TSTP Solution File: PHI005^4 by Zipperpin---2.1.9999

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%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PHI005^4 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Rj0tvYFgdU true

% Computer : n004.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 12:58:49 EDT 2023

% Result   : Theorem 59.01s 8.27s
% Output   : Refutation 59.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  103 (  27 unt;  13 typ;   0 def)
%            Number of atoms       :  346 (  21 equ;  39 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  973 (  75   ~;  28   |;  18   &; 691   @)
%                                         (   0 <=>;  70  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  212 ( 212   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  11 usr;   6 con; 0-3 aty)
%                                         (  85  !!;   6  ??;   0 @@+;   0 @@-)
%            Number of variables   :  330 ( 164   ^; 163   !;   3   ?; 330   :)

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

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

thf('#l_lift20063_type',type,
    '#l_lift20063': qML_mu > qML_i > $o ).

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

thf('#sk103_type',type,
    '#sk103': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).

thf('#l_lift20060_type',type,
    '#l_lift20060': ( qML_mu > qML_i > $o ) > qML_mu > qML_i > $o ).

thf('#sk316_type',type,
    '#sk316': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).

thf('#sk118_type',type,
    '#sk118': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_mu ).

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

thf('#sk46_type',type,
    '#sk46': qML_i ).

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

thf(scott_NE_QML_mu_type,type,
    scott_NE_QML_mu: qML_mu > qML_i > $o ).

thf('#sk301_type',type,
    '#sk301': ( qML_mu > qML_i > $o ) > ( qML_mu > qML_i > $o ) > qML_i ).

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_cl18,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_cl19,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_cl18]) ).

thf(fact_6_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_cl6,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_6_ess__def]) ).

thf(zip_derived_cl62,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_cl6]) ).

thf(zip_derived_cl63,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_cl62]) ).

thf(fact_3_A1b,axiom,
    ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
      ( ~ ( scott_P @ X2 @ W2 )
     => ( scott_P
        @ ^ [Y: qML_mu,Z: qML_i] :
            ~ ( X2 @ Y @ Z )
        @ W2 ) ) ).

thf(zip_derived_cl3,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_3_A1b]) ).

thf(zip_derived_cl22,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_cl3]) ).

thf(zip_derived_cl23,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_cl22]) ).

thf(zip_derived_cl26,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_cl23]) ).

thf(fact_2_A4,axiom,
    ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
      ( ( scott_P @ X2 @ W2 )
     => ! [X_1: qML_i] : ( scott_P @ X2 @ 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_cl12,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_cl13,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_cl12]) ).

thf(zip_derived_cl16,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_cl13]) ).

thf(zip_derived_cl17,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_cl16]) ).

thf(zip_derived_cl203,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o,X2: qML_i] :
      ( ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 )
      | ( scott_P @ X1 @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl17]) ).

thf(zip_derived_cl26_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_cl23]) ).

thf(zip_derived_cl5834,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift20060' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl5862,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o,X2: qML_i] :
      ( ( scott_P @ ( '#l_lift20060' @ X1 ) @ X0 )
      | ( scott_P @ X1 @ X2 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl203,zip_derived_cl5834]) ).

thf(zip_derived_cl19_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_cl18]) ).

thf(zip_derived_cl199,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_cl19]) ).

thf(zip_derived_cl209,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_cl199]) ).

thf(zip_derived_cl210,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_cl209]) ).

thf(zip_derived_cl3218,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_cl210]) ).

thf(zip_derived_cl5834_003,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift20060' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl5864,plain,
    ! [X0: qML_mu > qML_i > $o,X1: qML_i,X2: qML_mu] :
      ( ~ ( scott_P @ ( '#l_lift20060' @ X0 ) @ X1 )
      | ~ ( X0 @ X2 @ X1 )
      | ~ ( scott_G @ X2 @ X1 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl3218,zip_derived_cl5834]) ).

thf(fact_4_A2,axiom,
    ! [W2: qML_i,X2: qML_mu > qML_i > $o,Xa: qML_mu > qML_i > $o] :
      ( ( ! [V: qML_i,Xb: qML_mu] :
            ( ( X2 @ Xb @ V )
           => ( Xa @ Xb @ V ) )
        & ( scott_P @ X2 @ W2 ) )
     => ( scott_P @ Xa @ W2 ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: qML_i] :
        ( !!
        @ ^ [Y1: qML_mu > qML_i > $o] :
            ( !!
            @ ^ [Y2: qML_mu > qML_i > $o] :
                ( ( ( !!
                    @ ^ [Y3: qML_i] :
                        ( !!
                        @ ^ [Y4: qML_mu] :
                            ( ( Y1 @ Y4 @ Y3 )
                           => ( Y2 @ Y4 @ Y3 ) ) ) )
                  & ( scott_P @ Y1 @ Y0 ) )
               => ( scott_P @ Y2 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_4_A2]) ).

thf(zip_derived_cl64,plain,
    ! [X2: qML_i] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( !!
          @ ^ [Y1: qML_mu > qML_i > $o] :
              ( ( ( !!
                  @ ^ [Y2: qML_i] :
                      ( !!
                      @ ^ [Y3: qML_mu] :
                          ( ( Y0 @ Y3 @ Y2 )
                         => ( Y1 @ Y3 @ Y2 ) ) ) )
                & ( scott_P @ Y0 @ X2 ) )
             => ( scott_P @ Y1 @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

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

thf(zip_derived_cl67,plain,
    ! [X0: qML_i] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( ( ( !!
              @ ^ [Y1: qML_i] :
                  ( !!
                  @ ^ [Y2: qML_mu] :
                      ( ( scott_NE_QML_mu @ Y2 @ Y1 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( scott_P @ scott_NE_QML_mu @ X0 ) )
         => ( scott_P @ Y0 @ X0 ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl83,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ( ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_NE_QML_mu @ Y1 @ Y0 )
                 => ( X2 @ Y1 @ Y0 ) ) ) )
        & ( scott_P @ scott_NE_QML_mu @ X0 ) )
     => ( scott_P @ X2 @ X0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl84,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_NE_QML_mu @ Y1 @ Y0 )
                 => ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
        & ( scott_P @ scott_NE_QML_mu @ X0 ) )
     => ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl83]) ).

thf(fact_5_A5,axiom,
    ! [X_1: qML_i] : ( scott_P @ scott_NE_QML_mu @ X_1 ) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: qML_i] : ( scott_P @ scott_NE_QML_mu @ Y0 ) ),
    inference(cnf,[status(esa)],[fact_5_A5]) ).

thf(zip_derived_cl11,plain,
    ! [X2: qML_i] : ( scott_P @ scott_NE_QML_mu @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl117,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_NE_QML_mu @ Y1 @ Y0 )
                 => ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
        & $true )
     => ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl84,zip_derived_cl11]) ).

thf(zip_derived_cl118,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( !!
        @ ^ [Y0: qML_i] :
            ( !!
            @ ^ [Y1: qML_mu] :
                ( ( scott_NE_QML_mu @ Y1 @ Y0 )
               => ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
     => ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl117]) ).

thf(zip_derived_cl119,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ~ ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_NE_QML_mu @ Y1 @ Y0 )
                 => ( (~) @ ( X1 @ Y1 @ Y0 ) ) ) ) )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl118]) ).

thf(zip_derived_cl120,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ~ ( !!
          @ ^ [Y0: qML_mu] :
              ( ( scott_NE_QML_mu @ Y0 @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
             => ( (~) @ ( X1 @ Y0 @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) ) ) ) )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl119]) ).

thf(zip_derived_cl121,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ~ ( ( scott_NE_QML_mu @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
         => ( (~) @ ( X1 @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) ) ) )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl120]) ).

thf(zip_derived_cl122,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( scott_NE_QML_mu @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl5834_004,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift20060' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl5842,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( scott_NE_QML_mu @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
      | ( scott_P @ ( '#l_lift20060' @ X1 ) @ X0 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl122,zip_derived_cl5834]) ).

thf(zip_derived_cl123,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( X1 @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
      | ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl5834_005,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift20060' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl5843,plain,
    ! [X0: qML_i,X1: qML_mu > qML_i > $o] :
      ( ( X1 @ ( '#sk316' @ X1 @ scott_NE_QML_mu ) @ ( '#sk301' @ X1 @ scott_NE_QML_mu ) )
      | ( scott_P @ ( '#l_lift20060' @ X1 ) @ X0 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl123,zip_derived_cl5834]) ).

thf(fact_8_NE__def,axiom,
    ( scott_NE_QML_mu
    = ( ^ [X: qML_mu,W: qML_i] :
        ! [Y: qML_mu > qML_i > $o] :
          ( ( scott_ess_QML_mu @ Y @ X @ W )
         => ! [V2: qML_i] :
            ? [Z: qML_mu] : ( Y @ Z @ V2 ) ) ) ) ).

thf(zip_derived_cl8,plain,
    ( scott_NE_QML_mu
    = ( ^ [Y0: qML_mu,Y1: qML_i] :
          ( !!
          @ ^ [Y2: qML_mu > qML_i > $o] :
              ( ( scott_ess_QML_mu @ Y2 @ Y0 @ Y1 )
             => ( !!
                @ ^ [Y3: qML_i] :
                    ( ??
                    @ ^ [Y4: qML_mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_8_NE__def]) ).

thf(zip_derived_cl20,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ( scott_NE_QML_mu @ X2 @ X3 )
      = ( ^ [Y0: qML_mu,Y1: qML_i] :
            ( !!
            @ ^ [Y2: qML_mu > qML_i > $o] :
                ( ( scott_ess_QML_mu @ Y2 @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y3: qML_i] :
                      ( ??
                      @ ^ [Y4: qML_mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) )
        @ X2
        @ X3 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl21,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ( scott_NE_QML_mu @ X2 @ X3 )
      = ( !!
        @ ^ [Y0: qML_mu > qML_i > $o] :
            ( ( scott_ess_QML_mu @ Y0 @ X2 @ X3 )
           => ( !!
              @ ^ [Y1: qML_i] :
                  ( ??
                  @ ^ [Y2: qML_mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl20]) ).

thf(fact_1_A3,axiom,
    ! [X_1: qML_i] : ( scott_P @ scott_G @ X_1 ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: qML_i] : ( scott_P @ scott_G @ Y0 ) ),
    inference(cnf,[status(esa)],[fact_1_A3]) ).

thf(zip_derived_cl10,plain,
    ! [X2: qML_i] : ( scott_P @ scott_G @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl65_006,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( ( ( !!
              @ ^ [Y1: qML_i] :
                  ( !!
                  @ ^ [Y2: qML_mu] :
                      ( ( X4 @ Y2 @ Y1 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( scott_P @ X4 @ X2 ) )
         => ( scott_P @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl68,plain,
    ! [X0: qML_i] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( ( ( !!
              @ ^ [Y1: qML_i] :
                  ( !!
                  @ ^ [Y2: qML_mu] :
                      ( ( scott_G @ Y2 @ Y1 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( scott_P @ scott_G @ X0 ) )
         => ( scott_P @ Y0 @ X0 ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl97,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ( ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_G @ Y1 @ Y0 )
                 => ( X2 @ Y1 @ Y0 ) ) ) )
        & ( scott_P @ scott_G @ X0 ) )
     => ( scott_P @ X2 @ X0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl10_007,plain,
    ! [X2: qML_i] : ( scott_P @ scott_G @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl101,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ( ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_G @ Y1 @ Y0 )
                 => ( X2 @ Y1 @ Y0 ) ) ) )
        & $true )
     => ( scott_P @ X2 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl97,zip_derived_cl10]) ).

thf(zip_derived_cl102,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ( !!
        @ ^ [Y0: qML_i] :
            ( !!
            @ ^ [Y1: qML_mu] :
                ( ( scott_G @ Y1 @ Y0 )
               => ( X2 @ Y1 @ Y0 ) ) ) )
     => ( scott_P @ X2 @ X0 ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl101]) ).

thf(zip_derived_cl103,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ~ ( !!
          @ ^ [Y0: qML_i] :
              ( !!
              @ ^ [Y1: qML_mu] :
                  ( ( scott_G @ Y1 @ Y0 )
                 => ( X2 @ Y1 @ Y0 ) ) ) )
      | ( scott_P @ X2 @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).

thf(zip_derived_cl104,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ~ ( !!
          @ ^ [Y0: qML_mu] :
              ( ( scott_G @ Y0 @ ( '#sk103' @ scott_G @ X2 ) )
             => ( X2 @ Y0 @ ( '#sk103' @ scott_G @ X2 ) ) ) )
      | ( scott_P @ X2 @ X0 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl103]) ).

thf(zip_derived_cl105,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ~ ( ( scott_G @ ( '#sk118' @ scott_G @ X2 ) @ ( '#sk103' @ scott_G @ X2 ) )
         => ( X2 @ ( '#sk118' @ scott_G @ X2 ) @ ( '#sk103' @ scott_G @ X2 ) ) )
      | ( scott_P @ X2 @ X0 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl104]) ).

thf(zip_derived_cl107,plain,
    ! [X0: qML_i,X2: qML_mu > qML_i > $o] :
      ( ~ ( X2 @ ( '#sk118' @ scott_G @ X2 ) @ ( '#sk103' @ scott_G @ X2 ) )
      | ( scott_P @ X2 @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).

thf(fact_7_A1a,axiom,
    ! [W2: qML_i,X2: qML_mu > qML_i > $o] :
      ( ( scott_P
        @ ^ [Y: qML_mu,Z: qML_i] :
            ~ ( X2 @ Y @ Z )
        @ W2 )
     => ~ ( scott_P @ X2 @ W2 ) ) ).

thf(zip_derived_cl7,plain,
    ( !!
    @ ^ [Y0: qML_i] :
        ( !!
        @ ^ [Y1: qML_mu > qML_i > $o] :
            ( ( scott_P
              @ ^ [Y2: qML_mu,Y3: qML_i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
              @ Y0 )
           => ( (~) @ ( scott_P @ Y1 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_7_A1a]) ).

thf(zip_derived_cl47,plain,
    ! [X2: qML_i] :
      ( !!
      @ ^ [Y0: qML_mu > qML_i > $o] :
          ( ( scott_P
            @ ^ [Y1: qML_mu,Y2: qML_i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
            @ X2 )
         => ( (~) @ ( scott_P @ Y0 @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl48,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ( scott_P
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
     => ( (~) @ ( scott_P @ X4 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl52,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ~ ( scott_P
          @ ^ [Y0: qML_mu,Y1: qML_i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
          @ X2 )
      | ~ ( scott_P @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl5834_008,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift20060' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl5837,plain,
    ! [X2: qML_i,X4: qML_mu > qML_i > $o] :
      ( ~ ( scott_P @ ( '#l_lift20060' @ X4 ) @ X2 )
      | ~ ( scott_P @ X4 @ X2 ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl52,zip_derived_cl5834]) ).

thf(zip_derived_cl5834_009,plain,
    ! [X4: qML_mu > qML_i > $o,X5: qML_mu,X6: qML_i] :
      ( ( '#l_lift20060' @ X4 @ X5 @ X6 )
      = ( (~) @ ( X4 @ X5 @ X6 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl63_010,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_cl62]) ).

thf(zip_derived_cl223,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(eq_elim,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl465,plain,
    ! [X2: qML_mu > qML_i > $o,X3: qML_mu,X4: qML_i] :
      ( ( X2 @ X3 @ X4 )
      | ~ ( scott_ess_QML_mu @ X2 @ X3 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl223]) ).

thf(conj_0,conjecture,
    ! [W3: qML_i,V: qML_i] :
    ? [X2: qML_mu] : ( scott_G @ X2 @ V ) ).

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

thf(zip_derived_cl9,plain,
    ~ ( !!
      @ ^ [Y0: qML_i] :
          ( !!
          @ ^ [Y1: qML_i] :
              ( ??
              @ ^ [Y2: qML_mu] : ( scott_G @ Y2 @ Y1 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl44,plain,
    ~ ( !!
      @ ^ [Y0: qML_i] :
          ( ??
          @ ^ [Y1: qML_mu] : ( scott_G @ Y1 @ Y0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl45,plain,
    ~ ( ??
      @ ^ [Y0: qML_mu] : ( scott_G @ Y0 @ '#sk46' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl46,plain,
    ! [X2: qML_mu] :
      ~ ( scott_G @ X2 @ '#sk46' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl512,plain,
    ! [X0: qML_mu,X1: qML_i] :
      ~ ( scott_ess_QML_mu
        @ ^ [Y0: qML_mu,Y1: qML_i] :
            ( scott_G
            @ ( ^ [Y2: qML_mu,Y3: qML_i] : Y2
              @ Y0
              @ Y1 )
            @ ( ^ [Y2: qML_mu,Y3: qML_i] : '#sk46'
              @ Y0
              @ Y1 ) )
        @ X0
        @ X1 ),
    inference('sup-',[status(thm)],[zip_derived_cl465,zip_derived_cl46]) ).

thf(zip_derived_cl556,plain,
    ! [X0: qML_mu,X1: qML_i] :
      ~ ( scott_ess_QML_mu
        @ ^ [Y0: qML_mu,Y1: qML_i] : ( scott_G @ Y0 @ '#sk46' )
        @ X0
        @ X1 ),
    inference(ho_norm,[status(thm)],[zip_derived_cl512]) ).

thf(zip_derived_cl5856,plain,
    ! [X2: qML_mu,X3: qML_i] :
      ( ( '#l_lift20063' @ X2 @ X3 )
      = ( scott_G @ X2 @ '#sk46' ) ),
    define([status(thm)]) ).

thf(zip_derived_cl46_011,plain,
    ! [X2: qML_mu] :
      ~ ( scott_G @ X2 @ '#sk46' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl5865,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl19,zip_derived_cl63,zip_derived_cl5862,zip_derived_cl5864,zip_derived_cl5842,zip_derived_cl5843,zip_derived_cl21,zip_derived_cl10,zip_derived_cl107,zip_derived_cl5837,zip_derived_cl5834,zip_derived_cl5856,zip_derived_cl46]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : PHI005^4 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Rj0tvYFgdU true
% 0.14/0.36  % Computer : n004.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 : Sun Aug 27 08:48:37 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.70  % Total configuration time : 828
% 0.22/0.70  % Estimated wc time : 1656
% 0.22/0.70  % Estimated cpu time (8 cpus) : 207.0
% 1.00/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.00/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.00/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.00/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.00/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.00/0.78  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.00/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.00/0.78  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 59.01/8.27  % Solved by lams/20_acsne_simpl.sh.
% 59.01/8.27  % done 426 iterations in 7.439s
% 59.01/8.27  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 59.01/8.27  % SZS output start Refutation
% See solution above
% 59.01/8.27  
% 59.01/8.27  
% 60.02/8.28  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 60.02/8.29  % Terminating...
% 60.03/8.42  % Runner terminated.
% 60.07/8.43  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------