TSTP Solution File: SEV292^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV292^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QeyCLpe0ih true

% Computer : n031.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 20:00:20 EDT 2023

% Result   : Theorem 1.72s 1.11s
% Output   : Refutation 1.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   63 (  13 unt;   9 typ;   0 def)
%            Number of atoms       :  570 ( 152 equ;  72 cnn)
%            Maximal formula atoms :   30 (  10 avg)
%            Number of connectives : 1740 ( 263   ~;  31   |; 313   &; 822   @)
%                                         (   0 <=>;  78  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  382 ( 382   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (   9 usr;   5 con; 0-2 aty)
%                                         (  53  !!; 180  ??;   0 @@+;   0 @@-)
%            Number of variables   :  457 ( 401   ^;  31   !;  25   ?; 457   :)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk7_type',type,
    '#sk7': ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(c_less__eq__type,type,
    c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf('#sk25_type',type,
    '#sk25': ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(cP_type,type,
    cP: ( ( $i > $o ) > $o ) > $o ).

thf(cSUCC_type,type,
    cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).

thf(cZERO_type,type,
    cZERO: ( $i > $o ) > $o ).

thf(cONE_type,type,
    cONE: ( $i > $o ) > $o ).

thf('#form24_type',type,
    '#form24': ( ( $i > $o ) > $o ) > $o ).

thf('#sk278_type',type,
    '#sk278': ( ( $i > $o ) > $o ) > $o ).

thf(c_less__eq__def,axiom,
    ( c_less__eq_
    = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
        ! [Xp: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( Xp @ Xx )
            & ! [Xz: ( $i > $o ) > $o] :
                ( ( Xp @ Xz )
               => ( Xp @ ( cSUCC @ Xz ) ) ) )
         => ( Xp @ Xy ) ) ) ) ).

thf(cSUCC_def,axiom,
    ( cSUCC
    = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
        ? [Xx: $i] :
          ( ( Xn
            @ ^ [Xt: $i] :
                ( ( Xt != Xx )
                & ( Xp @ Xt ) ) )
          & ( Xp @ Xx ) ) ) ) ).

thf('0',plain,
    ( cSUCC
    = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
        ? [Xx: $i] :
          ( ( Xn
            @ ^ [Xt: $i] :
                ( ( Xt != Xx )
                & ( Xp @ Xt ) ) )
          & ( Xp @ Xx ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cSUCC_def]) ).

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

thf('2',plain,
    ( c_less__eq_
    = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
        ! [Xp: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( Xp @ Xx )
            & ! [Xz: ( $i > $o ) > $o] :
                ( ( Xp @ Xz )
               => ( Xp @ ( cSUCC @ Xz ) ) ) )
         => ( Xp @ Xy ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[c_less__eq__def,'1']) ).

thf('3',plain,
    ( c_less__eq_
    = ( ^ [V_1: ( $i > $o ) > $o,V_2: ( $i > $o ) > $o] :
        ! [X4: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( X4 @ V_1 )
            & ! [X6: ( $i > $o ) > $o] :
                ( ( X4 @ X6 )
               => ( X4 @ ( cSUCC @ X6 ) ) ) )
         => ( X4 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(cONE_def,axiom,
    ( cONE
    = ( cSUCC @ cZERO ) ) ).

thf(cZERO_def,axiom,
    ( cZERO
    = ( ^ [Xp: $i > $o] :
          ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).

thf('4',plain,
    ( cZERO
    = ( ^ [Xp: $i > $o] :
          ~ ? [Xx: $i] : ( Xp @ Xx ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cZERO_def]) ).

thf('5',plain,
    ( cZERO
    = ( ^ [V_1: $i > $o] :
          ~ ? [X4: $i] : ( V_1 @ X4 ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( cONE
    = ( cSUCC @ cZERO ) ),
    inference(simplify_rw_rule,[status(thm)],[cONE_def,'1','5']) ).

thf('7',plain,
    ( cONE
    = ( cSUCC @ cZERO ) ),
    define([status(thm)]) ).

thf(cBLEDSOE7A,conjecture,
    ( ( cP @ cONE )
   => ? [Xx: ( $i > $o ) > $o] :
        ( ( cP @ Xx )
        & ( c_less__eq_ @ Xx @ ( cSUCC @ cONE ) )
        & ( c_less__eq_ @ cZERO @ Xx ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ( cP
      @ ^ [V_1: $i > $o] :
        ? [X4: $i] :
          ( ( V_1 @ X4 )
          & ~ ? [X6: $i] :
                ( ( V_1 @ X6 )
                & ( X6 != X4 ) ) ) )
   => ? [X8: ( $i > $o ) > $o] :
        ( ! [X22: ( ( $i > $o ) > $o ) > $o] :
            ( ( ! [X26: ( $i > $o ) > $o] :
                  ( ( X22 @ X26 )
                 => ( X22
                    @ ^ [V_6: $i > $o] :
                      ? [X28: $i] :
                        ( ( V_6 @ X28 )
                        & ( X26
                          @ ^ [V_7: $i] :
                              ( ( V_6 @ V_7 )
                              & ( V_7 != X28 ) ) ) ) ) )
              & ( X22
                @ ^ [V_5: $i > $o] :
                    ~ ? [X24: $i] : ( V_5 @ X24 ) ) )
           => ( X22 @ X8 ) )
        & ! [X10: ( ( $i > $o ) > $o ) > $o] :
            ( ( ! [X12: ( $i > $o ) > $o] :
                  ( ( X10 @ X12 )
                 => ( X10
                    @ ^ [V_2: $i > $o] :
                      ? [X14: $i] :
                        ( ( V_2 @ X14 )
                        & ( X12
                          @ ^ [V_3: $i] :
                              ( ( V_2 @ V_3 )
                              & ( V_3 != X14 ) ) ) ) ) )
              & ( X10 @ X8 ) )
           => ( X10
              @ ^ [V_4: $i > $o] :
                ? [X16: $i] :
                  ( ( V_4 @ X16 )
                  & ? [X18: $i] :
                      ( ( V_4 @ X18 )
                      & ( X18 != X16 )
                      & ~ ? [X20: $i] :
                            ( ( V_4 @ X20 )
                            & ( X20 != X16 )
                            & ( X20 != X18 ) ) ) ) ) )
        & ( cP @ X8 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ( cP
        @ ^ [V_1: $i > $o] :
          ? [X4: $i] :
            ( ( V_1 @ X4 )
            & ~ ? [X6: $i] :
                  ( ( V_1 @ X6 )
                  & ( X6 != X4 ) ) ) )
     => ? [X8: ( $i > $o ) > $o] :
          ( ! [X22: ( ( $i > $o ) > $o ) > $o] :
              ( ( ! [X26: ( $i > $o ) > $o] :
                    ( ( X22 @ X26 )
                   => ( X22
                      @ ^ [V_6: $i > $o] :
                        ? [X28: $i] :
                          ( ( V_6 @ X28 )
                          & ( X26
                            @ ^ [V_7: $i] :
                                ( ( V_6 @ V_7 )
                                & ( V_7 != X28 ) ) ) ) ) )
                & ( X22
                  @ ^ [V_5: $i > $o] :
                      ~ ? [X24: $i] : ( V_5 @ X24 ) ) )
             => ( X22 @ X8 ) )
          & ! [X10: ( ( $i > $o ) > $o ) > $o] :
              ( ( ! [X12: ( $i > $o ) > $o] :
                    ( ( X10 @ X12 )
                   => ( X10
                      @ ^ [V_2: $i > $o] :
                        ? [X14: $i] :
                          ( ( V_2 @ X14 )
                          & ( X12
                            @ ^ [V_3: $i] :
                                ( ( V_2 @ V_3 )
                                & ( V_3 != X14 ) ) ) ) ) )
                & ( X10 @ X8 ) )
             => ( X10
                @ ^ [V_4: $i > $o] :
                  ? [X16: $i] :
                    ( ( V_4 @ X16 )
                    & ? [X18: $i] :
                        ( ( V_4 @ X18 )
                        & ( X18 != X16 )
                        & ~ ? [X20: $i] :
                              ( ( V_4 @ X20 )
                              & ( X20 != X16 )
                              & ( X20 != X18 ) ) ) ) ) )
          & ( cP @ X8 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( cP
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
     => ( ??
        @ ^ [Y0: ( $i > $o ) > $o] :
            ( ( !!
              @ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
                  ( ( ( !!
                      @ ^ [Y2: ( $i > $o ) > $o] :
                          ( ( Y1 @ Y2 )
                         => ( Y1
                            @ ^ [Y3: $i > $o] :
                                ( ??
                                @ ^ [Y4: $i] :
                                    ( ( Y3 @ Y4 )
                                    & ( Y2
                                      @ ^ [Y5: $i] :
                                          ( ( Y3 @ Y5 )
                                          & ( Y5 != Y4 ) ) ) ) ) ) ) )
                    & ( Y1
                      @ ^ [Y2: $i > $o] :
                          ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) )
                 => ( Y1 @ Y0 ) ) )
            & ( !!
              @ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
                  ( ( ( !!
                      @ ^ [Y2: ( $i > $o ) > $o] :
                          ( ( Y1 @ Y2 )
                         => ( Y1
                            @ ^ [Y3: $i > $o] :
                                ( ??
                                @ ^ [Y4: $i] :
                                    ( ( Y3 @ Y4 )
                                    & ( Y2
                                      @ ^ [Y5: $i] :
                                          ( ( Y3 @ Y5 )
                                          & ( Y5 != Y4 ) ) ) ) ) ) ) )
                    & ( Y1 @ Y0 ) )
                 => ( Y1
                    @ ^ [Y2: $i > $o] :
                        ( ??
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                            & ( ??
                              @ ^ [Y4: $i] :
                                  ( ( Y2 @ Y4 )
                                  & ( Y4 != Y3 )
                                  & ( (~)
                                    @ ( ??
                                      @ ^ [Y5: $i] :
                                          ( ( Y2 @ Y5 )
                                          & ( Y5 != Y3 )
                                          & ( Y5 != Y4 ) ) ) ) ) ) ) ) ) ) )
            & ( cP @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    ~ ( ??
      @ ^ [Y0: ( $i > $o ) > $o] :
          ( ( !!
            @ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
                ( ( ( !!
                    @ ^ [Y2: ( $i > $o ) > $o] :
                        ( ( Y1 @ Y2 )
                       => ( Y1
                          @ ^ [Y3: $i > $o] :
                              ( ??
                              @ ^ [Y4: $i] :
                                  ( ( Y3 @ Y4 )
                                  & ( Y2
                                    @ ^ [Y5: $i] :
                                        ( ( Y3 @ Y5 )
                                        & ( Y5 != Y4 ) ) ) ) ) ) ) )
                  & ( Y1
                    @ ^ [Y2: $i > $o] :
                        ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) )
               => ( Y1 @ Y0 ) ) )
          & ( !!
            @ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
                ( ( ( !!
                    @ ^ [Y2: ( $i > $o ) > $o] :
                        ( ( Y1 @ Y2 )
                       => ( Y1
                          @ ^ [Y3: $i > $o] :
                              ( ??
                              @ ^ [Y4: $i] :
                                  ( ( Y3 @ Y4 )
                                  & ( Y2
                                    @ ^ [Y5: $i] :
                                        ( ( Y3 @ Y5 )
                                        & ( Y5 != Y4 ) ) ) ) ) ) ) )
                  & ( Y1 @ Y0 ) )
               => ( Y1
                  @ ^ [Y2: $i > $o] :
                      ( ??
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                          & ( ??
                            @ ^ [Y4: $i] :
                                ( ( Y2 @ Y4 )
                                & ( Y4 != Y3 )
                                & ( (~)
                                  @ ( ??
                                    @ ^ [Y5: $i] :
                                        ( ( Y2 @ Y5 )
                                        & ( Y5 != Y3 )
                                        & ( Y5 != Y4 ) ) ) ) ) ) ) ) ) ) )
          & ( cP @ Y0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ! [X2: ( $i > $o ) > $o] :
      ~ ( ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0
                  @ ^ [Y1: $i > $o] :
                      ( (~)
                      @ ( ??
                        @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 ) ) )
        & ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
        & ( cP @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl25,plain,
    ~ ( ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y1 @ Y3 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( ??
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 )
                            & ( (~)
                              @ ( ??
                                @ ^ [Y4: $i] :
                                    ( ( Y1 @ Y4 )
                                    & ( Y4 != Y2 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
      & ( cP
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl1,plain,
    ( cP
    @ ^ [Y0: $i > $o] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( Y0 @ Y1 )
            & ( (~)
              @ ( ??
                @ ^ [Y2: $i] :
                    ( ( Y0 @ Y2 )
                    & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl64,plain,
    ~ ( ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y1 @ Y3 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( ??
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 )
                            & ( (~)
                              @ ( ??
                                @ ^ [Y4: $i] :
                                    ( ( Y1 @ Y4 )
                                    & ( Y4 != Y2 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
      & $true ),
    inference(demod,[status(thm)],[zip_derived_cl25,zip_derived_cl1]) ).

thf(zip_derived_cl65,plain,
    ~ ( ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y1 @ Y3 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( ??
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 )
                            & ( (~)
                              @ ( ??
                                @ ^ [Y4: $i] :
                                    ( ( Y1 @ Y4 )
                                    & ( Y4 != Y2 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl66,plain,
    ( ~ ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y1 @ Y3 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( ??
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 )
                            & ( (~)
                              @ ( ??
                                @ ^ [Y4: $i] :
                                    ( ( Y1 @ Y4 )
                                    & ( Y4 != Y2 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl3_001,plain,
    ! [X2: ( $i > $o ) > $o] :
      ~ ( ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0
                  @ ^ [Y1: $i > $o] :
                      ( (~)
                      @ ( ??
                        @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 ) ) )
        & ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
        & ( cP @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0
                  @ ^ [Y1: $i > $o] :
                      ( (~)
                      @ ( ??
                        @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 ) ) )
      | ~ ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( ( ( !!
              @ ^ [Y0: ( $i > $o ) > $o] :
                  ( ( '#sk7' @ X2 @ Y0 )
                 => ( '#sk7' @ X2
                    @ ^ [Y1: $i > $o] :
                        ( ??
                        @ ^ [Y2: $i] :
                            ( ( Y1 @ Y2 )
                            & ( Y0
                              @ ^ [Y3: $i] :
                                  ( ( Y1 @ Y3 )
                                  & ( Y3 != Y2 ) ) ) ) ) ) ) )
            & ( '#sk7' @ X2
              @ ^ [Y0: $i > $o] :
                  ( (~)
                  @ ( ??
                    @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
         => ( '#sk7' @ X2 @ X2 ) )
      | ~ ( cP @ X2 )
      | ~ ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( '#sk7' @ X2 @ X2 )
      | ~ ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( '#form24' @ X2 )
      | ~ ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl67,plain,
    ( ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( !!
                @ ^ [Y1: ( $i > $o ) > $o] :
                    ( ( Y0 @ Y1 )
                   => ( Y0
                      @ ^ [Y2: $i > $o] :
                          ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                              & ( Y1
                                @ ^ [Y4: $i] :
                                    ( ( Y2 @ Y4 )
                                    & ( Y4 != Y3 ) ) ) ) ) ) ) )
              & ( Y0
                @ ^ [Y1: $i > $o] :
                    ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
           => ( Y0
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl66,zip_derived_cl10]) ).

thf(zip_derived_cl68,plain,
    ( ~ ( ( ( !!
            @ ^ [Y0: ( $i > $o ) > $o] :
                ( ( '#sk278' @ Y0 )
               => ( '#sk278'
                  @ ^ [Y1: $i > $o] :
                      ( ??
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                          & ( Y0
                            @ ^ [Y3: $i] :
                                ( ( Y1 @ Y3 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) )
          & ( '#sk278'
            @ ^ [Y0: $i > $o] :
                ( (~)
                @ ( ??
                  @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
       => ( '#sk278'
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] :
                          ( ( Y0 @ Y2 )
                          & ( Y2 != Y1 ) ) ) ) ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl69,plain,
    ( ( ( !!
        @ ^ [Y0: ( $i > $o ) > $o] :
            ( ( '#sk278' @ Y0 )
           => ( '#sk278'
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( Y0
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 ) ) ) ) ) ) ) )
      & ( '#sk278'
        @ ^ [Y0: $i > $o] :
            ( (~)
            @ ( ??
              @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl72,plain,
    ( ( '#sk278'
      @ ^ [Y0: $i > $o] :
          ( (~)
          @ ( ??
            @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl71,plain,
    ( ( !!
      @ ^ [Y0: ( $i > $o ) > $o] :
          ( ( '#sk278' @ Y0 )
         => ( '#sk278'
            @ ^ [Y1: $i > $o] :
                ( ??
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                    & ( Y0
                      @ ^ [Y3: $i] :
                          ( ( Y1 @ Y3 )
                          & ( Y3 != Y2 ) ) ) ) ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl73,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( ( '#sk278' @ X2 )
       => ( '#sk278'
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( X2
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
      | ~ ( '#form24'
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] :
                          ( ( Y0 @ Y2 )
                          & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl76,plain,
    ( ( ( '#sk278'
        @ ^ [Y0: $i > $o] :
            ( (~)
            @ ( ??
              @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
     => ( '#sk278'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl73]) ).

thf(zip_derived_cl79,plain,
    ( ~ ( '#sk278'
        @ ^ [Y0: $i > $o] :
            ( (~)
            @ ( ??
              @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
    | ( '#sk278'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl70,plain,
    ( ~ ( '#sk278'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
    | ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl80,plain,
    ( ~ ( '#form24'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( (~)
                  @ ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
    | ~ ( '#sk278'
        @ ^ [Y0: $i > $o] :
            ( (~)
            @ ( ??
              @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl79,zip_derived_cl70]) ).

thf(zip_derived_cl81,plain,
    ~ ( '#form24'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl72,zip_derived_cl80]) ).

thf(zip_derived_cl10_002,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( '#form24' @ X2 )
      | ~ ( !!
          @ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( !!
                  @ ^ [Y1: ( $i > $o ) > $o] :
                      ( ( Y0 @ Y1 )
                     => ( Y0
                        @ ^ [Y2: $i > $o] :
                            ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                                & ( Y1
                                  @ ^ [Y4: $i] :
                                      ( ( Y2 @ Y4 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) )
                & ( Y0 @ X2 ) )
             => ( Y0
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 )
                              & ( (~)
                                @ ( ??
                                  @ ^ [Y4: $i] :
                                      ( ( Y1 @ Y4 )
                                      & ( Y4 != Y2 )
                                      & ( Y4 != Y3 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl11,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( ( ( !!
              @ ^ [Y0: ( $i > $o ) > $o] :
                  ( ( '#sk25' @ X2 @ Y0 )
                 => ( '#sk25' @ X2
                    @ ^ [Y1: $i > $o] :
                        ( ??
                        @ ^ [Y2: $i] :
                            ( ( Y1 @ Y2 )
                            & ( Y0
                              @ ^ [Y3: $i] :
                                  ( ( Y1 @ Y3 )
                                  & ( Y3 != Y2 ) ) ) ) ) ) ) )
            & ( '#sk25' @ X2 @ X2 ) )
         => ( '#sk25' @ X2
            @ ^ [Y0: $i > $o] :
                ( ??
                @ ^ [Y1: $i] :
                    ( ( Y0 @ Y1 )
                    & ( ??
                      @ ^ [Y2: $i] :
                          ( ( Y0 @ Y2 )
                          & ( Y2 != Y1 )
                          & ( (~)
                            @ ( ??
                              @ ^ [Y3: $i] :
                                  ( ( Y0 @ Y3 )
                                  & ( Y3 != Y1 )
                                  & ( Y3 != Y2 ) ) ) ) ) ) ) ) ) )
      | ( '#form24' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl15,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( ( !!
          @ ^ [Y0: ( $i > $o ) > $o] :
              ( ( '#sk25' @ X2 @ Y0 )
             => ( '#sk25' @ X2
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( Y0
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) )
        & ( '#sk25' @ X2 @ X2 ) )
      | ( '#form24' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl19,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( '#sk25' @ X2 @ X2 )
      | ( '#form24' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl18,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( !!
        @ ^ [Y0: ( $i > $o ) > $o] :
            ( ( '#sk25' @ X2 @ Y0 )
           => ( '#sk25' @ X2
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( Y0
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 ) ) ) ) ) ) ) )
      | ( '#form24' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl21,plain,
    ! [X2: ( $i > $o ) > $o,X4: ( $i > $o ) > $o] :
      ( ( ( '#sk25' @ X2 @ X4 )
       => ( '#sk25' @ X2
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( X4
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
      | ( '#form24' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl23,plain,
    ! [X0: ( $i > $o ) > $o] :
      ( ( ( '#sk25' @ X0
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] :
                          ( ( Y0 @ Y2 )
                          & ( Y2 != Y1 ) ) ) ) ) ) )
       => ( '#sk25' @ X0
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 )
                        & ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y0 @ Y3 )
                                & ( Y3 != Y1 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) ) ) )
      | ( '#form24' @ X0 ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl35,plain,
    ! [X0: ( $i > $o ) > $o] :
      ( ~ ( '#sk25' @ X0
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( (~)
                    @ ( ??
                      @ ^ [Y2: $i] :
                          ( ( Y0 @ Y2 )
                          & ( Y2 != Y1 ) ) ) ) ) ) )
      | ( '#sk25' @ X0
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 )
                      & ( (~)
                        @ ( ??
                          @ ^ [Y3: $i] :
                              ( ( Y0 @ Y3 )
                              & ( Y3 != Y1 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) ) )
      | ( '#form24' @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl110,plain,
    ( ( '#form24'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) )
    | ( '#form24'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) )
    | ( '#sk25'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) )
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( ??
                @ ^ [Y2: $i] :
                    ( ( Y0 @ Y2 )
                    & ( Y2 != Y1 )
                    & ( (~)
                      @ ( ??
                        @ ^ [Y3: $i] :
                            ( ( Y0 @ Y3 )
                            & ( Y3 != Y1 )
                            & ( Y3 != Y2 ) ) ) ) ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl35]) ).

thf(zip_derived_cl81_003,plain,
    ~ ( '#form24'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl72,zip_derived_cl80]) ).

thf(zip_derived_cl81_004,plain,
    ~ ( '#form24'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( (~)
                @ ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl72,zip_derived_cl80]) ).

thf(zip_derived_cl111,plain,
    ( '#sk25'
    @ ^ [Y0: $i > $o] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( Y0 @ Y1 )
            & ( (~)
              @ ( ??
                @ ^ [Y2: $i] :
                    ( ( Y0 @ Y2 )
                    & ( Y2 != Y1 ) ) ) ) ) )
    @ ^ [Y0: $i > $o] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( Y0 @ Y1 )
            & ( ??
              @ ^ [Y2: $i] :
                  ( ( Y0 @ Y2 )
                  & ( Y2 != Y1 )
                  & ( (~)
                    @ ( ??
                      @ ^ [Y3: $i] :
                          ( ( Y0 @ Y3 )
                          & ( Y3 != Y1 )
                          & ( Y3 != Y2 ) ) ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl110,zip_derived_cl81,zip_derived_cl81]) ).

thf(zip_derived_cl16,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( '#sk25' @ X2
          @ ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 )
                        & ( (~)
                          @ ( ??
                            @ ^ [Y3: $i] :
                                ( ( Y0 @ Y3 )
                                & ( Y3 != Y1 )
                                & ( Y3 != Y2 ) ) ) ) ) ) ) ) )
      | ( '#form24' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl122,plain,
    ( '#form24'
    @ ^ [Y0: $i > $o] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( Y0 @ Y1 )
            & ( (~)
              @ ( ??
                @ ^ [Y2: $i] :
                    ( ( Y0 @ Y2 )
                    & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl111,zip_derived_cl16]) ).

thf(zip_derived_cl127,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl81,zip_derived_cl122]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SEV292^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.13/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QeyCLpe0ih true
% 0.14/0.36  % Computer : n031.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug 24 03:10:50 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
% 0.22/0.37  % Running in HO mode
% 0.22/0.70  % Total configuration time : 828
% 0.22/0.70  % Estimated wc time : 1656
% 0.22/0.70  % 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
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.14/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.14/0.80  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.14/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.14/0.82  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.46/0.84  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.72/1.11  % Solved by lams/20_acsne_simpl.sh.
% 1.72/1.11  % done 27 iterations in 0.224s
% 1.72/1.11  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.72/1.11  % SZS output start Refutation
% See solution above
% 1.72/1.11  
% 1.72/1.11  
% 1.72/1.11  % Terminating...
% 1.73/1.26  % Runner terminated.
% 1.89/1.27  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------