TSTP Solution File: GRA003+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yvgnZ6HAcm true

% Computer : n005.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 00:10:09 EDT 2023

% Result   : Theorem 1.32s 0.80s
% Output   : Refutation 1.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   65 (  18 unt;  19 typ;   0 def)
%            Number of atoms       :  130 (  34 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  371 (  50   ~;  42   |;  31   &; 237   @)
%                                         (   1 <=>;   8  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   7 con; 0-3 aty)
%            Number of variables   :   79 (   0   ^;  75   !;   4   ?;  79   :)

% Comments : 
%------------------------------------------------------------------------------
thf(edge_type,type,
    edge: $i > $o ).

thf(sequential_type,type,
    sequential: $i > $i > $o ).

thf(length_of_type,type,
    length_of: $i > $i ).

thf(sk__11_type,type,
    sk__11: $i ).

thf(in_path_type,type,
    in_path: $i > $i > $o ).

thf(vertex_type,type,
    vertex: $i > $o ).

thf(precedes_type,type,
    precedes: $i > $i > $i > $o ).

thf(head_of_type,type,
    head_of: $i > $i ).

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

thf(on_path_type,type,
    on_path: $i > $i > $o ).

thf(sk__10_type,type,
    sk__10: $i ).

thf(shortest_path_type,type,
    shortest_path: $i > $i > $i > $o ).

thf(less_or_equal_type,type,
    less_or_equal: $i > $i > $o ).

thf(tail_of_type,type,
    tail_of: $i > $i ).

thf(sk__12_type,type,
    sk__12: $i ).

thf(empty_type,type,
    empty: $i ).

thf(path_type,type,
    path: $i > $i > $i > $o ).

thf(path_cons_type,type,
    path_cons: $i > $i > $i ).

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

thf(vertices_and_edges,conjecture,
    ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
      ( ( ( shortest_path @ V1 @ V2 @ P )
        & ( precedes @ E1 @ E2 @ P ) )
     => ( ( vertex @ V1 )
        & ( vertex @ V2 )
        & ( V1 != V2 )
        & ( edge @ E1 )
        & ( edge @ E2 )
        & ( E1 != E2 )
        & ( path @ V1 @ V2 @ P ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
        ( ( ( shortest_path @ V1 @ V2 @ P )
          & ( precedes @ E1 @ E2 @ P ) )
       => ( ( vertex @ V1 )
          & ( vertex @ V2 )
          & ( V1 != V2 )
          & ( edge @ E1 )
          & ( edge @ E2 )
          & ( E1 != E2 )
          & ( path @ V1 @ V2 @ P ) ) ),
    inference('cnf.neg',[status(esa)],[vertices_and_edges]) ).

thf(zip_derived_cl59,plain,
    shortest_path @ sk__8 @ sk__9 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl61,plain,
    ( ~ ( vertex @ sk__8 )
    | ~ ( vertex @ sk__9 )
    | ( sk__8 = sk__9 )
    | ~ ( edge @ sk__10 )
    | ~ ( edge @ sk__11 )
    | ( sk__10 = sk__11 )
    | ~ ( path @ sk__8 @ sk__9 @ sk__12 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(path_properties,axiom,
    ! [V1: $i,V2: $i,P: $i] :
      ( ( path @ V1 @ V2 @ P )
     => ( ( vertex @ V1 )
        & ( vertex @ V2 )
        & ? [E: $i] :
            ( ( ( ( V2
                  = ( head_of @ E ) )
                & ( P
                  = ( path_cons @ E @ empty ) ) )
            <~> ? [TP: $i] :
                  ( ( P
                    = ( path_cons @ E @ TP ) )
                  & ( path @ ( head_of @ E ) @ V2 @ TP ) ) )
            & ( V1
              = ( tail_of @ E ) )
            & ( edge @ E ) ) ) ) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( vertex @ X0 )
      | ~ ( path @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[path_properties]) ).

thf(zip_derived_cl64,plain,
    ( ~ ( path @ sk__8 @ sk__9 @ sk__12 )
    | ( sk__10 = sk__11 )
    | ~ ( edge @ sk__11 )
    | ~ ( edge @ sk__10 )
    | ( sk__8 = sk__9 )
    | ~ ( vertex @ sk__9 ) ),
    inference(clc,[status(thm)],[zip_derived_cl61,zip_derived_cl11]) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( vertex @ X0 )
      | ~ ( path @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[path_properties]) ).

thf(zip_derived_cl65,plain,
    ( ( sk__8 = sk__9 )
    | ~ ( edge @ sk__10 )
    | ~ ( edge @ sk__11 )
    | ( sk__10 = sk__11 )
    | ~ ( path @ sk__8 @ sk__9 @ sk__12 ) ),
    inference(clc,[status(thm)],[zip_derived_cl64,zip_derived_cl12]) ).

thf(shortest_path_defn,axiom,
    ! [V1: $i,V2: $i,SP: $i] :
      ( ( shortest_path @ V1 @ V2 @ SP )
    <=> ( ( path @ V1 @ V2 @ SP )
        & ( V1 != V2 )
        & ! [P: $i] :
            ( ( path @ V1 @ V2 @ P )
           => ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) ).

thf(zip_derived_cl38,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( path @ X0 @ X1 @ X2 )
      | ~ ( shortest_path @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[shortest_path_defn]) ).

thf(zip_derived_cl59_001,plain,
    shortest_path @ sk__8 @ sk__9 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl66,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup+',[status(thm)],[zip_derived_cl38,zip_derived_cl59]) ).

thf(zip_derived_cl73,plain,
    ( ( sk__8 = sk__9 )
    | ~ ( edge @ sk__10 )
    | ~ ( edge @ sk__11 )
    | ( sk__10 = sk__11 ) ),
    inference(demod,[status(thm)],[zip_derived_cl65,zip_derived_cl66]) ).

thf(zip_derived_cl66_002,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup+',[status(thm)],[zip_derived_cl38,zip_derived_cl59]) ).

thf(on_path_properties,axiom,
    ! [V1: $i,V2: $i,P: $i,E: $i] :
      ( ( ( path @ V1 @ V2 @ P )
        & ( on_path @ E @ P ) )
     => ( ( edge @ E )
        & ( in_path @ ( head_of @ E ) @ P )
        & ( in_path @ ( tail_of @ E ) @ P ) ) ) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( path @ X0 @ X1 @ X2 )
      | ~ ( on_path @ X3 @ X2 )
      | ( edge @ X3 ) ),
    inference(cnf,[status(esa)],[on_path_properties]) ).

thf(zip_derived_cl75,plain,
    ! [X0: $i] :
      ( ( edge @ X0 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl22]) ).

thf(zip_derived_cl66_003,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup+',[status(thm)],[zip_derived_cl38,zip_derived_cl59]) ).

thf(zip_derived_cl60,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(precedes_properties,axiom,
    ! [P: $i,V1: $i,V2: $i] :
      ( ( path @ V1 @ V2 @ P )
     => ! [E1: $i,E2: $i] :
          ( ( precedes @ E1 @ E2 @ P )
         => ( ( on_path @ E1 @ P )
            & ( on_path @ E2 @ P )
            & ( ( sequential @ E1 @ E2 )
            <~> ? [E3: $i] :
                  ( ( precedes @ E3 @ E2 @ P )
                  & ( sequential @ E1 @ E3 ) ) ) ) ) ) ).

thf(zip_derived_cl37,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( precedes @ X0 @ X1 @ X2 )
      | ( on_path @ X0 @ X2 )
      | ~ ( path @ X3 @ X4 @ X2 ) ),
    inference(cnf,[status(esa)],[precedes_properties]) ).

thf(zip_derived_cl72,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( path @ X1 @ X0 @ sk__12 )
      | ( on_path @ sk__10 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl37]) ).

thf(zip_derived_cl79,plain,
    on_path @ sk__10 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl72]) ).

thf(zip_derived_cl80,plain,
    edge @ sk__10,
    inference('sup+',[status(thm)],[zip_derived_cl75,zip_derived_cl79]) ).

thf(zip_derived_cl84,plain,
    ( ( sk__8 = sk__9 )
    | ~ ( edge @ sk__11 )
    | ( sk__10 = sk__11 ) ),
    inference(demod,[status(thm)],[zip_derived_cl73,zip_derived_cl80]) ).

thf(zip_derived_cl75_004,plain,
    ! [X0: $i] :
      ( ( edge @ X0 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl22]) ).

thf(zip_derived_cl66_005,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup+',[status(thm)],[zip_derived_cl38,zip_derived_cl59]) ).

thf(zip_derived_cl60_006,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl36,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( precedes @ X0 @ X1 @ X2 )
      | ( on_path @ X1 @ X2 )
      | ~ ( path @ X3 @ X4 @ X2 ) ),
    inference(cnf,[status(esa)],[precedes_properties]) ).

thf(zip_derived_cl71,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( path @ X1 @ X0 @ sk__12 )
      | ( on_path @ sk__11 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl36]) ).

thf(zip_derived_cl78,plain,
    on_path @ sk__11 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl71]) ).

thf(zip_derived_cl81,plain,
    edge @ sk__11,
    inference('sup+',[status(thm)],[zip_derived_cl75,zip_derived_cl78]) ).

thf(zip_derived_cl87,plain,
    ( ( sk__8 = sk__9 )
    | ( sk__10 = sk__11 ) ),
    inference(demod,[status(thm)],[zip_derived_cl84,zip_derived_cl81]) ).

thf(zip_derived_cl59_007,plain,
    shortest_path @ sk__8 @ sk__9 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl60_008,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(shortest_path_properties,axiom,
    ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
      ( ( ( shortest_path @ V1 @ V2 @ P )
        & ( precedes @ E1 @ E2 @ P ) )
     => ( ~ ? [E3: $i] :
              ( ( ( head_of @ E3 )
                = ( head_of @ E2 ) )
              & ( ( tail_of @ E3 )
                = ( tail_of @ E1 ) ) )
        & ~ ( precedes @ E2 @ E1 @ P ) ) ) ).

thf(zip_derived_cl43,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( ( tail_of @ X1 )
       != ( tail_of @ X0 ) )
      | ( ( head_of @ X1 )
       != ( head_of @ X2 ) )
      | ~ ( precedes @ X0 @ X2 @ X3 )
      | ~ ( shortest_path @ X4 @ X5 @ X3 ) ),
    inference(cnf,[status(esa)],[shortest_path_properties]) ).

thf(zip_derived_cl96,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( shortest_path @ X1 @ X0 @ sk__12 )
      | ( ( head_of @ X2 )
       != ( head_of @ sk__11 ) )
      | ( ( tail_of @ X2 )
       != ( tail_of @ sk__10 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl43]) ).

thf(zip_derived_cl97,plain,
    ! [X0: $i] :
      ( ( ( tail_of @ X0 )
       != ( tail_of @ sk__10 ) )
      | ( ( head_of @ X0 )
       != ( head_of @ sk__11 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl59,zip_derived_cl96]) ).

thf(zip_derived_cl99,plain,
    ( ( head_of @ sk__10 )
   != ( head_of @ sk__11 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl97]) ).

thf(zip_derived_cl100,plain,
    ( ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( sk__8 = sk__9 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl99]) ).

thf(zip_derived_cl101,plain,
    sk__8 = sk__9,
    inference(simplify,[status(thm)],[zip_derived_cl100]) ).

thf(zip_derived_cl39,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 != X0 )
      | ~ ( shortest_path @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[shortest_path_defn]) ).

thf(zip_derived_cl63,plain,
    ! [X0: $i,X1: $i] :
      ~ ( shortest_path @ X1 @ X1 @ X0 ),
    inference(eq_res,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl102,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl101,zip_derived_cl63]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yvgnZ6HAcm true
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 03:41:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.21/0.35  % Python version: Python 3.6.8
% 0.21/0.36  % Running in FO mode
% 0.22/0.65  % Total configuration time : 435
% 0.22/0.65  % Estimated wc time : 1092
% 0.22/0.65  % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.74  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.28/0.75  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.28/0.76  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.32/0.80  % Solved by fo/fo4.sh.
% 1.32/0.80  % done 56 iterations in 0.021s
% 1.32/0.80  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.32/0.80  % SZS output start Refutation
% See solution above
% 1.32/0.80  
% 1.32/0.80  
% 1.32/0.80  % Terminating...
% 1.76/0.85  % Runner terminated.
% 1.76/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------