TSTP Solution File: SET673^3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET673^3 : 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.s6dqSepMLY 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 16:15:31 EDT 2023

% Result   : Theorem 0.59s 0.79s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   49 (  22 unt;   9 typ;   0 def)
%            Number of atoms       :  138 (  21 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  322 (  15   ~;   5   |;  41   &; 194   @)
%                                         (   0 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   77 (  77   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (   9 usr;   5 con; 0-4 aty)
%                                         (  32  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  113 (  77   ^;  36   !;   0   ?; 113   :)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk4_type',type,
    '#sk4': $i > $o ).

thf(restrict_rel_codomain_type,type,
    restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).

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

thf(is_rel_on_type,type,
    is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).

thf(subset_type,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

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

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

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

thf('#sk6_type',type,
    '#sk6': $i ).

thf(restrict_rel_codomain,axiom,
    ( restrict_rel_codomain
    = ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
          ( ( S @ Y )
          & ( R @ X @ Y ) ) ) ) ).

thf('0',plain,
    ( restrict_rel_codomain
    = ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
          ( ( S @ Y )
          & ( R @ X @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[restrict_rel_codomain]) ).

thf('1',plain,
    ( restrict_rel_codomain
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i,V_4: $i] :
          ( ( V_2 @ V_4 )
          & ( V_1 @ V_3 @ V_4 ) ) ) ),
    define([status(thm)]) ).

thf(is_rel_on,axiom,
    ( is_rel_on
    = ( ^ [R: $i > $i > $o,A: $i > $o,B: $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( R @ X @ Y )
         => ( ( A @ X )
            & ( B @ Y ) ) ) ) ) ).

thf('2',plain,
    ( is_rel_on
    = ( ^ [R: $i > $i > $o,A: $i > $o,B: $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( R @ X @ Y )
         => ( ( A @ X )
            & ( B @ Y ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[is_rel_on]) ).

thf('3',plain,
    ( is_rel_on
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i > $o] :
        ! [X4: $i,X6: $i] :
          ( ( V_1 @ X4 @ X6 )
         => ( ( V_2 @ X4 )
            & ( V_3 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('4',plain,
    ( subset
    = ( ^ [X: $i > $o,Y: $i > $o] :
        ! [U: $i] :
          ( ( X @ U )
         => ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[subset]) ).

thf('5',plain,
    ( subset
    = ( ^ [V_1: $i > $o,V_2: $i > $o] :
        ! [X4: $i] :
          ( ( V_1 @ X4 )
         => ( V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    ! [Z: $i > $o,R: $i > $i > $o,X: $i > $o,Y: $i > $o] :
      ( ( ( is_rel_on @ R @ X @ Y )
        & ( subset @ Y @ Z ) )
     => ( ( restrict_rel_codomain @ R @ Z )
        = R ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $o,X6: $i > $i > $o,X8: $i > $o,X10: $i > $o] :
      ( ( ! [X16: $i] :
            ( ( X10 @ X16 )
           => ( X4 @ X16 ) )
        & ! [X12: $i,X14: $i] :
            ( ( X6 @ X12 @ X14 )
           => ( ( X10 @ X14 )
              & ( X8 @ X12 ) ) ) )
     => ( ( ^ [V_1: $i,V_2: $i] :
              ( ( X6 @ V_1 @ V_2 )
              & ( X4 @ V_2 ) ) )
        = X6 ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $o,X6: $i > $i > $o,X8: $i > $o,X10: $i > $o] :
        ( ( ! [X16: $i] :
              ( ( X10 @ X16 )
             => ( X4 @ X16 ) )
          & ! [X12: $i,X14: $i] :
              ( ( X6 @ X12 @ X14 )
             => ( ( X10 @ X14 )
                & ( X8 @ X12 ) ) ) )
       => ( ( ^ [V_1: $i,V_2: $i] :
                ( ( X6 @ V_1 @ V_2 )
                & ( X4 @ V_2 ) ) )
          = X6 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i > $i > $o] :
              ( !!
              @ ^ [Y2: $i > $o] :
                  ( !!
                  @ ^ [Y3: $i > $o] :
                      ( ( ( !!
                          @ ^ [Y4: $i] :
                              ( ( Y3 @ Y4 )
                             => ( Y0 @ Y4 ) ) )
                        & ( !!
                          @ ^ [Y4: $i] :
                              ( !!
                              @ ^ [Y5: $i] :
                                  ( ( Y1 @ Y4 @ Y5 )
                                 => ( ( Y3 @ Y5 )
                                    & ( Y2 @ Y4 ) ) ) ) ) )
                     => ( ( ^ [Y4: $i,Y5: $i] :
                              ( ( Y1 @ Y4 @ Y5 )
                              & ( Y0 @ Y5 ) ) )
                        = Y1 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: $i > $i > $o] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( !!
              @ ^ [Y2: $i > $o] :
                  ( ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y3 ) ) )
                    & ( !!
                      @ ^ [Y3: $i] :
                          ( !!
                          @ ^ [Y4: $i] :
                              ( ( Y0 @ Y3 @ Y4 )
                             => ( ( Y2 @ Y4 )
                                & ( Y1 @ Y3 ) ) ) ) ) )
                 => ( ( ^ [Y3: $i,Y4: $i] :
                          ( ( Y0 @ Y3 @ Y4 )
                          & ( '#sk1' @ Y4 ) ) )
                    = Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y2 ) ) )
                & ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: $i] :
                          ( ( '#sk2' @ Y2 @ Y3 )
                         => ( ( Y1 @ Y3 )
                            & ( Y0 @ Y2 ) ) ) ) ) )
             => ( ( ^ [Y2: $i,Y3: $i] :
                      ( ( '#sk2' @ Y2 @ Y3 )
                      & ( '#sk1' @ Y3 ) ) )
                = '#sk2' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y1 ) ) )
            & ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( '#sk2' @ Y1 @ Y2 )
                     => ( ( Y0 @ Y2 )
                        & ( '#sk3' @ Y1 ) ) ) ) ) )
         => ( ( ^ [Y1: $i,Y2: $i] :
                  ( ( '#sk2' @ Y1 @ Y2 )
                  & ( '#sk1' @ Y2 ) ) )
            = '#sk2' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ~ ( ( ( !!
          @ ^ [Y0: $i] :
              ( ( '#sk4' @ Y0 )
             => ( '#sk1' @ Y0 ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( ( '#sk4' @ Y1 )
                    & ( '#sk3' @ Y0 ) ) ) ) ) )
     => ( ( ^ [Y0: $i,Y1: $i] :
              ( ( '#sk2' @ Y0 @ Y1 )
              & ( '#sk1' @ Y1 ) ) )
        = '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl6,plain,
    ( ( ^ [Y0: $i,Y1: $i] :
          ( ( '#sk2' @ Y0 @ Y1 )
          & ( '#sk1' @ Y1 ) ) )
   != '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9,plain,
    ( ( ^ [Y0: $i,Y1: $i] :
          ( ( '#sk2' @ Y0 @ Y1 )
          & ( '#sk1' @ Y1 ) ) )
   != '#sk2' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl17,plain,
    ( ( ( '#sk2' @ '#sk5' @ '#sk6' )
      & ( '#sk1' @ '#sk6' ) )
   != ( '#sk2' @ '#sk5' @ '#sk6' ) ),
    inference(neg_ext,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl17_001,plain,
    ( ( ( '#sk2' @ '#sk5' @ '#sk6' )
      & ( '#sk1' @ '#sk6' ) )
   != ( '#sk2' @ '#sk5' @ '#sk6' ) ),
    inference(neg_ext,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl20,plain,
    ( ( ( '#sk2' @ '#sk5' @ '#sk6' )
      & ( '#sk1' @ '#sk6' ) )
    | ( '#sk2' @ '#sk5' @ '#sk6' ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl24,plain,
    ( ( $false
      & ( '#sk1' @ '#sk6' ) )
    | ( '#sk2' @ '#sk5' @ '#sk6' ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl25,plain,
    '#sk2' @ '#sk5' @ '#sk6',
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl25_002,plain,
    '#sk2' @ '#sk5' @ '#sk6',
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl28,plain,
    ~ ( $true
      & ( '#sk1' @ '#sk6' ) ),
    inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl25,zip_derived_cl25]) ).

thf(zip_derived_cl29,plain,
    ~ ( '#sk1' @ '#sk6' ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl25_003,plain,
    '#sk2' @ '#sk5' @ '#sk6',
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl5,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk4' @ Y0 )
         => ( '#sk1' @ Y0 ) ) )
    & ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( '#sk2' @ Y0 @ Y1 )
             => ( ( '#sk4' @ Y1 )
                & ( '#sk3' @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl8,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( '#sk2' @ Y0 @ Y1 )
           => ( ( '#sk4' @ Y1 )
              & ( '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk2' @ X2 @ Y0 )
         => ( ( '#sk4' @ Y0 )
            & ( '#sk3' @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i] :
      ( ( '#sk2' @ X2 @ X4 )
     => ( ( '#sk4' @ X4 )
        & ( '#sk3' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( '#sk2' @ X2 @ X4 )
      | ( ( '#sk4' @ X4 )
        & ( '#sk3' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i,X4: $i] :
      ( ( '#sk4' @ X4 )
      | ~ ( '#sk2' @ X2 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl31,plain,
    '#sk4' @ '#sk6',
    inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl15]) ).

thf(zip_derived_cl7,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( '#sk4' @ Y0 )
       => ( '#sk1' @ Y0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ! [X2: $i] :
      ( ( '#sk4' @ X2 )
     => ( '#sk1' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i] :
      ( ~ ( '#sk4' @ X2 )
      | ( '#sk1' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl38,plain,
    '#sk1' @ '#sk6',
    inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl12]) ).

thf(zip_derived_cl41,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl38]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET673^3 : TPTP v8.1.2. Released v3.6.0.
% 0.07/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.s6dqSepMLY 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 : Sat Aug 26 10:21:20 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
% 0.57/0.69  % Total configuration time : 828
% 0.57/0.69  % Estimated wc time : 1656
% 0.57/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.79  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.79  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.79  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.79  % Solved by lams/35_full_unif4.sh.
% 0.59/0.79  % done 16 iterations in 0.019s
% 0.59/0.79  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.59/0.79  % SZS output start Refutation
% See solution above
% 0.59/0.80  
% 0.59/0.80  
% 0.59/0.80  % Terminating...
% 0.62/0.88  % Runner terminated.
% 0.62/0.89  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------