TSTP Solution File: SET752^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET752^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HpO9dVO4I0 true

% Computer : n025.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 16:15:50 EDT 2023

% Result   : Theorem 1.65s 0.82s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  100 (  22 unt;  10 typ;   0 def)
%            Number of atoms       :  400 ( 141 equ;   0 cnn)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  735 (  93   ~; 146   |;  80   &; 346   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  10 usr;   8 con; 0-3 aty)
%                                         (   6  !!;  64  ??;   0 @@+;   0 @@-)
%            Number of variables   :  138 ( 104   ^;  25   !;   9   ?; 138   :)

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

thf('#sk8_type',type,
    '#sk8': $i ).

thf(union_type,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#_fresh_sk4_type',type,
    '#_fresh_sk4': $i ).

thf('#sk5_type',type,
    '#sk5': $i ).

thf('#sk7_type',type,
    '#sk7': $i ).

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

thf(fun_image_type,type,
    fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).

thf('#form6_type',type,
    '#form6': $o ).

thf('#sk3_type',type,
    '#sk3': $i > $i ).

thf(fun_image,axiom,
    ( fun_image
    = ( ^ [F: $i > $i,A: $i > $o,Y: $i] :
        ? [X: $i] :
          ( ( Y
            = ( F @ X ) )
          & ( A @ X ) ) ) ) ).

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

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

thf(union,axiom,
    ( union
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ) ).

thf('2',plain,
    ( union
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[union]) ).

thf('3',plain,
    ( union
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          | ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    ! [X: $i > $o,Y: $i > $o,F: $i > $i] :
      ( ( fun_image @ F @ ( union @ X @ Y ) )
      = ( union @ ( fun_image @ F @ X ) @ ( fun_image @ F @ Y ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $o,X6: $i > $o,X8: $i > $i] :
      ( ( ^ [V_1: $i] :
          ? [X10: $i] :
            ( ( ( X6 @ X10 )
              | ( X4 @ X10 ) )
            & ( V_1
              = ( X8 @ X10 ) ) ) )
      = ( ^ [V_2: $i] :
            ( ? [X14: $i] :
                ( ( X6 @ X14 )
                & ( V_2
                  = ( X8 @ X14 ) ) )
            | ? [X12: $i] :
                ( ( X4 @ X12 )
                & ( V_2
                  = ( X8 @ X12 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $o,X6: $i > $o,X8: $i > $i] :
        ( ( ^ [V_1: $i] :
            ? [X10: $i] :
              ( ( ( X6 @ X10 )
                | ( X4 @ X10 ) )
              & ( V_1
                = ( X8 @ X10 ) ) ) )
        = ( ^ [V_2: $i] :
              ( ? [X14: $i] :
                  ( ( X6 @ X14 )
                  & ( V_2
                    = ( X8 @ X14 ) ) )
              | ? [X12: $i] :
                  ( ( X4 @ X12 )
                  & ( V_2
                    = ( X8 @ X12 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

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

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i > $i] :
              ( ( ^ [Y2: $i] :
                    ( ??
                    @ ^ [Y3: $i] :
                        ( ( ( Y0 @ Y3 )
                          | ( '#sk1' @ Y3 ) )
                        & ( Y2
                          = ( Y1 @ Y3 ) ) ) ) )
              = ( ^ [Y2: $i] :
                    ( ( ??
                      @ ^ [Y3: $i] :
                          ( ( Y0 @ Y3 )
                          & ( Y2
                            = ( Y1 @ Y3 ) ) ) )
                    | ( ??
                      @ ^ [Y3: $i] :
                          ( ( '#sk1' @ Y3 )
                          & ( Y2
                            = ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: $i > $i] :
          ( ( ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i] :
                    ( ( ( '#sk2' @ Y2 )
                      | ( '#sk1' @ Y2 ) )
                    & ( Y1
                      = ( Y0 @ Y2 ) ) ) ) )
          = ( ^ [Y1: $i] :
                ( ( ??
                  @ ^ [Y2: $i] :
                      ( ( '#sk2' @ Y2 )
                      & ( Y1
                        = ( Y0 @ Y2 ) ) ) )
                | ( ??
                  @ ^ [Y2: $i] :
                      ( ( '#sk1' @ Y2 )
                      & ( Y1
                        = ( Y0 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ( ( ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( ( '#sk2' @ Y1 )
                | ( '#sk1' @ Y1 ) )
              & ( Y0
                = ( '#sk3' @ Y1 ) ) ) ) )
   != ( ^ [Y0: $i] :
          ( ( ??
            @ ^ [Y1: $i] :
                ( ( '#sk2' @ Y1 )
                & ( Y0
                  = ( '#sk3' @ Y1 ) ) ) )
          | ( ??
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y1 )
                & ( Y0
                  = ( '#sk3' @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ( ( ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( ( '#sk2' @ Y1 )
                | ( '#sk1' @ Y1 ) )
              & ( Y0
                = ( '#sk3' @ Y1 ) ) ) ) )
   != ( ^ [Y0: $i] :
          ( ( ??
            @ ^ [Y1: $i] :
                ( ( '#sk2' @ Y1 )
                & ( Y0
                  = ( '#sk3' @ Y1 ) ) ) )
          | ( ??
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y1 )
                & ( Y0
                  = ( '#sk3' @ Y1 ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ( ( ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i] :
              ( ( ( '#sk2' @ Y1 )
                | ( '#sk1' @ Y1 ) )
              & ( Y0
                = ( '#sk3' @ Y1 ) ) ) )
      @ '#_fresh_sk4' )
   != ( ^ [Y0: $i] :
          ( ( ??
            @ ^ [Y1: $i] :
                ( ( '#sk2' @ Y1 )
                & ( Y0
                  = ( '#sk3' @ Y1 ) ) ) )
          | ( ??
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y1 )
                & ( Y0
                  = ( '#sk3' @ Y1 ) ) ) ) )
      @ '#_fresh_sk4' ) ),
    inference(neg_ext_simpl,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl6,plain,
    ( ( ??
      @ ^ [Y0: $i] :
          ( ( ( '#sk2' @ Y0 )
            | ( '#sk1' @ Y0 ) )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
   != ( ( ??
        @ ^ [Y0: $i] :
            ( ( '#sk2' @ Y0 )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) )
      | ( ??
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ Y0 )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl7,plain,
    ( ( ??
      @ ^ [Y0: $i] :
          ( ( ( '#sk2' @ Y0 )
            | ( '#sk1' @ Y0 ) )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl9,plain,
    ( ( ( ( '#sk2' @ '#sk5' )
        | ( '#sk1' @ '#sk5' ) )
      & ( '#_fresh_sk4'
        = ( '#sk3' @ '#sk5' ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl10,plain,
    ( ( '#sk2' @ '#sk5' )
    | ( '#sk1' @ '#sk5' )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl12,plain,
    ( ~ '#form6'
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl13,plain,
    ( ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ~ '#form6' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl18,plain,
    ( ( ( '#sk2' @ '#sk7' )
      & ( '#_fresh_sk4'
        = ( '#sk3' @ '#sk7' ) ) )
    | ~ '#form6'
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl20,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl22,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ~ '#form6' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl23,plain,
    ( ( ( '#sk1' @ '#sk8' )
      & ( '#_fresh_sk4'
        = ( '#sk3' @ '#sk8' ) ) )
    | ~ '#form6'
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl27,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk8' ) )
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl29,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk8' ) )
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ~ '#form6' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl10_001,plain,
    ( ( '#sk2' @ '#sk5' )
    | ( '#sk1' @ '#sk5' )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl12_002,plain,
    ( ~ '#form6'
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl14,plain,
    ( '#form6'
    | ( '#sk2' @ '#sk5' )
    | ( '#sk1' @ '#sk5' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl10,zip_derived_cl12]) ).

thf(zip_derived_cl17,plain,
    ( ( '#sk2' @ '#sk5' )
    | ( '#sk1' @ '#sk5' )
    | '#form6' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl11,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk5' ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl15,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk5' ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl12_003,plain,
    ( ~ '#form6'
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl16,plain,
    ( '#form6'
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk5' ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl15,zip_derived_cl12]) ).

thf(zip_derived_cl6_004,plain,
    ( ( ??
      @ ^ [Y0: $i] :
          ( ( ( '#sk2' @ Y0 )
            | ( '#sk1' @ Y0 ) )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
   != ( ( ??
        @ ^ [Y0: $i] :
            ( ( '#sk2' @ Y0 )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) )
      | ( ??
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ Y0 )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl8,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( ( ( '#sk2' @ Y0 )
              | ( '#sk1' @ Y0 ) )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) )
    | ~ ( ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk2' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) )
        | ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk1' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl30,plain,
    ( '#form6'
    | ~ ( ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk2' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) )
        | ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk1' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl31,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( ( '#sk2' @ Y0 )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) )
    | '#form6' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl35,plain,
    ! [X2: $i] :
      ( ~ ( ( '#sk2' @ X2 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ X2 ) ) )
      | '#form6' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | '#form6' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl8_005,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( ( ( '#sk2' @ Y0 )
              | ( '#sk1' @ Y0 ) )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) )
    | ~ ( ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk2' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) )
        | ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk1' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl30_006,plain,
    ( '#form6'
    | ~ ( ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk2' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) )
        | ( ??
          @ ^ [Y0: $i] :
              ( ( '#sk1' @ Y0 )
              & ( '#_fresh_sk4'
                = ( '#sk3' @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl12_007,plain,
    ( ~ '#form6'
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl33,plain,
    ( ~ '#form6'
    | ~ ( ??
        @ ^ [Y0: $i] :
            ( ( ( '#sk2' @ Y0 )
              | ( '#sk1' @ Y0 ) )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl8,zip_derived_cl30,zip_derived_cl12]) ).

thf(zip_derived_cl34,plain,
    ! [X2: $i] :
      ( ~ ( ( ( '#sk2' @ X2 )
            | ( '#sk1' @ X2 ) )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ X2 ) ) )
      | ~ '#form6' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl37,plain,
    ! [X2: $i] :
      ( ~ ( ( '#sk2' @ X2 )
          | ( '#sk1' @ X2 ) )
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl40,plain,
    ! [X2: $i] :
      ( ~ ( ( '#sk2' @ X2 )
          | ( '#sk1' @ X2 ) )
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | ~ '#form6' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl41,plain,
    ! [X2: $i] :
      ( ~ ( '#sk2' @ X2 )
      | ~ '#form6'
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl61,plain,
    ! [X2: $i] :
      ( ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | ~ ( '#sk2' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl43,zip_derived_cl41]) ).

thf(zip_derived_cl63,plain,
    ( ( '#_fresh_sk4' != '#_fresh_sk4' )
    | '#form6'
    | ~ ( '#sk2' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl61]) ).

thf(zip_derived_cl67,plain,
    ( ~ ( '#sk2' @ '#sk5' )
    | '#form6' ),
    inference(simplify,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl71,plain,
    ( '#form6'
    | ( '#sk1' @ '#sk5' )
    | '#form6' ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl67]) ).

thf(zip_derived_cl74,plain,
    ( ( '#sk1' @ '#sk5' )
    | '#form6' ),
    inference(simplify,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl16_008,plain,
    ( '#form6'
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk5' ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl15,zip_derived_cl12]) ).

thf(zip_derived_cl32,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ Y0 )
            & ( '#_fresh_sk4'
              = ( '#sk3' @ Y0 ) ) ) )
    | '#form6' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i] :
      ( ~ ( ( '#sk1' @ X2 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ X2 ) ) )
      | '#form6' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ X2 )
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ X2 )
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | '#form6' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ X2 )
      | ~ '#form6'
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl78,plain,
    ! [X2: $i] :
      ( ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | ~ ( '#sk1' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl44,zip_derived_cl42]) ).

thf(zip_derived_cl80,plain,
    ( ( '#_fresh_sk4' != '#_fresh_sk4' )
    | '#form6'
    | ~ ( '#sk1' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl78]) ).

thf(zip_derived_cl84,plain,
    ( ~ ( '#sk1' @ '#sk5' )
    | '#form6' ),
    inference(simplify,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl95,plain,
    '#form6',
    inference(clc,[status(thm)],[zip_derived_cl74,zip_derived_cl84]) ).

thf(zip_derived_cl130,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk8' ) )
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl95]) ).

thf(zip_derived_cl26,plain,
    ( ( '#sk1' @ '#sk8' )
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl42_009,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ X2 )
      | ~ '#form6'
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl51,plain,
    ( ~ '#form6'
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ( '#_fresh_sk4'
     != ( '#sk3' @ '#sk8' ) )
    | ~ '#form6' ),
    inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl42]) ).

thf(zip_derived_cl57,plain,
    ( ( '#_fresh_sk4'
     != ( '#sk3' @ '#sk8' ) )
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) )
    | ~ '#form6' ),
    inference(simplify,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl95_010,plain,
    '#form6',
    inference(clc,[status(thm)],[zip_derived_cl74,zip_derived_cl84]) ).

thf(zip_derived_cl98,plain,
    ( ( '#_fresh_sk4'
     != ( '#sk3' @ '#sk8' ) )
    | ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk7' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl95]) ).

thf(zip_derived_cl131,plain,
    ( '#_fresh_sk4'
    = ( '#sk3' @ '#sk7' ) ),
    inference(clc,[status(thm)],[zip_derived_cl130,zip_derived_cl98]) ).

thf(zip_derived_cl61_011,plain,
    ! [X2: $i] :
      ( ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) )
      | ~ ( '#sk2' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl43,zip_derived_cl41]) ).

thf(zip_derived_cl133,plain,
    ( ( '#_fresh_sk4' != '#_fresh_sk4' )
    | ~ ( '#sk2' @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl61]) ).

thf(zip_derived_cl19,plain,
    ( ( '#sk2' @ '#sk7' )
    | ( ??
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ Y0 )
          & ( '#_fresh_sk4'
            = ( '#sk3' @ Y0 ) ) ) )
    | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl21,plain,
    ( ( ( '#sk1' @ '#sk8' )
      & ( '#_fresh_sk4'
        = ( '#sk3' @ '#sk8' ) ) )
    | ~ '#form6'
    | ( '#sk2' @ '#sk7' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl24,plain,
    ( ( '#sk1' @ '#sk8' )
    | ( '#sk2' @ '#sk7' )
    | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl42_012,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ X2 )
      | ~ '#form6'
      | ( '#_fresh_sk4'
       != ( '#sk3' @ X2 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl52,plain,
    ( ~ '#form6'
    | ( '#sk2' @ '#sk7' )
    | ( '#_fresh_sk4'
     != ( '#sk3' @ '#sk8' ) )
    | ~ '#form6' ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl42]) ).

thf(zip_derived_cl58,plain,
    ( ( '#_fresh_sk4'
     != ( '#sk3' @ '#sk8' ) )
    | ( '#sk2' @ '#sk7' )
    | ~ '#form6' ),
    inference(simplify,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl95_013,plain,
    '#form6',
    inference(clc,[status(thm)],[zip_derived_cl74,zip_derived_cl84]) ).

thf(zip_derived_cl125,plain,
    ( ( '#_fresh_sk4'
     != ( '#sk3' @ '#sk8' ) )
    | ( '#sk2' @ '#sk7' ) ),
    inference(demod,[status(thm)],[zip_derived_cl58,zip_derived_cl95]) ).

thf(zip_derived_cl25,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk8' ) )
    | ( '#sk2' @ '#sk7' )
    | ~ '#form6' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl28,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk8' ) )
    | ( '#sk2' @ '#sk7' )
    | ~ '#form6' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl95_014,plain,
    '#form6',
    inference(clc,[status(thm)],[zip_derived_cl74,zip_derived_cl84]) ).

thf(zip_derived_cl99,plain,
    ( ( '#_fresh_sk4'
      = ( '#sk3' @ '#sk8' ) )
    | ( '#sk2' @ '#sk7' ) ),
    inference(demod,[status(thm)],[zip_derived_cl28,zip_derived_cl95]) ).

thf(zip_derived_cl126,plain,
    '#sk2' @ '#sk7',
    inference(clc,[status(thm)],[zip_derived_cl125,zip_derived_cl99]) ).

thf(zip_derived_cl137,plain,
    '#_fresh_sk4' != '#_fresh_sk4',
    inference(demod,[status(thm)],[zip_derived_cl133,zip_derived_cl126]) ).

thf(zip_derived_cl138,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl137]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET752^4 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HpO9dVO4I0 true
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 15:09:38 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Running portfolio for 300 s
% 0.12/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  % Number of cores: 8
% 0.20/0.35  % Python version: Python 3.6.8
% 0.20/0.35  % Running in HO mode
% 0.21/0.66  % Total configuration time : 828
% 0.21/0.66  % Estimated wc time : 1656
% 0.21/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.65/0.82  % Solved by lams/20_acsne_simpl.sh.
% 1.65/0.82  % done 36 iterations in 0.046s
% 1.65/0.82  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.65/0.82  % SZS output start Refutation
% See solution above
% 1.65/0.82  
% 1.65/0.82  
% 1.65/0.82  % Terminating...
% 2.11/0.87  % Runner terminated.
% 2.11/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------