TSTP Solution File: GEO195+3 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO195+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 : Wed May 31 12:08:12 EDT 2023

% Result   : Theorem 0.11s 0.45s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   45 (  12 unt;   0 def)
%            Number of atoms       :  112 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  103 (  36   ~;  48   |;  12   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  119 (; 116   !;   3   ?)

% 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(f13,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_lines(Y,Z)
        | apart_point_and_line(X,Z) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X,Y] :
      ( distinct_lines(X,Y)
     => convergent_lines(X,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(f17,axiom,
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,conjecture,
    ! [X,Y,Z] :
      ( ( convergent_lines(X,Y)
        & convergent_lines(Z,Y)
        & convergent_lines(X,Z) )
     => ( apart_point_and_line(intersection_point(X,Y),Z)
       => apart_point_and_line(intersection_point(Y,X),Z) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [X,Y,Z] :
        ( ( convergent_lines(X,Y)
          & convergent_lines(Z,Y)
          & convergent_lines(X,Z) )
       => ( apart_point_and_line(intersection_point(X,Y),Z)
         => apart_point_and_line(intersection_point(Y,X),Z) ) ),
    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(f63,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | distinct_lines(Y,Z)
      | apart_point_and_line(X,Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f64,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,Y)
      | ! [Z] :
          ( distinct_lines(Y,Z)
          | apart_point_and_line(X,Z) ) ),
    inference(miniscoping,[status(esa)],[f63]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_lines(X1,X2)
      | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f69,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | convergent_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f69]) ).

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

fof(f72,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f127,plain,
    ? [X,Y,Z] :
      ( convergent_lines(X,Y)
      & convergent_lines(Z,Y)
      & convergent_lines(X,Z)
      & apart_point_and_line(intersection_point(X,Y),Z)
      & ~ apart_point_and_line(intersection_point(Y,X),Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f128,plain,
    ( convergent_lines(sk0_0,sk0_1)
    & convergent_lines(sk0_2,sk0_1)
    & convergent_lines(sk0_0,sk0_2)
    & apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_2)
    & ~ apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_2) ),
    inference(skolemization,[status(esa)],[f127]) ).

fof(f132,plain,
    apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_2),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f140,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,parallel_through_point(X1,X2))
      | convergent_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f71,f49]) ).

fof(f141,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)],[f140,f49]) ).

fof(f144,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(parallel_through_point(X1,X2),X0) ),
    inference(resolution,[status(thm)],[f141,f40]) ).

fof(f146,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,parallel_through_point(X1,X3))
      | convergent_lines(X2,X0) ),
    inference(resolution,[status(thm)],[f144,f49]) ).

fof(f158,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X0)
      | convergent_lines(X3,X1)
      | ~ convergent_lines(X2,X3) ),
    inference(resolution,[status(thm)],[f146,f141]) ).

fof(f189,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X0)
      | ~ convergent_lines(X2,X1) ),
    inference(resolution,[status(thm)],[f158,f40]) ).

fof(f194,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(parallel_through_point(X2,X3),X1)
      | convergent_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f189,f144]) ).

fof(f195,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(parallel_through_point(X0,X2),X1) ),
    inference(resolution,[status(thm)],[f189,f71]) ).

fof(f197,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(parallel_through_point(X0,X1),X2)
      | ~ convergent_lines(X3,X2)
      | convergent_lines(X3,X0) ),
    inference(resolution,[status(thm)],[f189,f140]) ).

fof(f204,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,parallel_through_point(X0,X3))
      | convergent_lines(X2,X1) ),
    inference(resolution,[status(thm)],[f195,f49]) ).

fof(f221,plain,
    ! [X0,X1,X2,X3] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(X3,X1)
      | convergent_lines(X3,X2) ),
    inference(resolution,[status(thm)],[f197,f194]) ).

fof(f243,plain,
    ! [X0,X1,X2,X3] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X1)
      | convergent_lines(X3,X0)
      | ~ convergent_lines(X2,X3) ),
    inference(resolution,[status(thm)],[f204,f141]) ).

fof(f303,plain,
    ! [X0,X1,X2,X3] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | convergent_lines(parallel_through_point(X1,X3),X2) ),
    inference(resolution,[status(thm)],[f221,f71]) ).

fof(f337,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,parallel_through_point(X1,X2)) ),
    inference(resolution,[status(thm)],[f303,f40]) ).

fof(f347,plain,
    ! [X0,X1,X2] : ~ convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
    inference(resolution,[status(thm)],[f337,f71]) ).

fof(f354,plain,
    ! [X0,X1,X2,X3] : ~ convergent_lines(parallel_through_point(parallel_through_point(parallel_through_point(X0,X1),X2),X3),X0),
    inference(resolution,[status(thm)],[f347,f337]) ).

fof(f662,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X0)
      | ~ convergent_lines(X1,X2) ),
    inference(resolution,[status(thm)],[f243,f40]) ).

fof(f707,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X1,X0) ),
    inference(resolution,[status(thm)],[f662,f40]) ).

fof(f730,plain,
    ! [X0,X1,X2,X3] : ~ convergent_lines(X0,parallel_through_point(parallel_through_point(parallel_through_point(X0,X1),X2),X3)),
    inference(resolution,[status(thm)],[f707,f354]) ).

fof(f952,plain,
    ! [X0] :
      ( distinct_lines(sk0_2,X0)
      | apart_point_and_line(intersection_point(sk0_0,sk0_1),X0) ),
    inference(resolution,[status(thm)],[f65,f132]) ).

fof(f1117,plain,
    ! [X0] :
      ( apart_point_and_line(intersection_point(sk0_0,sk0_1),X0)
      | convergent_lines(sk0_2,X0) ),
    inference(resolution,[status(thm)],[f952,f70]) ).

fof(f1135,plain,
    ! [X0] : convergent_lines(sk0_2,parallel_through_point(X0,intersection_point(sk0_0,sk0_1))),
    inference(resolution,[status(thm)],[f1117,f72]) ).

fof(f1171,plain,
    $false,
    inference(resolution,[status(thm)],[f1135,f730]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : GEO195+3 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26  % Computer : n016.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 300
% 0.06/0.26  % DateTime : Tue May 30 12:29:59 EDT 2023
% 0.06/0.26  % CPUTime  : 
% 0.11/0.27  % Drodi V3.5.1
% 0.11/0.45  % Refutation found
% 0.11/0.45  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47  % Elapsed time: 0.203219 seconds
% 0.11/0.47  % CPU time: 1.233570 seconds
% 0.11/0.47  % Memory used: 16.401 MB
%------------------------------------------------------------------------------