TSTP Solution File: GEO268+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 20:17:49 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   53 (   7 unt;   0 def)
%            Number of atoms       :  124 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  123 (  52   ~;  53   |;   9   &)
%                                         (   6 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   72 (  68   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( unequally_directed_opposite_lines(X,Y)
    <=> unequally_directed_lines(X,reverse_line(Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] :
      ( equally_directed_lines(X,Y)
    <=> ~ unequally_directed_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [L] : equally_directed_lines(L,L),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [L,M,N] :
      ( unequally_directed_lines(L,M)
     => ( unequally_directed_lines(L,N)
        | unequally_directed_lines(M,N) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [L,M] :
      ( unequally_directed_lines(L,M)
      | unequally_directed_lines(L,reverse_line(M)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [L,M] :
      ( ( unequally_directed_lines(L,M)
        & unequally_directed_lines(L,reverse_line(M)) )
     => ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [L,M] :
      ~ ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f37,conjecture,
    ! [L,M] :
      ( unequally_directed_lines(L,M)
    <=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f38,negated_conjecture,
    ~ ! [L,M] :
        ( unequally_directed_lines(L,M)
      <=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
    inference(negated_conjecture,[status(cth)],[f37]) ).

fof(f39,plain,
    ! [X,Y] :
      ( ( ~ unequally_directed_opposite_lines(X,Y)
        | unequally_directed_lines(X,reverse_line(Y)) )
      & ( unequally_directed_opposite_lines(X,Y)
        | ~ unequally_directed_lines(X,reverse_line(Y)) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f40,plain,
    ( ! [X,Y] :
        ( ~ unequally_directed_opposite_lines(X,Y)
        | unequally_directed_lines(X,reverse_line(Y)) )
    & ! [X,Y] :
        ( unequally_directed_opposite_lines(X,Y)
        | ~ unequally_directed_lines(X,reverse_line(Y)) ) ),
    inference(miniscoping,[status(esa)],[f39]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ unequally_directed_opposite_lines(X0,X1)
      | unequally_directed_lines(X0,reverse_line(X1)) ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( unequally_directed_opposite_lines(X0,X1)
      | ~ unequally_directed_lines(X0,reverse_line(X1)) ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f51,plain,
    ! [X,Y] :
      ( ( ~ equally_directed_lines(X,Y)
        | ~ unequally_directed_lines(X,Y) )
      & ( equally_directed_lines(X,Y)
        | unequally_directed_lines(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f52,plain,
    ( ! [X,Y] :
        ( ~ equally_directed_lines(X,Y)
        | ~ unequally_directed_lines(X,Y) )
    & ! [X,Y] :
        ( equally_directed_lines(X,Y)
        | unequally_directed_lines(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f51]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ equally_directed_lines(X0,X1)
      | ~ unequally_directed_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f100,plain,
    ! [X0] : equally_directed_lines(X0,X0),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f101,plain,
    ! [L,M,N] :
      ( ~ unequally_directed_lines(L,M)
      | unequally_directed_lines(L,N)
      | unequally_directed_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f102,plain,
    ! [L,M] :
      ( ~ unequally_directed_lines(L,M)
      | ! [N] :
          ( unequally_directed_lines(L,N)
          | unequally_directed_lines(M,N) ) ),
    inference(miniscoping,[status(esa)],[f101]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ~ unequally_directed_lines(X0,X1)
      | unequally_directed_lines(X0,X2)
      | unequally_directed_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( unequally_directed_lines(X0,X1)
      | unequally_directed_lines(X0,reverse_line(X1)) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f111,plain,
    ! [L,M] :
      ( ~ unequally_directed_lines(L,M)
      | ~ unequally_directed_lines(L,reverse_line(M))
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ unequally_directed_lines(X0,X1)
      | ~ unequally_directed_lines(X0,reverse_line(X1))
      | left_convergent_lines(X0,X1)
      | left_convergent_lines(X0,reverse_line(X1)) ),
    inference(cnf_transformation,[status(esa)],[f111]) ).

fof(f117,plain,
    ! [L,M] :
      ( ~ left_convergent_lines(L,M)
      & ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f118,plain,
    ( ! [L,M] : ~ left_convergent_lines(L,M)
    & ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(miniscoping,[status(esa)],[f117]) ).

fof(f119,plain,
    ! [X0,X1] : ~ left_convergent_lines(X0,X1),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f152,plain,
    ? [L,M] :
      ( unequally_directed_lines(L,M)
    <~> unequally_directed_opposite_lines(L,reverse_line(M)) ),
    inference(pre_NNF_transformation,[status(esa)],[f38]) ).

fof(f153,plain,
    ? [L,M] :
      ( ( unequally_directed_lines(L,M)
        | unequally_directed_opposite_lines(L,reverse_line(M)) )
      & ( ~ unequally_directed_lines(L,M)
        | ~ unequally_directed_opposite_lines(L,reverse_line(M)) ) ),
    inference(NNF_transformation,[status(esa)],[f152]) ).

fof(f154,plain,
    ( ( unequally_directed_lines(sk0_0,sk0_1)
      | unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1)) )
    & ( ~ unequally_directed_lines(sk0_0,sk0_1)
      | ~ unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1)) ) ),
    inference(skolemization,[status(esa)],[f153]) ).

fof(f155,plain,
    ( unequally_directed_lines(sk0_0,sk0_1)
    | unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1)) ),
    inference(cnf_transformation,[status(esa)],[f154]) ).

fof(f156,plain,
    ( ~ unequally_directed_lines(sk0_0,sk0_1)
    | ~ unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1)) ),
    inference(cnf_transformation,[status(esa)],[f154]) ).

fof(f160,plain,
    ( spl0_0
  <=> unequally_directed_lines(sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f162,plain,
    ( ~ unequally_directed_lines(sk0_0,sk0_1)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f160]) ).

fof(f163,plain,
    ( spl0_1
  <=> unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f164,plain,
    ( unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f165,plain,
    ( ~ unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f166,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f155,f160,f163]) ).

fof(f167,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f156,f160,f163]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( ~ unequally_directed_lines(X0,X1)
      | ~ unequally_directed_lines(X0,reverse_line(X1))
      | left_convergent_lines(X0,reverse_line(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f112,f119]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ unequally_directed_lines(X0,X1)
      | ~ unequally_directed_lines(X0,reverse_line(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f176,f119]) ).

fof(f180,plain,
    ! [X0] : ~ unequally_directed_lines(X0,X0),
    inference(resolution,[status(thm)],[f100,f53]) ).

fof(f182,plain,
    ! [X0] : unequally_directed_lines(reverse_line(X0),X0),
    inference(resolution,[status(thm)],[f180,f110]) ).

fof(f196,plain,
    ! [X0] : ~ unequally_directed_lines(reverse_line(reverse_line(X0)),X0),
    inference(resolution,[status(thm)],[f177,f182]) ).

fof(f213,plain,
    ! [X0] :
      ( ~ unequally_directed_lines(sk0_0,X0)
      | unequally_directed_lines(X0,sk0_1)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f162,f103]) ).

fof(f218,plain,
    ( ~ unequally_directed_lines(sk0_0,reverse_line(reverse_line(sk0_1)))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f213,f196]) ).

fof(f244,plain,
    ( ~ unequally_directed_opposite_lines(sk0_0,reverse_line(sk0_1))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f218,f41]) ).

fof(f245,plain,
    ( $false
    | ~ spl0_1
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f244,f164]) ).

fof(f246,plain,
    ( ~ spl0_1
    | spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f245]) ).

fof(f248,plain,
    ( ~ unequally_directed_lines(sk0_0,reverse_line(reverse_line(sk0_1)))
    | spl0_1 ),
    inference(resolution,[status(thm)],[f165,f42]) ).

fof(f250,plain,
    ( unequally_directed_lines(sk0_0,reverse_line(sk0_1))
    | spl0_1 ),
    inference(resolution,[status(thm)],[f248,f110]) ).

fof(f254,plain,
    ( ~ unequally_directed_lines(sk0_0,sk0_1)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f250,f177]) ).

fof(f255,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f254,f160,f163]) ).

fof(f256,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f166,f167,f246,f255]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n002.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 : Tue Apr 30 01:55:40 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.21/0.39  % Refutation found
% 0.21/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42  % Elapsed time: 0.062565 seconds
% 0.21/0.42  % CPU time: 0.343489 seconds
% 0.21/0.42  % Total memory used: 11.811 MB
% 0.21/0.42  % Net memory used: 11.626 MB
%------------------------------------------------------------------------------