TSTP Solution File: GEO218+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO218+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 12:08:22 EDT 2023

% Result   : Theorem 0.12s 0.41s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   77 (  18 unt;   0 def)
%            Number of atoms       :  203 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  211 (  85   ~;  87   |;  29   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  149 (; 143   !;   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(f19,axiom,
    ! [L,M] :
      ( convergent_lines(L,M)
      | unorthogonal_lines(L,M) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [L,M,N] :
      ( ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
     => ( ( convergent_lines(L,N)
          & unorthogonal_lines(L,N) )
        | ( convergent_lines(M,N)
          & unorthogonal_lines(M,N) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [L,M,N] :
      ( ( ( ~ convergent_lines(L,M)
          | ~ unorthogonal_lines(L,M) )
        & ( ~ convergent_lines(L,N)
          | ~ unorthogonal_lines(L,N) ) )
     => ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ! [L,M,N] :
      ( ( ~ unorthogonal_lines(L,M)
        & ~ unorthogonal_lines(L,N) )
     => ~ convergent_lines(M,N) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,axiom,
    ! [X,Y] :
      ( parallel_lines(X,Y)
    <=> ~ convergent_lines(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f35,axiom,
    ! [X,Y] :
      ( orthogonal_lines(X,Y)
    <=> ~ unorthogonal_lines(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,conjecture,
    ! [L,M,N] :
      ( ( parallel_lines(L,M)
        & orthogonal_lines(L,N) )
     => orthogonal_lines(M,N) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [L,M,N] :
        ( ( parallel_lines(L,M)
          & orthogonal_lines(L,N) )
       => orthogonal_lines(M,N) ),
    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(f76,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | unorthogonal_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f77,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(L,M)
      | ~ unorthogonal_lines(L,M)
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) )
      | ( convergent_lines(M,N)
        & unorthogonal_lines(M,N) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f78,plain,
    ! [L,N] :
      ( pd0_0(N,L)
     => ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) ) ),
    introduced(predicate_definition,[f77]) ).

fof(f79,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(L,M)
      | ~ unorthogonal_lines(L,M)
      | pd0_0(N,L)
      | ( convergent_lines(M,N)
        & unorthogonal_lines(M,N) ) ),
    inference(formula_renaming,[status(thm)],[f77,f78]) ).

fof(f80,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
      | ~ unorthogonal_lines(L,M)
      | ! [N] :
          ( pd0_0(N,L)
          | ( convergent_lines(M,N)
            & unorthogonal_lines(M,N) ) ) ),
    inference(miniscoping,[status(esa)],[f79]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | ~ unorthogonal_lines(X0,X1)
      | pd0_0(X2,X0)
      | unorthogonal_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f83,plain,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f90,plain,
    ! [L,M,N] :
      ( ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) )
      | ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f25]) ).

fof(f91,plain,
    ! [L,M] :
      ( pd0_1(M,L)
     => ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) ) ),
    introduced(predicate_definition,[f90]) ).

fof(f92,plain,
    ! [L,M,N] :
      ( pd0_1(M,L)
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) )
      | ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N) ),
    inference(formula_renaming,[status(thm)],[f90,f91]) ).

fof(f93,plain,
    ! [M,N] :
      ( ! [L] :
          ( pd0_1(M,L)
          | ( convergent_lines(L,N)
            & unorthogonal_lines(L,N) ) )
      | ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N) ),
    inference(miniscoping,[status(esa)],[f92]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( pd0_1(X0,X1)
      | convergent_lines(X1,X2)
      | ~ convergent_lines(X0,X2)
      | ~ unorthogonal_lines(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f96,plain,
    ! [L,M,N] :
      ( unorthogonal_lines(L,M)
      | unorthogonal_lines(L,N)
      | ~ convergent_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f97,plain,
    ! [M,N] :
      ( ! [L] :
          ( unorthogonal_lines(L,M)
          | unorthogonal_lines(L,N) )
      | ~ convergent_lines(M,N) ),
    inference(miniscoping,[status(esa)],[f96]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( unorthogonal_lines(X0,X1)
      | unorthogonal_lines(X0,X2)
      | ~ convergent_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f115,plain,
    ! [X,Y] :
      ( ( ~ parallel_lines(X,Y)
        | ~ convergent_lines(X,Y) )
      & ( parallel_lines(X,Y)
        | convergent_lines(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f33]) ).

fof(f116,plain,
    ( ! [X,Y] :
        ( ~ parallel_lines(X,Y)
        | ~ convergent_lines(X,Y) )
    & ! [X,Y] :
        ( parallel_lines(X,Y)
        | convergent_lines(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f115]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ~ parallel_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f116]) ).

fof(f123,plain,
    ! [X,Y] :
      ( ( ~ orthogonal_lines(X,Y)
        | ~ unorthogonal_lines(X,Y) )
      & ( orthogonal_lines(X,Y)
        | unorthogonal_lines(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f35]) ).

fof(f124,plain,
    ( ! [X,Y] :
        ( ~ orthogonal_lines(X,Y)
        | ~ unorthogonal_lines(X,Y) )
    & ! [X,Y] :
        ( orthogonal_lines(X,Y)
        | unorthogonal_lines(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f123]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ orthogonal_lines(X0,X1)
      | ~ unorthogonal_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( orthogonal_lines(X0,X1)
      | unorthogonal_lines(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f127,plain,
    ? [L,M,N] :
      ( parallel_lines(L,M)
      & orthogonal_lines(L,N)
      & ~ orthogonal_lines(M,N) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f128,plain,
    ? [M,N] :
      ( ? [L] :
          ( parallel_lines(L,M)
          & orthogonal_lines(L,N) )
      & ~ orthogonal_lines(M,N) ),
    inference(miniscoping,[status(esa)],[f127]) ).

fof(f129,plain,
    ( parallel_lines(sk0_2,sk0_0)
    & orthogonal_lines(sk0_2,sk0_1)
    & ~ orthogonal_lines(sk0_0,sk0_1) ),
    inference(skolemization,[status(esa)],[f128]) ).

fof(f130,plain,
    parallel_lines(sk0_2,sk0_0),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f131,plain,
    orthogonal_lines(sk0_2,sk0_1),
    inference(cnf_transformation,[status(esa)],[f129]) ).

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

fof(f133,plain,
    ! [L,N] :
      ( ~ pd0_0(N,L)
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f78]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | convergent_lines(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f133]) ).

fof(f136,plain,
    ! [L,M] :
      ( ~ pd0_1(M,L)
      | ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f91]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ~ pd0_1(X0,X1)
      | unorthogonal_lines(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f136]) ).

fof(f139,plain,
    unorthogonal_lines(sk0_0,sk0_1),
    inference(resolution,[status(thm)],[f126,f132]) ).

fof(f141,plain,
    ! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
    inference(resolution,[status(thm)],[f76,f83]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ orthogonal_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f76,f125]) ).

fof(f143,plain,
    convergent_lines(sk0_2,sk0_1),
    inference(resolution,[status(thm)],[f142,f131]) ).

fof(f149,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(orthogonal_through_point(X0,X1),X2)
      | convergent_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f49,f141]) ).

fof(f150,plain,
    ! [X0] :
      ( convergent_lines(sk0_2,X0)
      | convergent_lines(sk0_1,X0) ),
    inference(resolution,[status(thm)],[f49,f143]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( convergent_lines(sk0_1,X0)
      | convergent_lines(sk0_2,X1)
      | convergent_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f150,f49]) ).

fof(f155,plain,
    ! [X0] :
      ( convergent_lines(sk0_1,X0)
      | convergent_lines(X0,sk0_2) ),
    inference(resolution,[status(thm)],[f151,f40]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( convergent_lines(X0,sk0_2)
      | convergent_lines(sk0_1,X1)
      | convergent_lines(X0,X1) ),
    inference(resolution,[status(thm)],[f155,f49]) ).

fof(f183,plain,
    ! [X0] :
      ( convergent_lines(X0,sk0_2)
      | convergent_lines(X0,sk0_1) ),
    inference(resolution,[status(thm)],[f165,f40]) ).

fof(f330,plain,
    ! [X0,X1,X2] :
      ( unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X1,X2)
      | ~ orthogonal_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f98,f125]) ).

fof(f334,plain,
    ! [X0] :
      ( unorthogonal_lines(sk0_2,X0)
      | ~ convergent_lines(X0,sk0_1) ),
    inference(resolution,[status(thm)],[f330,f131]) ).

fof(f377,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | ~ unorthogonal_lines(X0,X1)
      | unorthogonal_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f82,f134]) ).

fof(f378,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X2,X1)
      | ~ unorthogonal_lines(X2,X1)
      | unorthogonal_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f94,f138]) ).

fof(f388,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(orthogonal_through_point(X0,X1),X2)
      | ~ convergent_lines(X0,X2)
      | ~ unorthogonal_lines(X0,X2) ),
    inference(resolution,[status(thm)],[f378,f83]) ).

fof(f389,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(orthogonal_through_point(X0,X1),X2)
      | ~ unorthogonal_lines(X0,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f388,f149]) ).

fof(f392,plain,
    ! [X0,X1] : ~ unorthogonal_lines(X0,orthogonal_through_point(X0,X1)),
    inference(resolution,[status(thm)],[f389,f40]) ).

fof(f394,plain,
    ! [X0] : ~ convergent_lines(orthogonal_through_point(sk0_2,X0),sk0_1),
    inference(resolution,[status(thm)],[f392,f334]) ).

fof(f404,plain,
    ~ unorthogonal_lines(sk0_2,sk0_1),
    inference(resolution,[status(thm)],[f394,f389]) ).

fof(f413,plain,
    ! [X0] :
      ( convergent_lines(sk0_2,X0)
      | ~ convergent_lines(sk0_1,X0)
      | ~ unorthogonal_lines(sk0_1,X0) ),
    inference(resolution,[status(thm)],[f404,f378]) ).

fof(f414,plain,
    ! [X0] :
      ( convergent_lines(sk0_2,X0)
      | ~ unorthogonal_lines(sk0_1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f413,f150]) ).

fof(f440,plain,
    ~ unorthogonal_lines(sk0_1,sk0_2),
    inference(resolution,[status(thm)],[f414,f40]) ).

fof(f441,plain,
    ! [X0] :
      ( ~ unorthogonal_lines(sk0_1,X0)
      | ~ parallel_lines(sk0_2,X0) ),
    inference(resolution,[status(thm)],[f414,f117]) ).

fof(f444,plain,
    ! [X0] :
      ( ~ convergent_lines(X0,sk0_1)
      | ~ unorthogonal_lines(X0,sk0_1)
      | convergent_lines(X0,sk0_2) ),
    inference(resolution,[status(thm)],[f440,f377]) ).

fof(f445,plain,
    ! [X0] :
      ( ~ unorthogonal_lines(X0,sk0_1)
      | convergent_lines(X0,sk0_2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f444,f183]) ).

fof(f449,plain,
    ! [X0] :
      ( unorthogonal_lines(sk0_1,X0)
      | ~ convergent_lines(X0,sk0_2) ),
    inference(resolution,[status(thm)],[f440,f98]) ).

fof(f482,plain,
    ~ unorthogonal_lines(sk0_1,sk0_0),
    inference(resolution,[status(thm)],[f441,f130]) ).

fof(f556,plain,
    ~ convergent_lines(sk0_0,sk0_2),
    inference(resolution,[status(thm)],[f449,f482]) ).

fof(f566,plain,
    ~ unorthogonal_lines(sk0_0,sk0_1),
    inference(resolution,[status(thm)],[f556,f445]) ).

fof(f567,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f566,f139]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO218+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 12:01:07 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.12/0.41  % Refutation found
% 0.12/0.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.42  % Elapsed time: 0.082868 seconds
% 0.18/0.42  % CPU time: 0.480240 seconds
% 0.18/0.42  % Memory used: 7.724 MB
%------------------------------------------------------------------------------