TSTP Solution File: GRA005+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRA005+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 : Tue Apr 30 20:18:34 EDT 2024

% Result   : Theorem 0.08s 0.29s
% Output   : CNFRefutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   18 (   6 unt;   0 def)
%            Number of atoms       :   58 (  22 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   68 (  28   ~;  14   |;  23   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :   59 (  44   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [V1,V2,E1,E2,P] :
      ( ( shortest_path(V1,V2,P)
        & precedes(E1,E2,P) )
     => ( ~ ? [E3] :
              ( tail_of(E3) = tail_of(E1)
              & head_of(E3) = head_of(E2) )
        & ~ precedes(E2,E1,P) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,conjecture,
    ! [V1,V2,E1,E2,P] :
      ( ( shortest_path(V1,V2,P)
        & precedes(E1,E2,P) )
     => ~ ? [E3] :
            ( edge(E3)
            & tail_of(E3) = tail_of(E1)
            & head_of(E3) = head_of(E2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    ~ ! [V1,V2,E1,E2,P] :
        ( ( shortest_path(V1,V2,P)
          & precedes(E1,E2,P) )
       => ~ ? [E3] :
              ( edge(E3)
              & tail_of(E3) = tail_of(E1)
              & head_of(E3) = head_of(E2) ) ),
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f89,plain,
    ! [V1,V2,E1,E2,P] :
      ( ~ shortest_path(V1,V2,P)
      | ~ precedes(E1,E2,P)
      | ( ! [E3] :
            ( tail_of(E3) != tail_of(E1)
            | head_of(E3) != head_of(E2) )
        & ~ precedes(E2,E1,P) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f90,plain,
    ! [E1,E2,P] :
      ( ! [V1,V2] : ~ shortest_path(V1,V2,P)
      | ~ precedes(E1,E2,P)
      | ( ! [E3] :
            ( tail_of(E3) != tail_of(E1)
            | head_of(E3) != head_of(E2) )
        & ~ precedes(E2,E1,P) ) ),
    inference(miniscoping,[status(esa)],[f89]) ).

fof(f91,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ shortest_path(X0,X1,X2)
      | ~ precedes(X3,X4,X2)
      | tail_of(X5) != tail_of(X3)
      | head_of(X5) != head_of(X4) ),
    inference(cnf_transformation,[status(esa)],[f90]) ).

fof(f116,plain,
    ? [V1,V2,E1,E2,P] :
      ( shortest_path(V1,V2,P)
      & precedes(E1,E2,P)
      & ? [E3] :
          ( edge(E3)
          & tail_of(E3) = tail_of(E1)
          & head_of(E3) = head_of(E2) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f117,plain,
    ? [E1,E2] :
      ( ? [P] :
          ( ? [V1,V2] : shortest_path(V1,V2,P)
          & precedes(E1,E2,P) )
      & ? [E3] :
          ( edge(E3)
          & tail_of(E3) = tail_of(E1)
          & head_of(E3) = head_of(E2) ) ),
    inference(miniscoping,[status(esa)],[f116]) ).

fof(f118,plain,
    ( shortest_path(sk0_11,sk0_12,sk0_10)
    & precedes(sk0_8,sk0_9,sk0_10)
    & edge(sk0_13)
    & tail_of(sk0_13) = tail_of(sk0_8)
    & head_of(sk0_13) = head_of(sk0_9) ),
    inference(skolemization,[status(esa)],[f117]) ).

fof(f119,plain,
    shortest_path(sk0_11,sk0_12,sk0_10),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f120,plain,
    precedes(sk0_8,sk0_9,sk0_10),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f122,plain,
    tail_of(sk0_13) = tail_of(sk0_8),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f123,plain,
    head_of(sk0_13) = head_of(sk0_9),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f284,plain,
    ! [X0,X1,X2,X3] :
      ( ~ shortest_path(X0,X1,X2)
      | ~ precedes(sk0_8,X3,X2)
      | head_of(sk0_13) != head_of(X3) ),
    inference(resolution,[status(thm)],[f91,f122]) ).

fof(f285,plain,
    ! [X0,X1,X2,X3] :
      ( ~ shortest_path(X0,X1,X2)
      | ~ precedes(sk0_8,X3,X2)
      | head_of(sk0_9) != head_of(X3) ),
    inference(forward_demodulation,[status(thm)],[f123,f284]) ).

fof(f300,plain,
    ! [X0,X1,X2] :
      ( ~ shortest_path(X0,X1,X2)
      | ~ precedes(sk0_8,sk0_9,X2) ),
    inference(equality_resolution,[status(esa)],[f285]) ).

fof(f304,plain,
    ~ precedes(sk0_8,sk0_9,sk0_10),
    inference(resolution,[status(thm)],[f300,f119]) ).

fof(f305,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f304,f120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09  % Problem  : GRA005+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.03/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Mon Apr 29 22:29:20 EDT 2024
% 0.08/0.28  % CPUTime  : 
% 0.08/0.29  % Drodi V3.6.0
% 0.08/0.29  % Refutation found
% 0.08/0.29  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.29  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.30  % Elapsed time: 0.016444 seconds
% 0.08/0.30  % CPU time: 0.028102 seconds
% 0.08/0.30  % Total memory used: 13.514 MB
% 0.08/0.30  % Net memory used: 13.498 MB
%------------------------------------------------------------------------------