TSTP Solution File: GEO226+3 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO226+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 20:17:39 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   41 (  10 unt;   0 def)
%            Number of atoms       :  101 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  103 (  43   ~;  31   |;  20   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   74 (  68   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] : ~ convergent_lines(X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,axiom,
    ! [X,Y] :
      ( incident_point_and_line(X,Y)
    <=> ~ apart_point_and_line(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,conjecture,
    ! [L,M] :
      ( ( line(L)
        & line(M)
        & convergent_lines(L,M) )
     => ? [X] :
          ( point(X)
         => ( incident_point_and_line(X,L)
            & incident_point_and_line(X,M) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [L,M] :
        ( ( line(L)
          & line(M)
          & convergent_lines(L,M) )
       => ? [X] :
            ( point(X)
           => ( incident_point_and_line(X,L)
              & incident_point_and_line(X,M) ) ) ),
    inference(negated_conjecture,[status(cth)],[f36]) ).

fof(f40,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f47,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f48,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ! [Z] :
          ( convergent_lines(X,Z)
          | convergent_lines(Y,Z) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f54,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ~ apart_point_and_line(intersection_point(X,Y),X) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ~ apart_point_and_line(intersection_point(X,Y),Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f71,plain,
    ! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f119,plain,
    ! [X,Y] :
      ( ( ~ incident_point_and_line(X,Y)
        | ~ apart_point_and_line(X,Y) )
      & ( incident_point_and_line(X,Y)
        | apart_point_and_line(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f34]) ).

fof(f120,plain,
    ( ! [X,Y] :
        ( ~ incident_point_and_line(X,Y)
        | ~ apart_point_and_line(X,Y) )
    & ! [X,Y] :
        ( incident_point_and_line(X,Y)
        | apart_point_and_line(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f119]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( incident_point_and_line(X0,X1)
      | apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f120]) ).

fof(f127,plain,
    ? [L,M] :
      ( line(L)
      & line(M)
      & convergent_lines(L,M)
      & ! [X] :
          ( point(X)
          & ( ~ incident_point_and_line(X,L)
            | ~ incident_point_and_line(X,M) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f128,plain,
    ? [L,M] :
      ( line(L)
      & line(M)
      & convergent_lines(L,M)
      & ! [X] : point(X)
      & ! [X] :
          ( ~ incident_point_and_line(X,L)
          | ~ incident_point_and_line(X,M) ) ),
    inference(miniscoping,[status(esa)],[f127]) ).

fof(f129,plain,
    ( line(sk0_0)
    & line(sk0_1)
    & convergent_lines(sk0_0,sk0_1)
    & ! [X] : point(X)
    & ! [X] :
        ( ~ incident_point_and_line(X,sk0_0)
        | ~ incident_point_and_line(X,sk0_1) ) ),
    inference(skolemization,[status(esa)],[f128]) ).

fof(f132,plain,
    convergent_lines(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ incident_point_and_line(X0,sk0_0)
      | ~ incident_point_and_line(X0,sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X0) ),
    inference(resolution,[status(thm)],[f49,f40]) ).

fof(f145,plain,
    ! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
    inference(resolution,[status(thm)],[f71,f142]) ).

fof(f147,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,parallel_through_point(X1,X2))
      | convergent_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f71,f49]) ).

fof(f157,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,X0)
      | convergent_lines(X2,parallel_through_point(X1,X3)) ),
    inference(resolution,[status(thm)],[f147,f49]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( convergent_lines(sk0_1,X0)
      | convergent_lines(sk0_0,parallel_through_point(X0,X1)) ),
    inference(resolution,[status(thm)],[f157,f132]) ).

fof(f179,plain,
    convergent_lines(sk0_1,sk0_0),
    inference(resolution,[status(thm)],[f165,f145]) ).

fof(f431,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | incident_point_and_line(intersection_point(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f55,f122]) ).

fof(f432,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | incident_point_and_line(intersection_point(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f57,f122]) ).

fof(f433,plain,
    ! [X0] :
      ( ~ convergent_lines(sk0_1,X0)
      | ~ incident_point_and_line(intersection_point(sk0_1,X0),sk0_0) ),
    inference(resolution,[status(thm)],[f431,f134]) ).

fof(f444,plain,
    ( spl0_0
  <=> convergent_lines(sk0_1,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f446,plain,
    ( ~ convergent_lines(sk0_1,sk0_0)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f444]) ).

fof(f447,plain,
    ( ~ convergent_lines(sk0_1,sk0_0)
    | ~ convergent_lines(sk0_1,sk0_0) ),
    inference(resolution,[status(thm)],[f433,f432]) ).

fof(f448,plain,
    ~ spl0_0,
    inference(split_clause,[status(thm)],[f447,f444]) ).

fof(f449,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f446,f179]) ).

fof(f450,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f449]) ).

fof(f451,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f448,f450]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GEO226+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Apr 30 01:19:50 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.40  % Refutation found
% 0.14/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42  % Elapsed time: 0.065111 seconds
% 0.21/0.42  % CPU time: 0.428406 seconds
% 0.21/0.42  % Total memory used: 13.362 MB
% 0.21/0.42  % Net memory used: 12.996 MB
%------------------------------------------------------------------------------