TSTP Solution File: SET649^3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET649^3 : 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.PtT5WkGqO7 true

% Computer : n016.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 16:15:19 EDT 2023

% Result   : Theorem 0.20s 0.76s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   37 (  21 unt;  10 typ;   0 def)
%            Number of atoms       :   48 (  15 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  113 (   6   ~;   3   |;   8   &;  81   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   76 (  76   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   3 con; 0-4 aty)
%            Number of variables   :   76 (  36   ^;  30   !;  10   ?;  76   :)

% Comments : 
%------------------------------------------------------------------------------
thf(rel_domain_type,type,
    rel_domain: ( $i > $i > $o ) > $i > $o ).

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

thf(rel_codomain_type,type,
    rel_codomain: ( $i > $i > $o ) > $i > $o ).

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

thf(sk__7_type,type,
    sk__7: $i > $o ).

thf(sk__8_type,type,
    sk__8: $i ).

thf(cartesian_product_type,type,
    cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).

thf(sub_rel_type,type,
    sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

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

thf(sk__9_type,type,
    sk__9: $i ).

thf(rel_domain,axiom,
    ( rel_domain
    = ( ^ [R: $i > $i > $o,X: $i] :
        ? [Y: $i] : ( R @ X @ Y ) ) ) ).

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

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

thf(rel_codomain,axiom,
    ( rel_codomain
    = ( ^ [R: $i > $i > $o,Y: $i] :
        ? [X: $i] : ( R @ X @ Y ) ) ) ).

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

thf('3',plain,
    ( rel_codomain
    = ( ^ [V_1: $i > $i > $o,V_2: $i] :
        ? [X4: $i] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(sub_rel,axiom,
    ( sub_rel
    = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( R1 @ X @ Y )
         => ( R2 @ X @ Y ) ) ) ) ).

thf('4',plain,
    ( sub_rel
    = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( R1 @ X @ Y )
         => ( R2 @ X @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[sub_rel]) ).

thf('5',plain,
    ( sub_rel
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $i > $o] :
        ! [X4: $i,X6: $i] :
          ( ( V_1 @ X4 @ X6 )
         => ( V_2 @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(cartesian_product,axiom,
    ( cartesian_product
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i,V: $i] :
          ( ( X @ U )
          & ( Y @ V ) ) ) ) ).

thf('6',plain,
    ( cartesian_product
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i,V: $i] :
          ( ( X @ U )
          & ( Y @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cartesian_product]) ).

thf('7',plain,
    ( cartesian_product
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i,V_4: $i] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_4 ) ) ) ),
    define([status(thm)]) ).

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

thf('8',plain,
    ( subset
    = ( ^ [X: $i > $o,Y: $i > $o] :
        ! [U: $i] :
          ( ( X @ U )
         => ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[subset]) ).

thf('9',plain,
    ( subset
    = ( ^ [V_1: $i > $o,V_2: $i > $o] :
        ! [X4: $i] :
          ( ( V_1 @ X4 )
         => ( V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    ! [R: $i > $i > $o,X: $i > $o,Y: $i > $o] :
      ( ( ( subset @ ( rel_domain @ R ) @ X )
        & ( subset @ ( rel_codomain @ R ) @ Y ) )
     => ( sub_rel @ R @ ( cartesian_product @ X @ Y ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $i > $o,X6: $i > $o,X8: $i > $o] :
      ( ( ! [X10: $i] :
            ( ? [X12: $i] : ( X4 @ X10 @ X12 )
           => ( X6 @ X10 ) )
        & ! [X14: $i] :
            ( ? [X16: $i] : ( X4 @ X16 @ X14 )
           => ( X8 @ X14 ) ) )
     => ! [X18: $i,X20: $i] :
          ( ( X4 @ X18 @ X20 )
         => ( ( X6 @ X18 )
            & ( X8 @ X20 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $i > $o,X6: $i > $o,X8: $i > $o] :
        ( ( ! [X10: $i] :
              ( ? [X12: $i] : ( X4 @ X10 @ X12 )
             => ( X6 @ X10 ) )
          & ! [X14: $i] :
              ( ? [X16: $i] : ( X4 @ X16 @ X14 )
             => ( X8 @ X14 ) ) )
       => ! [X18: $i,X20: $i] :
            ( ( X4 @ X18 @ X20 )
           => ( ( X6 @ X18 )
              & ( X8 @ X20 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ( ~ ( sk__6 @ sk__8 )
    | ~ ( sk__7 @ sk__9 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    sk__5 @ sk__8 @ sk__9,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__7 @ X0 )
      | ~ ( sk__5 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    sk__7 @ sk__9,
    inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl2]) ).

thf(zip_derived_cl6,plain,
    ~ ( sk__6 @ sk__8 ),
    inference(demod,[status(thm)],[zip_derived_cl1,zip_derived_cl4]) ).

thf(zip_derived_cl0_001,plain,
    sk__5 @ sk__8 @ sk__9,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3,plain,
    ! [X2: $i,X3: $i] :
      ( ( sk__6 @ X2 )
      | ~ ( sk__5 @ X2 @ X3 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    sk__6 @ sk__8,
    inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).

thf(zip_derived_cl9,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl7]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET649^3 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.PtT5WkGqO7 true
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 10:22:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.72  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.76  % Solved by lams/40_c.s.sh.
% 0.20/0.76  % done 7 iterations in 0.010s
% 0.20/0.76  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.20/0.76  % SZS output start Refutation
% See solution above
% 0.20/0.76  
% 0.20/0.76  
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.77  % Terminating...
% 1.30/0.85  % Runner terminated.
% 1.30/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------