TSTP Solution File: SEV428^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV428^1 : TPTP v8.1.2. Released 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.KizK4TNpse true

% Computer : n009.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 20:00:45 EDT 2023

% Result   : Theorem 0.58s 0.83s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   54 (  14 unt;   8 typ;   0 def)
%            Number of atoms       :  176 (   6 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  443 (  20   ~;  15   |;  72   &; 317   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   99 (  99   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (   8 usr;   6 con; 0-2 aty)
%                                         (   2  !!;  10  ??;   0 @@+;   0 @@-)
%            Number of variables   :   92 (  72   ^;  11   !;   9   ?;  92   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_type,type,
    c: ( $i > $o ) > $o ).

thf('#form28_type',type,
    '#form28': $o ).

thf(eps_type,type,
    eps: ( $i > $o ) > $i ).

thf(setunion_type,type,
    setunion: ( ( $i > $o ) > $o ) > $i > $o ).

thf(epsio_type,type,
    epsio: ( ( $i > $o ) > $o ) > $i > $o ).

thf(choosenonempty_type,type,
    choosenonempty: ( ( $i > $o ) > $o ) > $i > $o ).

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

thf(a_type,type,
    a: $i ).

thf(choiceaxio,axiom,
    ! [P: ( $i > $o ) > $o] :
      ( ? [X: $i > $o] : ( P @ X )
     => ( P @ ( epsio @ P ) ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: ( $i > $o ) > $o] :
        ( ( ??
          @ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) )
       => ( Y0 @ ( epsio @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[choiceaxio]) ).

thf(zip_derived_cl11,plain,
    ! [X2: ( $i > $o ) > $o] :
      ( ( ??
        @ ^ [Y0: $i > $o] : ( X2 @ Y0 ) )
     => ( X2 @ ( epsio @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl19,plain,
    ( ( ??
      @ ^ [Y0: $i > $o] :
          ( ( Y0 @ ( eps @ Y0 ) )
          & ( c @ Y0 ) ) )
   => ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl28,plain,
    ( ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) ) )
    | ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( X2 @ ( eps @ X2 ) )
          & ( c @ X2 ) )
      | ( ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) )
          @ ( eps
            @ ( epsio
              @ ^ [Y0: $i > $o] :
                  ( ( Y0 @ ( eps @ Y0 ) )
                  & ( c @ Y0 ) ) ) ) )
        & ( c
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl33,plain,
    ( ~ '#form28'
    | ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl34,plain,
    ( ( epsio
      @ ^ [Y0: $i > $o] :
          ( ( Y0 @ ( eps @ Y0 ) )
          & ( c @ Y0 ) )
      @ ( eps
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) )
    | ~ '#form28' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl29_001,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( X2 @ ( eps @ X2 ) )
          & ( c @ X2 ) )
      | ( ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) )
          @ ( eps
            @ ( epsio
              @ ^ [Y0: $i > $o] :
                  ( ( Y0 @ ( eps @ Y0 ) )
                  & ( c @ Y0 ) ) ) ) )
        & ( c
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl32,plain,
    ( ~ ( ( '#sk1' @ ( eps @ '#sk1' ) )
        & ( c @ '#sk1' ) )
    | ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl29]) ).

thf(setuniond,axiom,
    ( setunion
    = ( ^ [C: ( $i > $o ) > $o,X: $i] :
        ? [Y: $i > $o] :
          ( ( Y @ X )
          & ( C @ Y ) ) ) ) ).

thf('0',plain,
    ( setunion
    = ( ^ [C: ( $i > $o ) > $o,X: $i] :
        ? [Y: $i > $o] :
          ( ( Y @ X )
          & ( C @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[setuniond]) ).

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

thf(ca,axiom,
    setunion @ c @ a ).

thf(zf_stmt_0,axiom,
    ? [X4: $i > $o] :
      ( ( c @ X4 )
      & ( X4 @ a ) ) ).

thf(zip_derived_cl2,plain,
    ( ??
    @ ^ [Y0: $i > $o] :
        ( ( c @ Y0 )
        & ( Y0 @ a ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl4,plain,
    ( ( c @ '#sk1' )
    & ( '#sk1' @ a ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl5,plain,
    c @ '#sk1',
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl38,plain,
    ( ~ ( ( '#sk1' @ ( eps @ '#sk1' ) )
        & $true )
    | ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl32,zip_derived_cl5]) ).

thf(zip_derived_cl39,plain,
    ( ~ ( '#sk1' @ ( eps @ '#sk1' ) )
    | ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl33_002,plain,
    ( ~ '#form28'
    | ( ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ ( eps
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl40,plain,
    ( '#form28'
    | ~ ( '#sk1' @ ( eps @ '#sk1' ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl33]) ).

thf(zip_derived_cl6,plain,
    '#sk1' @ a,
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(choiceax,axiom,
    ! [P: $i > $o] :
      ( ? [X: $i] : ( P @ X )
     => ( P @ ( eps @ P ) ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i > $o] :
        ( ( ??
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) )
       => ( Y0 @ ( eps @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[choiceax]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i > $o] :
      ( ( ??
        @ ^ [Y0: $i] : ( X2 @ Y0 ) )
     => ( X2 @ ( eps @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i > $o] :
      ( ~ ( ??
          @ ^ [Y0: $i] : ( X2 @ Y0 ) )
      | ( X2 @ ( eps @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl10,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( X2 @ X4 )
      | ( X2 @ ( eps @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl43,plain,
    ( ^ [Y0: $i] :
        ( '#sk1'
        @ ( ^ [Y1: $i] : Y1
          @ Y0 ) )
    @ ( eps
      @ ^ [Y0: $i] :
          ( '#sk1'
          @ ( ^ [Y1: $i] : Y1
            @ Y0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl10]) ).

thf(zip_derived_cl51,plain,
    '#sk1' @ ( eps @ '#sk1' ),
    inference(ho_norm,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl67,plain,
    '#form28',
    inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl51]) ).

thf(zip_derived_cl75,plain,
    ( epsio
    @ ^ [Y0: $i > $o] :
        ( ( Y0 @ ( eps @ Y0 ) )
        & ( c @ Y0 ) )
    @ ( eps
      @ ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl67]) ).

thf(choosenonemptyd,axiom,
    ( choosenonempty
    = ( ^ [C: ( $i > $o ) > $o] :
          ( epsio
          @ ^ [Y: $i > $o] :
              ( ( C @ Y )
              & ( Y @ ( eps @ Y ) ) ) ) ) ) ).

thf('2',plain,
    ( choosenonempty
    = ( ^ [C: ( $i > $o ) > $o] :
          ( epsio
          @ ^ [Y: $i > $o] :
              ( ( C @ Y )
              & ( Y @ ( eps @ Y ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[choosenonemptyd]) ).

thf('3',plain,
    ( choosenonempty
    = ( ^ [V_1: ( $i > $o ) > $o] :
          ( epsio
          @ ^ [V_2: $i > $o] :
              ( ( V_1 @ V_2 )
              & ( V_2 @ ( eps @ V_2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(conj,conjecture,
    ( ? [X: $i] : ( choosenonempty @ c @ X )
    & ( c @ ( choosenonempty @ c ) ) ) ).

thf(zf_stmt_1,conjecture,
    ( ? [X4: $i] :
        ( epsio
        @ ^ [V_1: $i > $o] :
            ( ( V_1 @ ( eps @ V_1 ) )
            & ( c @ V_1 ) )
        @ X4 )
    & ( c
      @ ( epsio
        @ ^ [V_2: $i > $o] :
            ( ( V_2 @ ( eps @ V_2 ) )
            & ( c @ V_2 ) ) ) ) ) ).

thf(zf_stmt_2,negated_conjecture,
    ~ ( ? [X4: $i] :
          ( epsio
          @ ^ [V_1: $i > $o] :
              ( ( V_1 @ ( eps @ V_1 ) )
              & ( c @ V_1 ) )
          @ X4 )
      & ( c
        @ ( epsio
          @ ^ [V_2: $i > $o] :
              ( ( V_2 @ ( eps @ V_2 ) )
              & ( c @ V_2 ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3,plain,
    ~ ( ( ??
        @ ^ [Y0: $i] :
            ( epsio
            @ ^ [Y1: $i > $o] :
                ( ( Y1 @ ( eps @ Y1 ) )
                & ( c @ Y1 ) )
            @ Y0 ) )
      & ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl17,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( epsio
            @ ^ [Y1: $i > $o] :
                ( ( Y1 @ ( eps @ Y1 ) )
                & ( c @ Y1 ) )
            @ Y0 ) )
    | ~ ( c
        @ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i] :
      ( ~ ( epsio
          @ ^ [Y0: $i > $o] :
              ( ( Y0 @ ( eps @ Y0 ) )
              & ( c @ Y0 ) )
          @ X2 )
      | ~ ( c
          @ ( epsio
            @ ^ [Y0: $i > $o] :
                ( ( Y0 @ ( eps @ Y0 ) )
                & ( c @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl35,plain,
    ( ( c
      @ ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) ) ) )
    | ~ '#form28' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl67_003,plain,
    '#form28',
    inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl51]) ).

thf(zip_derived_cl73,plain,
    ( c
    @ ( epsio
      @ ^ [Y0: $i > $o] :
          ( ( Y0 @ ( eps @ Y0 ) )
          & ( c @ Y0 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl35,zip_derived_cl67]) ).

thf(zip_derived_cl74,plain,
    ! [X2: $i] :
      ~ ( epsio
        @ ^ [Y0: $i > $o] :
            ( ( Y0 @ ( eps @ Y0 ) )
            & ( c @ Y0 ) )
        @ X2 ),
    inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl73]) ).

thf(zip_derived_cl76,plain,
    $false,
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl74]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEV428^1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KizK4TNpse true
% 0.14/0.35  % Computer : n009.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 : Thu Aug 24 02:25:51 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.53/0.64  % Total configuration time : 828
% 0.53/0.64  % Estimated wc time : 1656
% 0.53/0.64  % Estimated cpu time (8 cpus) : 207.0
% 0.53/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.74  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.58/0.83  % Solved by lams/20_acsne_simpl.sh.
% 0.58/0.83  % done 15 iterations in 0.041s
% 0.58/0.83  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.58/0.83  % SZS output start Refutation
% See solution above
% 0.58/0.83  
% 0.58/0.83  
% 0.58/0.83  % Terminating...
% 1.63/0.87  % Runner terminated.
% 1.63/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------