TSTP Solution File: SET672^3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET672^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VfEnzuT7rI true

% Computer : n031.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 16:15:30 EDT 2023

% Result   : Theorem 0.23s 0.76s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   23 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :   24 (   6 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   86 (   5   ~;   2   |;  12   &;  57   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   54 (  54   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   3 con; 0-4 aty)
%            Number of variables   :   49 (  21   ^;  28   !;   0   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__2_type,type,
    sk__2: $i > $o ).

thf(sk__5_type,type,
    sk__5: $i ).

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

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

thf(sk__6_type,type,
    sk__6: $i ).

thf(sk__3_type,type,
    sk__3: $i > $i > $o ).

thf(sk__4_type,type,
    sk__4: $i > $o ).

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

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $o,X6: $i > $i > $o,X8: $i > $o,X10: $i > $o] :
      ( ! [X12: $i,X14: $i] :
          ( ( X6 @ X12 @ X14 )
         => ( ( X8 @ X12 )
            & ( X10 @ X14 ) ) )
     => ! [X16: $i,X18: $i] :
          ( ( ( X4 @ X18 )
            & ( X6 @ X16 @ X18 ) )
         => ( ( X8 @ X16 )
            & ( X4 @ X18 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $o,X6: $i > $i > $o,X8: $i > $o,X10: $i > $o] :
        ( ! [X12: $i,X14: $i] :
            ( ( X6 @ X12 @ X14 )
           => ( ( X8 @ X12 )
              & ( X10 @ X14 ) ) )
       => ! [X16: $i,X18: $i] :
            ( ( ( X4 @ X18 )
              & ( X6 @ X16 @ X18 ) )
           => ( ( X8 @ X16 )
              & ( X4 @ X18 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ( ~ ( sk__4 @ sk__5 )
    | ~ ( sk__2 @ sk__6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    sk__2 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5,plain,
    ~ ( sk__4 @ sk__5 ),
    inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl4]) ).

thf(zip_derived_cl3,plain,
    sk__3 @ sk__5 @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__4 @ X0 )
      | ~ ( sk__3 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    sk__4 @ sk__5,
    inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl0]) ).

thf(zip_derived_cl8,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl6]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET672^3 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VfEnzuT7rI true
% 0.15/0.36  % Computer : n031.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 : Sat Aug 26 12:34:08 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.15/0.36  % Running portfolio for 300 s
% 0.15/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36  % 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/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.76  % Solved by lams/40_c.s.sh.
% 0.23/0.76  % done 4 iterations in 0.014s
% 0.23/0.76  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.23/0.76  % SZS output start Refutation
% See solution above
% 0.23/0.76  
% 0.23/0.76  
% 0.23/0.77  % Terminating...
% 1.45/0.87  % Runner terminated.
% 1.45/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------