
    | ( '#sk115' @ ( '#sk16' @ '#sk118' @ '#sk117' ) )
    | ~ '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl169]) ).

thf(zip_derived_cl64,plain,
    ( ( i @ '#sk113' @ '#sk118' )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl176,plain,
    ( ~ '#form3'
    | ( '#sk115' @ ( '#sk16' @ '#sk118' @ '#sk117' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl172,zip_derived_cl64]) ).

thf(zip_derived_cl62_005,plain,
    ( ( k @ '#sk113' @ '#sk117' )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( l @ X6 @ ( '#sk16' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | ~ ( i @ X2 @ X4 )
      | ~ '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl75,plain,
    ! [X0: $i] :
      ( ~ '#form3'
      | ~ '#form3'
      | ~ ( i @ '#sk113' @ X0 )
      | ( l @ '#sk117' @ ( '#sk16' @ X0 @ '#sk117' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl24]) ).

thf(zip_derived_cl79,plain,
    ! [X0: $i] :
      ( ( l @ '#sk117' @ ( '#sk16' @ X0 @ '#sk117' ) )
      | ~ ( i @ '#sk113' @ X0 )
      | ~ '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl75]) ).

thf(zip_derived_cl63,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( l @ '#sk117' @ Y0 ) )
          | ( (~) @ ( '#sk115' @ Y0 ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl67,plain,
    ! [X2: $i] :
      ( ( (~) @ ( l @ '#sk117' @ X2 ) )
      | ( (~) @ ( '#sk115' @ X2 ) )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl69,plain,
    ! [X2: $i] :
      ( ~ ( l @ '#sk117' @ X2 )
      | ~ ( '#sk115' @ X2 )
      | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl107,plain,
    ! [X0: $i] :
      ( ~ '#form3'
      | ~ ( i @ '#sk113' @ X0 )
      | ~ '#form3'
      | ~ ( '#sk115' @ ( '#sk16' @ X0 @ '#sk117' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl69]) ).

thf(zip_derived_cl109,plain,
    ! [X0: $i] :
      ( ~ ( '#sk115' @ ( '#sk16' @ X0 @ '#sk117' ) )
      | ~ ( i @ '#sk113' @ X0 )
      | ~ '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl107]) ).

thf(zip_derived_cl177,plain,
    ( ~ '#form3'
    | ~ '#form3'
    | ~ ( i @ '#sk113' @ '#sk118' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl109]) ).

thf(zip_derived_cl179,plain,
    ( ~ ( i @ '#sk113' @ '#sk118' )
    | ~ '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl177]) ).

thf(zip_derived_cl64_006,plain,
    ( ( i @ '#sk113' @ '#sk118' )
    | ~ '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl181,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl186,plain,
    k @ '#sk112' @ '#sk116',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).

thf(zip_derived_cl60,plain,
    ( ( i @ '#sk112' @ '#sk114' )
    | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl4_007,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( k @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( l @ Y0 @ Y1 ) )
                    | ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( k @ Y0 @ Y2 )
                      & ( i @ Y0 @ Y1 ) )
                   => ( ??
                      @ ^ [Y3: $i] :
                          ( ( j @ Y1 @ Y3 )
                          & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl7_008,plain,
    ( ~ '#form3'
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( k @ Y0 @ Y2 )
                    & ( i @ Y0 @ Y1 ) )
                 => ( ??
                    @ ^ [Y3: $i] :
                        ( ( j @ Y1 @ Y3 )
                        & ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i,X4: $i > $o] :
      ( '#form3'
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( k @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( l @ Y0 @ Y1 ) )
                    | ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl4,zip_derived_cl7]) ).

thf(zip_derived_cl10,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( k @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( l @ Y0 @ Y1 ) )
                    | ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( (~) @ ( k @ X2 @ X6 ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( l @ X6 @ Y0 ) )
              | ( (~) @ ( X4 @ Y0 ) ) ) ) )
      | '#form3'
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( k @ X2 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( l @ X6 @ Y0 ) )
              | ( (~) @ ( X4 @ Y0 ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( ( (~) @ ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) ) )
          | ( (~) @ ( X4 @ ( '#sk12' @ X4 @ X6 ) ) ) )
      | '#form3'
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | ~ ( k @ X2 @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( (~) @ ( i @ X2 @ X8 ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( j @ X8 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) )
      | '#form3'
      | ~ ( k @ X2 @ X6 )
      | ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( i @ X2 @ X8 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( j @ X8 @ Y0 ) )
              | ( X4 @ Y0 ) ) )
      | ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( ( (~) @ ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) ) )
          | ( X4 @ ( '#sk27' @ X4 @ X8 ) ) )
      | '#form3'
      | ~ ( k @ X2 @ X6 )
      | ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( i @ X2 @ X8 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( X4 @ ( '#sk27' @ X4 @ X8 ) )
      | ~ ( i @ X2 @ X8 )
      | ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl93,plain,
    ! [X0: $i,X1: $i > $o] :
      ( '#form3'
      | '#form3'
      | ~ ( k @ '#sk112' @ X0 )
      | ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl30]) ).

thf(zip_derived_cl101,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) )
      | ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( k @ '#sk112' @ X0 )
      | '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl181_009,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl739,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) )
      | ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( k @ '#sk112' @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl101,zip_derived_cl181]) ).

thf(zip_derived_cl740,plain,
    ! [X0: $i > $o] :
      ( ( l @ '#sk116' @ ( '#sk12' @ X0 @ '#sk116' ) )
      | ~ ( X0 @ ( '#sk27' @ X0 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl739]) ).

thf(zip_derived_cl186_010,plain,
    k @ '#sk112' @ '#sk116',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).

thf(zip_derived_cl60_011,plain,
    ( ( i @ '#sk112' @ '#sk114' )
    | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( i @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( j @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( (~) @ ( i @ X2 @ X8 ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( j @ X8 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) )
      | '#form3'
      | ~ ( k @ X2 @ X6 )
      | ( X4 @ ( '#sk12' @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( i @ X2 @ X8 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( j @ X8 @ Y0 ) )
              | ( X4 @ Y0 ) ) )
      | ( X4 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( ( (~) @ ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) ) )
          | ( X4 @ ( '#sk27' @ X4 @ X8 ) ) )
      | '#form3'
      | ~ ( k @ X2 @ X6 )
      | ( X4 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( i @ X2 @ X8 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) )
      | ~ ( i @ X2 @ X8 )
      | ( X4 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl92,plain,
    ! [X0: $i,X1: $i > $o] :
      ( '#form3'
      | '#form3'
      | ~ ( k @ '#sk112' @ X0 )
      | ( X1 @ ( '#sk12' @ X1 @ X0 ) )
      | ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl31]) ).

thf(zip_derived_cl100,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
      | ( X1 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( k @ '#sk112' @ X0 )
      | '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl181_012,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl522,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
      | ( X1 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( k @ '#sk112' @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl100,zip_derived_cl181]) ).

thf(zip_derived_cl523,plain,
    ! [X0: $i > $o] :
      ( ( X0 @ ( '#sk12' @ X0 @ '#sk116' ) )
      | ( j @ '#sk114' @ ( '#sk27' @ X0 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl522]) ).

thf(zip_derived_cl186_013,plain,
    k @ '#sk112' @ '#sk116',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).

thf(zip_derived_cl60_014,plain,
    ( ( i @ '#sk112' @ '#sk114' )
    | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl181_015,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl187,plain,
    i @ '#sk112' @ '#sk114',
    inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl181]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( X4 @ ( '#sk27' @ X4 @ X8 ) )
      | ~ ( i @ X2 @ X8 )
      | ( X4 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl181_016,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl185,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( X4 @ ( '#sk27' @ X4 @ X8 ) )
      | ~ ( i @ X2 @ X8 )
      | ( X4 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 ) ),
    inference(demod,[status(thm)],[zip_derived_cl32,zip_derived_cl181]) ).

thf(zip_derived_cl326,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( k @ '#sk112' @ X0 )
      | ( X1 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl187,zip_derived_cl185]) ).

thf(zip_derived_cl348,plain,
    ! [X0: $i > $o] :
      ( ~ ( X0 @ ( '#sk27' @ X0 @ '#sk114' ) )
      | ( X0 @ ( '#sk12' @ X0 @ '#sk116' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl326]) ).

thf(zip_derived_cl532,plain,
    ( ( j @ '#sk114' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) )
    | ( j @ '#sk114' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl523,zip_derived_cl348]) ).

thf(zip_derived_cl602,plain,
    j @ '#sk114' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ),
    inference(simplify,[status(thm)],[zip_derived_cl532]) ).

thf(zip_derived_cl56,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( ( j @ '#sk114' @ Y0 )
            & ( l @ '#sk116' @ Y0 ) ) )
    | '#form3' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl61,plain,
    ! [X2: $i] :
      ( ~ ( ( j @ '#sk114' @ X2 )
          & ( l @ '#sk116' @ X2 ) )
      | '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl66,plain,
    ! [X2: $i] :
      ( ~ ( j @ '#sk114' @ X2 )
      | ~ ( l @ '#sk116' @ X2 )
      | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl181_017,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl188,plain,
    ! [X2: $i] :
      ( ~ ( j @ '#sk114' @ X2 )
      | ~ ( l @ '#sk116' @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl181]) ).

thf(zip_derived_cl640,plain,
    ~ ( l @ '#sk116' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl602,zip_derived_cl188]) ).

thf(zip_derived_cl763,plain,
    ~ ( j @ '#sk114' @ ( '#sk27' @ ( j @ '#sk114' ) @ '#sk114' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl740,zip_derived_cl640]) ).

thf(zip_derived_cl186_018,plain,
    k @ '#sk112' @ '#sk116',
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).

thf(zip_derived_cl60_019,plain,
    ( ( i @ '#sk112' @ '#sk114' )
    | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) )
      | ~ ( i @ X2 @ X8 )
      | ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
      | ~ ( k @ X2 @ X6 )
      | '#form3' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl94,plain,
    ! [X0: $i,X1: $i > $o] :
      ( '#form3'
      | '#form3'
      | ~ ( k @ '#sk112' @ X0 )
      | ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
      | ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl29]) ).

thf(zip_derived_cl102,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
      | ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( k @ '#sk112' @ X0 )
      | '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl181_020,plain,
    ~ '#form3',
    inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).

thf(zip_derived_cl803,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
      | ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
      | ~ ( k @ '#sk112' @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl181]) ).

thf(zip_derived_cl804,plain,
    ! [X0: $i > $o] :
      ( ( l @ '#sk116' @ ( '#sk12' @ X0 @ '#sk116' ) )
      | ( j @ '#sk114' @ ( '#sk27' @ X0 @ '#sk114' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl803]) ).

thf(zip_derived_cl640_021,plain,
    ~ ( l @ '#sk116' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl602,zip_derived_cl188]) ).

thf(zip_derived_cl818,plain,
    j @ '#sk114' @ ( '#sk27' @ ( j @ '#sk114' ) @ '#sk114' ),
    inference('sup-',[status(thm)],[zip_derived_cl804,zip_derived_cl640]) ).

thf(zip_derived_cl828,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl763,zip_derived_cl818]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL872^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TcpTz20unw true
% 0.14/0.35  % Computer : n026.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 : Fri Aug 25 07:45:47 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % 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
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.81  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.36/0.87  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.53/1.40  % Solved by lams/20_acsne_simpl.sh.
% 1.53/1.40  % done 136 iterations in 0.598s
% 1.53/1.40  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.53/1.40  % SZS output start Refutation
% See solution above
% 1.53/1.40  
% 1.53/1.40  
% 1.53/1.40  % Terminating...
% 1.53/1.53  % Runner terminated.
% 1.53/1.54  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------