TSTP Solution File: SEV289^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV289^5 : 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.yFLLn1FG8k true

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:00:19 EDT 2023

% Result   : Theorem 0.58s 0.82s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   43 (  10 unt;   6 typ;   0 def)
%            Number of atoms       :  194 (  46 equ;  12 cnn)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  571 (  70   ~;   3   |;  90   &; 304   @)
%                                         (   0 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  190 ( 190   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   6 usr;   5 con; 0-2 aty)
%                                         (  21  !!;  38  ??;   0 @@+;   0 @@-)
%            Number of variables   :  198 ( 160   ^;  22   !;  16   ?; 198   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cNAT_type,type,
    cNAT: ( ( $i > $o ) > $o ) > $o ).

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

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

thf('#sk9_type',type,
    '#sk9': ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).

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

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

thf(cNAT_def,axiom,
    ( cNAT
    = ( ^ [Xn: ( $i > $o ) > $o] :
        ! [Xp: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( Xp @ cZERO )
            & ! [Xx: ( $i > $o ) > $o] :
                ( ( Xp @ Xx )
               => ( Xp @ ( cSUCC @ Xx ) ) ) )
         => ( Xp @ Xn ) ) ) ) ).

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

thf('2',plain,
    ( cZERO
    = ( ^ [Xp: $i > $o] :
          ~ ? [Xx: $i] : ( Xp @ Xx ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cZERO_def]) ).

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

thf('4',plain,
    ( cNAT
    = ( ^ [Xn: ( $i > $o ) > $o] :
        ! [Xp: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( Xp @ cZERO )
            & ! [Xx: ( $i > $o ) > $o] :
                ( ( Xp @ Xx )
               => ( Xp @ ( cSUCC @ Xx ) ) ) )
         => ( Xp @ Xn ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cNAT_def,'1','3']) ).

thf('5',plain,
    ( cNAT
    = ( ^ [V_1: ( $i > $o ) > $o] :
        ! [X4: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( X4 @ cZERO )
            & ! [X6: ( $i > $o ) > $o] :
                ( ( X4 @ X6 )
               => ( X4 @ ( cSUCC @ X6 ) ) ) )
         => ( X4 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(cTTTP6101,conjecture,
    ! [Xx: ( $i > $o ) > $o] :
      ( ( cNAT @ Xx )
     => ( cNAT @ ( cSUCC @ Xx ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: ( $i > $o ) > $o] :
      ( ! [X6: ( ( $i > $o ) > $o ) > $o] :
          ( ( ! [X10: ( $i > $o ) > $o] :
                ( ( X6 @ X10 )
               => ( X6
                  @ ^ [V_2: $i > $o] :
                    ? [X12: $i] :
                      ( ( V_2 @ X12 )
                      & ( X10
                        @ ^ [V_3: $i] :
                            ( ( V_2 @ V_3 )
                            & ( V_3 != X12 ) ) ) ) ) )
            & ( X6
              @ ^ [V_1: $i > $o] :
                  ~ ? [X8: $i] : ( V_1 @ X8 ) ) )
         => ( X6 @ X4 ) )
     => ! [X14: ( ( $i > $o ) > $o ) > $o] :
          ( ( ! [X18: ( $i > $o ) > $o] :
                ( ( X14 @ X18 )
               => ( X14
                  @ ^ [V_5: $i > $o] :
                    ? [X20: $i] :
                      ( ( V_5 @ X20 )
                      & ( X18
                        @ ^ [V_6: $i] :
                            ( ( V_5 @ V_6 )
                            & ( V_6 != X20 ) ) ) ) ) )
            & ( X14
              @ ^ [V_4: $i > $o] :
                  ~ ? [X16: $i] : ( V_4 @ X16 ) ) )
         => ( X14
            @ ^ [V_7: $i > $o] :
              ? [X22: $i] :
                ( ( V_7 @ X22 )
                & ( X4
                  @ ^ [V_8: $i] :
                      ( ( V_7 @ V_8 )
                      & ( V_8 != X22 ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: ( $i > $o ) > $o] :
        ( ! [X6: ( ( $i > $o ) > $o ) > $o] :
            ( ( ! [X10: ( $i > $o ) > $o] :
                  ( ( X6 @ X10 )
                 => ( X6
                    @ ^ [V_2: $i > $o] :
                      ? [X12: $i] :
                        ( ( V_2 @ X12 )
                        & ( X10
                          @ ^ [V_3: $i] :
                              ( ( V_2 @ V_3 )
                              & ( V_3 != X12 ) ) ) ) ) )
              & ( X6
                @ ^ [V_1: $i > $o] :
                    ~ ? [X8: $i] : ( V_1 @ X8 ) ) )
           => ( X6 @ X4 ) )
       => ! [X14: ( ( $i > $o ) > $o ) > $o] :
            ( ( ! [X18: ( $i > $o ) > $o] :
                  ( ( X14 @ X18 )
                 => ( X14
                    @ ^ [V_5: $i > $o] :
                      ? [X20: $i] :
                        ( ( V_5 @ X20 )
                        & ( X18
                          @ ^ [V_6: $i] :
                              ( ( V_5 @ V_6 )
                              & ( V_6 != X20 ) ) ) ) ) )
              & ( X14
                @ ^ [V_4: $i > $o] :
                    ~ ? [X16: $i] : ( V_4 @ X16 ) ) )
           => ( X14
              @ ^ [V_7: $i > $o] :
                ? [X22: $i] :
                  ( ( V_7 @ X22 )
                  & ( X4
                    @ ^ [V_8: $i] :
                        ( ( V_7 @ V_8 )
                        & ( V_8 != X22 ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

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

thf(zip_derived_cl1,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 @ '#sk1' ) ) )
     => ( !!
        @ ^ [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 )
                      & ( '#sk1'
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,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 @ '#sk1' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl4,plain,
    ! [X2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( !!
          @ ^ [Y0: ( $i > $o ) > $o] :
              ( ( X2 @ Y0 )
             => ( X2
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( Y0
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) )
        & ( X2
          @ ^ [Y0: $i > $o] :
              ( (~)
              @ ( ??
                @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
     => ( X2 @ '#sk1' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl5,plain,
    ( ( ( !!
        @ ^ [Y0: ( $i > $o ) > $o] :
            ( ( '#sk2' @ Y0 )
           => ( '#sk2'
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( Y0
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 ) ) ) ) ) ) ) )
      & ( '#sk2'
        @ ^ [Y0: $i > $o] :
            ( (~)
            @ ( ??
              @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
   => ( '#sk2' @ '#sk1' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl3,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 )
                    & ( '#sk1'
                      @ ^ [Y3: $i] :
                          ( ( Y1 @ Y3 )
                          & ( Y3 != Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ~ ( ( ( !!
          @ ^ [Y0: ( $i > $o ) > $o] :
              ( ( '#sk2' @ Y0 )
             => ( '#sk2'
                @ ^ [Y1: $i > $o] :
                    ( ??
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                        & ( Y0
                          @ ^ [Y3: $i] :
                              ( ( Y1 @ Y3 )
                              & ( Y3 != Y2 ) ) ) ) ) ) ) )
        & ( '#sk2'
          @ ^ [Y0: $i > $o] :
              ( (~)
              @ ( ??
                @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
     => ( '#sk2'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( '#sk1'
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl8,plain,
    ( ( !!
      @ ^ [Y0: ( $i > $o ) > $o] :
          ( ( '#sk2' @ Y0 )
         => ( '#sk2'
            @ ^ [Y1: $i > $o] :
                ( ??
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                    & ( Y0
                      @ ^ [Y3: $i] :
                          ( ( Y1 @ Y3 )
                          & ( Y3 != Y2 ) ) ) ) ) ) ) )
    & ( '#sk2'
      @ ^ [Y0: $i > $o] :
          ( (~)
          @ ( ??
            @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl12,plain,
    ( '#sk2'
    @ ^ [Y0: $i > $o] :
        ( (~)
        @ ( ??
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl11,plain,
    ( !!
    @ ^ [Y0: ( $i > $o ) > $o] :
        ( ( '#sk2' @ Y0 )
       => ( '#sk2'
          @ ^ [Y1: $i > $o] :
              ( ??
              @ ^ [Y2: $i] :
                  ( ( Y1 @ Y2 )
                  & ( Y0
                    @ ^ [Y3: $i] :
                        ( ( Y1 @ Y3 )
                        & ( Y3 != Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl14,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( '#sk2' @ X2 )
     => ( '#sk2'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( X2
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl19,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#sk2'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( X2
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl9,plain,
    ~ ( '#sk2'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( '#sk1'
                @ ^ [Y2: $i] :
                    ( ( Y0 @ Y2 )
                    & ( Y2 != Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl22,plain,
    ! [X0: ( $i > $o ) > $o] :
      ( ( ( ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( X0
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) )
       != ( ^ [Y0: $i > $o] :
              ( ??
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                  & ( '#sk1'
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y2 )
                        & ( Y2 != Y1 ) ) ) ) ) ) )
      | ~ ( '#sk2' @ X0 ) ),
    inference(ext_sup,[status(thm)],[zip_derived_cl19,zip_derived_cl9]) ).

thf(zip_derived_cl24,plain,
    ~ ( '#sk2'
      @ ^ [Y0: $i > $o] :
          ( '#sk1'
          @ ( ^ [Y1: $i > $o,Y2: $i] :
                ( Y1
                @ ( ^ [Y3: $i > $o,Y4: $i] : Y4
                  @ Y1
                  @ Y2 ) )
            @ Y0 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl25,plain,
    ~ ( '#sk2' @ '#sk1' ),
    inference(ho_norm,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl76,plain,
    ( ( ( !!
        @ ^ [Y0: ( $i > $o ) > $o] :
            ( ( '#sk2' @ Y0 )
           => ( '#sk2'
              @ ^ [Y1: $i > $o] :
                  ( ??
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                      & ( Y0
                        @ ^ [Y3: $i] :
                            ( ( Y1 @ Y3 )
                            & ( Y3 != Y2 ) ) ) ) ) ) ) )
      & $true )
   => $false ),
    inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl12,zip_derived_cl25]) ).

thf(zip_derived_cl77,plain,
    ( (~)
    @ ( !!
      @ ^ [Y0: ( $i > $o ) > $o] :
          ( ( '#sk2' @ Y0 )
         => ( '#sk2'
            @ ^ [Y1: $i > $o] :
                ( ??
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                    & ( Y0
                      @ ^ [Y3: $i] :
                          ( ( Y1 @ Y3 )
                          & ( Y3 != Y2 ) ) ) ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl78,plain,
    ~ ( !!
      @ ^ [Y0: ( $i > $o ) > $o] :
          ( ( '#sk2' @ Y0 )
         => ( '#sk2'
            @ ^ [Y1: $i > $o] :
                ( ??
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                    & ( Y0
                      @ ^ [Y3: $i] :
                          ( ( Y1 @ Y3 )
                          & ( Y3 != Y2 ) ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl77]) ).

thf(zip_derived_cl79,plain,
    ~ ( ( '#sk2' @ ( '#sk9' @ '#sk2' ) )
     => ( '#sk2'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( '#sk9' @ '#sk2'
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl81,plain,
    ~ ( '#sk2'
      @ ^ [Y0: $i > $o] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
              & ( '#sk9' @ '#sk2'
                @ ^ [Y2: $i] :
                    ( ( Y0 @ Y2 )
                    & ( Y2 != Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl80,plain,
    '#sk2' @ ( '#sk9' @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl19_001,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#sk2'
        @ ^ [Y0: $i > $o] :
            ( ??
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
                & ( X2
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y2 )
                      & ( Y2 != Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl82,plain,
    ( '#sk2'
    @ ^ [Y0: $i > $o] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( Y0 @ Y1 )
            & ( '#sk9' @ '#sk2'
              @ ^ [Y2: $i] :
                  ( ( Y0 @ Y2 )
                  & ( Y2 != Y1 ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl19]) ).

thf(zip_derived_cl84,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl81,zip_derived_cl82]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEV289^5 : 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.yFLLn1FG8k true
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 04:16:13 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36  % Number of cores: 8
% 0.22/0.36  % Python version: Python 3.6.8
% 0.22/0.36  % Running in HO mode
% 0.56/0.65  % Total configuration time : 828
% 0.56/0.65  % Estimated wc time : 1656
% 0.56/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.58/0.82  % Solved by lams/35_full_unif4.sh.
% 0.58/0.82  % done 20 iterations in 0.061s
% 0.58/0.82  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.58/0.82  % SZS output start Refutation
% See solution above
% 0.58/0.82  
% 0.58/0.82  
% 0.58/0.82  % Terminating...
% 0.60/0.86  % Runner terminated.
% 1.76/0.87  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------