TSTP Solution File: GRA010+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 00:00:08 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   52 (   6 unt;  35 typ;   0 def)
%            Number of atoms       :   65 (  14 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   71 (  23   ~;  25   |;  15   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   53 (  25   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   2 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;   9 con; 0-4 aty)
%            Number of variables   :   44 (  13 sgn;  21   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    edge: $i > $o ).

tff(decl_23,type,
    head_of: $i > $i ).

tff(decl_24,type,
    tail_of: $i > $i ).

tff(decl_25,type,
    vertex: $i > $o ).

tff(decl_26,type,
    complete: $o ).

tff(decl_27,type,
    path: ( $i * $i * $i ) > $o ).

tff(decl_28,type,
    empty: $i ).

tff(decl_29,type,
    path_cons: ( $i * $i ) > $i ).

tff(decl_30,type,
    on_path: ( $i * $i ) > $o ).

tff(decl_31,type,
    in_path: ( $i * $i ) > $o ).

tff(decl_32,type,
    sequential: ( $i * $i ) > $o ).

tff(decl_33,type,
    precedes: ( $i * $i * $i ) > $o ).

tff(decl_34,type,
    shortest_path: ( $i * $i * $i ) > $o ).

tff(decl_35,type,
    length_of: $i > $i ).

tff(decl_36,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(decl_37,type,
    triangle: ( $i * $i * $i ) > $o ).

tff(decl_38,type,
    edges: $i ).

tff(decl_39,type,
    number_of_in: ( $i * $i ) > $i ).

tff(decl_40,type,
    sequential_pairs: $i ).

tff(decl_41,type,
    n1: $i ).

tff(decl_42,type,
    minus: ( $i * $i ) > $i ).

tff(decl_43,type,
    triangles: $i ).

tff(decl_44,type,
    graph: $i ).

tff(decl_45,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk7_1: $i > $i ).

tff(decl_52,type,
    esk8_1: $i > $i ).

tff(decl_53,type,
    esk9_0: $i ).

tff(decl_54,type,
    esk10_0: $i ).

tff(decl_55,type,
    esk11_0: $i ).

tff(decl_56,type,
    esk12_2: ( $i * $i ) > $i ).

fof(complete_means_sequential_pairs_and_triangles,conjecture,
    ( complete
   => ! [X4,X2,X3] :
        ( ( path(X2,X3,X4)
          & ! [X7,X8] :
              ( ( on_path(X7,X4)
                & on_path(X8,X4)
                & sequential(X7,X8) )
             => ? [X9] : triangle(X7,X8,X9) ) )
       => number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).

fof(sequential_pairs_and_triangles,axiom,
    ! [X4,X2,X3] :
      ( ( path(X2,X3,X4)
        & ! [X7,X8] :
            ( ( on_path(X7,X4)
              & on_path(X8,X4)
              & sequential(X7,X8) )
           => ? [X9] : triangle(X7,X8,X9) ) )
     => number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).

fof(c_0_2,negated_conjecture,
    ~ ( complete
     => ! [X4,X2,X3] :
          ( ( path(X2,X3,X4)
            & ! [X7,X8] :
                ( ( on_path(X7,X4)
                  & on_path(X8,X4)
                  & sequential(X7,X8) )
               => ? [X9] : triangle(X7,X8,X9) ) )
         => number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
    inference(assume_negation,[status(cth)],[complete_means_sequential_pairs_and_triangles]) ).

fof(c_0_3,plain,
    ! [X76,X77,X78,X81] :
      ( ( on_path(esk7_1(X76),X76)
        | ~ path(X77,X78,X76)
        | number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
      & ( on_path(esk8_1(X76),X76)
        | ~ path(X77,X78,X76)
        | number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
      & ( sequential(esk7_1(X76),esk8_1(X76))
        | ~ path(X77,X78,X76)
        | number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
      & ( ~ triangle(esk7_1(X76),esk8_1(X76),X81)
        | ~ path(X77,X78,X76)
        | number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_pairs_and_triangles])])])])])]) ).

fof(c_0_4,negated_conjecture,
    ! [X87,X88] :
      ( complete
      & path(esk10_0,esk11_0,esk9_0)
      & ( ~ on_path(X87,esk9_0)
        | ~ on_path(X88,esk9_0)
        | ~ sequential(X87,X88)
        | triangle(X87,X88,esk12_2(X87,X88)) )
      & number_of_in(sequential_pairs,esk9_0) != number_of_in(triangles,esk9_0) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).

cnf(c_0_5,plain,
    ( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
    | ~ triangle(esk7_1(X1),esk8_1(X1),X2)
    | ~ path(X3,X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,negated_conjecture,
    ( triangle(X1,X2,esk12_2(X1,X2))
    | ~ on_path(X1,esk9_0)
    | ~ on_path(X2,esk9_0)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( sequential(esk7_1(X1),esk8_1(X1))
    | number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
    | ~ path(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_8,plain,
    ( on_path(esk8_1(X1),X1)
    | number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
    | ~ path(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_9,negated_conjecture,
    path(esk10_0,esk11_0,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_10,negated_conjecture,
    number_of_in(sequential_pairs,esk9_0) != number_of_in(triangles,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,plain,
    ( on_path(esk7_1(X1),X1)
    | number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
    | ~ path(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_12,negated_conjecture,
    ( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
    | ~ on_path(esk8_1(X1),esk9_0)
    | ~ on_path(esk7_1(X1),esk9_0)
    | ~ path(X2,X3,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    on_path(esk8_1(esk9_0),esk9_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    on_path(esk7_1(esk9_0),esk9_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    ~ path(X1,X2,esk9_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_9,c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.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   : Sun Aug 27 02:44:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.024000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.028000 s
%------------------------------------------------------------------------------