TSTP Solution File: PHI004^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PHI004^4 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KIJKQnTZ4O true

% Computer : n001.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 12:58:48 EDT 2023

% Result   : Theorem 47.83s 6.86s
% Output   : Refutation 47.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   46 (  13 unt;   8 typ;   0 def)
%            Number of atoms       :  130 (  11 equ;  17 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  369 (  37   ~;  18   |;   4   &; 259   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   86 (  86   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   6 usr;   5 con; 0-3 aty)
%                                         (  27  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  126 (  60   ^;  66   !;   0   ?; 126   :)

% Comments : 
%------------------------------------------------------------------------------
thf(qML_i_type,type,
    qML_i: $tType ).

thf(qML_mu_type,type,
    qML_mu: $tType ).

thf(scott_P_type,type,
    scott_P: ( qML_mu > qML_i > $o ) > qML_i > $o ).

thf('#sk15_type',type,
    '#sk15': qML_mu ).

thf(scott_G_type,type,
    scott_G: qML_mu > qML_i > $o ).

thf('#sk14_type',type,
    '#sk14': qML_i ).

thf(scott_ess_QML_mu_type,type,
    scott_ess_QML_mu: ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).

thf('#l_lift17477_type',type,
    '#l_lift17477': ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).

thf(fact_0_G__def,axiom,
    ( scott_G
    = ( ^ [X: qML_mu,W: qML_i] :
        ! [Y: qML_mu > qML_i > $o] :
          ( ( scott_P @ Y @ W )
         => ( Y @ X @ W ) ) ) ) ).

thf(zip_derived_cl0,plain,
    ( scott_G
    = ( ^ [Y0: qML_mu,Y1: qML_i] :
          ( !!
          @ ^ [Y2: qML_mu > qML_i > $o] :
              ( ( scott_P @ Y2 @ Y1 )
             => ( Y2 @ Y0 @ Y1 ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_0_G__def]) ).

thf(zip_derived_cl22,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ( scott_G @ X2 @ X3 )
      = ( ^ [Y0: qML_mu,Y1: qML_i] :
            ( !!
            @ ^ [Y2: qML_mu > qML_i > $o] :
                ( ( scott_P @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ X2
        @ X3 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl23,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ( scott_G @ X2 @ X3 )
      = ( !!
        @ ^ [Y0: qML_mu > qML_i > $o] :
            ( ( scott_P @ Y0 @ X3 )
           => ( Y0 @ X2 @ X3 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl22]) ).

thf(conj_0,conjecture,
    ! [W3: qML_i,X2: qML_mu] :
      ( ~ ( scott_G @ X2 @ W3 )
      | ( scott_ess_QML_mu @ scott_G @ X2 @ W3 ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [W3: qML_i,X2: qML_mu] :
        ( ~ ( scott_G @ X2 @ W3 )
        | ( scott_ess_QML_mu @ scott_G @ X2 @ W3 ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: qML_i] :
          ( !!
          @ ^ [Y1: qML_mu] :
              ( ( (~) @ ( scott_G @ Y1 @ Y0 ) )
              | ( scott_ess_QML_mu @ scott_G @ Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl32,plain,
    ~ ( !!
      @ ^ [Y0: qML_mu] :
          ( ( (~) @ ( scott_G @ Y0 @ '#sk14' ) )
          | ( scott_ess_QML_mu @ scott_G @ Y0 @ '#sk14' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl33,plain,
    ~ ( ( (~) @ ( scott_G @ '#sk15' @ '#sk14' ) )
      | ( scott_ess_QML_mu @ scott_G @ '#sk15' @ '#sk14' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl35,plain,
    ~ ( scott_ess_QML_mu @ scott_G @ '#sk15' @ '#sk14' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).

thf(fact_4_ess__def,axiom,
    ( scott_ess_QML_mu
    = ( ^ [Phi: qML_mu > qML_i > $o,X: qML_mu,W: qML_i] :
          ( ! [Y: qML_mu > qML_i > $o] :
              ( ( Y @ X @ W )
             => ! [V2: qML_i,Z: qML_mu] :
                  ( ( Phi @ Z @ V2 )
                 => ( Y @ Z @ V2 ) ) )
          & ( Phi @ X @ W ) ) ) ) ).

thf(zip_derived_cl4,plain,
    ( scott_ess_QML_mu
    = ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
          ( ( !!
            @ ^ [Y3: qML_mu > qML_i > $o] :
                ( ( Y3 @ Y1 @ Y2 )
               => ( !!
                  @ ^ [Y4: qML_i] :
                      ( !!
                      @ ^ [Y5: qML_mu] :
                          ( ( Y0 @ Y5 @ Y4 )
                         => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
          & ( Y0 @ Y1 @ Y2 ) ) ) ),
    inference(cnf,[status(esa)],[fact_4_ess__def]) ).

thf(zip_derived_cl64,plain,
    ! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
      ( ( scott_ess_QML_mu @ X2 @ X3 @ X4 )
      = ( ^ [Y0: qML_mu > qML_i > $o,Y1: qML_mu,Y2: qML_i] :
            ( ( !!
              @ ^ [Y3: qML_mu > qML_i > $o] :
                  ( ( Y3 @ Y1 @ Y2 )
                 => ( !!
                    @ ^ [Y4: qML_i] :
                        ( !!
                        @ ^ [Y5: qML_mu] :
                            ( ( Y0 @ Y5 @ Y4 )
                           => ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
            & ( Y0 @ Y1 @ Y2 ) )
        @ X2
        @ X3
        @ X4 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl65,plain,
    ! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
      ( ( scott_ess_QML_mu @ X2 @ X3 @ X4 )
      = ( ( !!
          @ ^ [Y0: qML_mu > qML_i > $o] :
              ( ( Y0 @ X3 @ X4 )
             => ( !!
                @ ^ [Y1: qML_i] :
                    ( !!
                    @ ^ [Y2: qML_mu] :
                        ( ( X2 @ Y2 @ Y1 )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
        & ( X2 @ X3 @ X4 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl34,plain,
    scott_G @ '#sk15' @ '#sk14',
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).

thf(fact_5_A1b,axiom,
    ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
      ( ~ ( scott_P @ X3 @ W2 )
     => ( scott_P
        @ ^ [Y: qML_mu,Z: qML_i] :
            ~ ( X3 @ Y @ Z )
        @ W2 ) ) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: qML_i] :
        ( !!
        @ ^ [Y1: qML_mu > qML_i > $o] :
            ( ( (~) @ ( scott_P @ Y1 @ Y0 ) )
           => ( scott_P
              @ ^ [Y2: qML_mu,Y3: qML_i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
              @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_5_A1b]) ).

thf(zip_derived_cl36,plain,
    ! [X2: qML_i] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( ( (~) @ ( scott_P @ Y0 @ X2 ) )
         => ( scott_P
            @ ^ [Y1: qML_mu,Y2: qML_i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
            @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl37,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ( (~) @ ( scott_P @ X4 @ X2 ) )
     => ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl40,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ( scott_P @ X4 @ X2 )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(fact_2_A4,axiom,
    ! [W2: qML_i,X3: qML_mu > qML_i > $o] :
      ( ( scott_P @ X3 @ W2 )
     => ! [X_1: qML_i] : ( scott_P @ X3 @ X_1 ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: qML_i] :
        ( !!
        @ ^ [Y1: qML_mu > qML_i > $o] :
            ( ( scott_P @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: qML_i] : ( scott_P @ Y1 @ Y2 ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_2_A4]) ).

thf(zip_derived_cl16,plain,
    ! [X2: qML_i] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( ( scott_P @ Y0 @ X2 )
         => ( !!
            @ ^ [Y1: qML_i] : ( scott_P @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl17,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ( scott_P @ X4 @ X2 )
     => ( !!
        @ ^ [Y0: qML_i] : ( scott_P @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl20,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ~ ( scott_P @ X4 @ X2 )
      | ( !!
        @ ^ [Y0: qML_i] : ( scott_P @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl21,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o,X6: qML_i] :
      ( ( scott_P @ X4 @ X6 )
      | ~ ( scott_P @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl216,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o,X2: qML_i] :
      ( ( scott_P @ X1 @ X0 )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl21]) ).

thf(zip_derived_cl40_001,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ( scott_P @ X4 @ X2 )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl6397,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift17477' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl6417,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o,X2: qML_i] :
      ( ( scott_P @ X1 @ X0 )
      | ( scott_P @ ( '#l_lift17477' @ X1 ) @ X2 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl216,zip_derived_cl6397]) ).

thf(zip_derived_cl23_002,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ( scott_G @ X2 @ X3 )
      = ( !!
        @ ^ [Y0: qML_mu > qML_i > $o] :
            ( ( scott_P @ Y0 @ X3 )
           => ( Y0 @ X2 @ X3 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl212,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ~ ( scott_G @ X2 @ X3 )
      | ( !!
        @ ^ [Y0: qML_mu > qML_i > $o] :
            ( ( scott_P @ Y0 @ X3 )
           => ( Y0 @ X2 @ X3 ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl249,plain,
    ! [X2: qML_mu,X3: qML_i,X5: qML_mu > qML_i > $o] :
      ( ( ( scott_P @ X5 @ X3 )
       => ( X5 @ X2 @ X3 ) )
      | ~ ( scott_G @ X2 @ X3 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl212]) ).

thf(zip_derived_cl250,plain,
    ! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
      ( ( ( scott_P
          @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
          @ X1 )
       => ( (~) @ ( X0 @ X2 @ X1 ) ) )
      | ~ ( scott_G @ X2 @ X1 ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl249]) ).

thf(zip_derived_cl2670,plain,
    ! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
      ( ~ ( scott_P
          @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
          @ X1 )
      | ~ ( X0 @ X2 @ X1 )
      | ~ ( scott_G @ X2 @ X1 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl250]) ).

thf(zip_derived_cl6397_003,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift17477' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl6416,plain,
    ! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
      ( ~ ( scott_P @ ( '#l_lift17477' @ X0 ) @ X1 )
      | ~ ( X0 @ X2 @ X1 )
      | ~ ( scott_G @ X2 @ X1 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl2670,zip_derived_cl6397]) ).

thf(zip_derived_cl6422,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl23,zip_derived_cl35,zip_derived_cl65,zip_derived_cl34,zip_derived_cl6417,zip_derived_cl6416]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : PHI004^4 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KIJKQnTZ4O true
% 0.15/0.36  % Computer : n001.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun Aug 27 09:25:32 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  % Running portfolio for 300 s
% 0.15/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37  % Number of cores: 8
% 0.15/0.37  % Python version: Python 3.6.8
% 0.15/0.37  % Running in HO mode
% 0.23/0.68  % Total configuration time : 828
% 0.23/0.68  % Estimated wc time : 1656
% 0.23/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.23/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.93/0.81  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 47.83/6.86  % Solved by lams/20_acsne_simpl.sh.
% 47.83/6.86  % done 739 iterations in 6.038s
% 47.83/6.86  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 47.83/6.86  % SZS output start Refutation
% See solution above
% 47.83/6.86  
% 47.83/6.86  
% 47.83/6.86  % Terminating...
% 47.84/6.90  % Runner terminated.
% 47.84/6.91  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------