TSTP Solution File: GEO254+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO254+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 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 20:17:46 EDT 2024

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   64 (  14 unt;   0 def)
%            Number of atoms       :  190 (   0 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  218 (  92   ~;  80   |;  37   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   3 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  124 ( 121   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [L,A,B] :
      ( before_on_line(L,A,B)
    <=> ( distinct_points(A,B)
        & ~ ( left_apart_point(A,L)
            | left_apart_point(A,reverse_line(L)) )
        & ~ ( left_apart_point(B,L)
            | left_apart_point(B,reverse_line(L)) )
        & ~ unequally_directed_lines(L,line_connecting(A,B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : ~ distinct_points(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B,C] :
      ( distinct_points(A,B)
     => ( distinct_points(A,C)
        | distinct_points(B,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [L] : ~ unequally_directed_lines(L,L),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,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(f14,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(f15,axiom,
    ! [A,L] :
      ~ ( left_apart_point(A,L)
        | left_apart_point(A,reverse_line(L)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [L,M] :
      ~ ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [A,B] : ~ unequally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,conjecture,
    ! [A,B,L] :
      ( ( distinct_points(A,B)
        & ~ apart_point_and_line(A,L)
        & ~ apart_point_and_line(B,L) )
     => ( before_on_line(L,A,B)
        & before_on_line(L,B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    ~ ! [A,B,L] :
        ( ( distinct_points(A,B)
          & ~ apart_point_and_line(A,L)
          & ~ apart_point_and_line(B,L) )
       => ( before_on_line(L,A,B)
          & before_on_line(L,B,A) ) ),
    inference(negated_conjecture,[status(cth)],[f32]) ).

fof(f52,plain,
    ! [L,A,B] :
      ( before_on_line(L,A,B)
    <=> ( distinct_points(A,B)
        & ~ left_apart_point(A,L)
        & ~ left_apart_point(A,reverse_line(L))
        & ~ left_apart_point(B,L)
        & ~ left_apart_point(B,reverse_line(L))
        & ~ unequally_directed_lines(L,line_connecting(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f53,plain,
    ! [L,A,B] :
      ( ( ~ before_on_line(L,A,B)
        | ( distinct_points(A,B)
          & ~ left_apart_point(A,L)
          & ~ left_apart_point(A,reverse_line(L))
          & ~ left_apart_point(B,L)
          & ~ left_apart_point(B,reverse_line(L))
          & ~ unequally_directed_lines(L,line_connecting(A,B)) ) )
      & ( before_on_line(L,A,B)
        | ~ distinct_points(A,B)
        | left_apart_point(A,L)
        | left_apart_point(A,reverse_line(L))
        | left_apart_point(B,L)
        | left_apart_point(B,reverse_line(L))
        | unequally_directed_lines(L,line_connecting(A,B)) ) ),
    inference(NNF_transformation,[status(esa)],[f52]) ).

fof(f54,plain,
    ( ! [L,A,B] :
        ( ~ before_on_line(L,A,B)
        | ( distinct_points(A,B)
          & ~ left_apart_point(A,L)
          & ~ left_apart_point(A,reverse_line(L))
          & ~ left_apart_point(B,L)
          & ~ left_apart_point(B,reverse_line(L))
          & ~ unequally_directed_lines(L,line_connecting(A,B)) ) )
    & ! [L,A,B] :
        ( before_on_line(L,A,B)
        | ~ distinct_points(A,B)
        | left_apart_point(A,L)
        | left_apart_point(A,reverse_line(L))
        | left_apart_point(B,L)
        | left_apart_point(B,reverse_line(L))
        | unequally_directed_lines(L,line_connecting(A,B)) ) ),
    inference(miniscoping,[status(esa)],[f53]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( before_on_line(X0,X1,X2)
      | ~ distinct_points(X1,X2)
      | left_apart_point(X1,X0)
      | left_apart_point(X1,reverse_line(X0))
      | left_apart_point(X2,X0)
      | left_apart_point(X2,reverse_line(X0))
      | unequally_directed_lines(X0,line_connecting(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f70,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f71,plain,
    ! [A,B,C] :
      ( ~ distinct_points(A,B)
      | distinct_points(A,C)
      | distinct_points(B,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f72,plain,
    ! [A,B] :
      ( ~ distinct_points(A,B)
      | ! [C] :
          ( distinct_points(A,C)
          | distinct_points(B,C) ) ),
    inference(miniscoping,[status(esa)],[f71]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ~ distinct_points(X0,X1)
      | distinct_points(X0,X2)
      | distinct_points(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f72]) ).

fof(f78,plain,
    ! [X0] : ~ unequally_directed_lines(X0,X0),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f79,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)],[f11]) ).

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

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ~ unequally_directed_lines(X0,X1)
      | unequally_directed_lines(X0,X2)
      | unequally_directed_lines(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f90,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)],[f14]) ).

fof(f91,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)],[f90]) ).

fof(f92,plain,
    ! [A,L] :
      ( ~ left_apart_point(A,L)
      & ~ left_apart_point(A,reverse_line(L)) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f93,plain,
    ( ! [A,L] : ~ left_apart_point(A,L)
    & ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
    inference(miniscoping,[status(esa)],[f92]) ).

fof(f94,plain,
    ! [X0,X1] : ~ left_apart_point(X0,X1),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f96,plain,
    ! [L,M] :
      ( ~ left_convergent_lines(L,M)
      & ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f97,plain,
    ( ! [L,M] : ~ left_convergent_lines(L,M)
    & ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(miniscoping,[status(esa)],[f96]) ).

fof(f98,plain,
    ! [X0,X1] : ~ left_convergent_lines(X0,X1),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f116,plain,
    ! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f130,plain,
    ? [A,B,L] :
      ( distinct_points(A,B)
      & ~ apart_point_and_line(A,L)
      & ~ apart_point_and_line(B,L)
      & ( ~ before_on_line(L,A,B)
        | ~ before_on_line(L,B,A) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f33]) ).

fof(f131,plain,
    ( distinct_points(sk0_0,sk0_1)
    & ~ apart_point_and_line(sk0_0,sk0_2)
    & ~ apart_point_and_line(sk0_1,sk0_2)
    & ( ~ before_on_line(sk0_2,sk0_0,sk0_1)
      | ~ before_on_line(sk0_2,sk0_1,sk0_0) ) ),
    inference(skolemization,[status(esa)],[f130]) ).

fof(f132,plain,
    distinct_points(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f131]) ).

fof(f135,plain,
    ( ~ before_on_line(sk0_2,sk0_0,sk0_1)
    | ~ before_on_line(sk0_2,sk0_1,sk0_0) ),
    inference(cnf_transformation,[status(esa)],[f131]) ).

fof(f139,plain,
    ( spl0_0
  <=> before_on_line(sk0_2,sk0_0,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f141,plain,
    ( ~ before_on_line(sk0_2,sk0_0,sk0_1)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f139]) ).

fof(f142,plain,
    ( spl0_1
  <=> before_on_line(sk0_2,sk0_1,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f144,plain,
    ( ~ before_on_line(sk0_2,sk0_1,sk0_0)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f142]) ).

fof(f145,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f135,f139,f142]) ).

fof(f147,plain,
    ! [X0,X1,X2] :
      ( before_on_line(X0,X1,X2)
      | ~ distinct_points(X1,X2)
      | left_apart_point(X1,reverse_line(X0))
      | left_apart_point(X2,X0)
      | left_apart_point(X2,reverse_line(X0))
      | unequally_directed_lines(X0,line_connecting(X1,X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f61,f94]) ).

fof(f148,plain,
    ! [X0,X1,X2] :
      ( before_on_line(X0,X1,X2)
      | ~ distinct_points(X1,X2)
      | left_apart_point(X2,X0)
      | left_apart_point(X2,reverse_line(X0))
      | unequally_directed_lines(X0,line_connecting(X1,X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f147,f94]) ).

fof(f156,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)],[f91,f98]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ~ unequally_directed_lines(X0,X1)
      | ~ unequally_directed_lines(X0,reverse_line(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f156,f98]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ~ distinct_points(X0,X1)
      | distinct_points(X1,X0) ),
    inference(resolution,[status(thm)],[f73,f70]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( ~ unequally_directed_lines(X0,X1)
      | unequally_directed_lines(X1,X0) ),
    inference(resolution,[status(thm)],[f81,f78]) ).

fof(f267,plain,
    ! [X0,X1,X2] :
      ( ~ unequally_directed_lines(line_connecting(X0,X1),X2)
      | unequally_directed_lines(X2,reverse_line(line_connecting(X1,X0))) ),
    inference(resolution,[status(thm)],[f116,f81]) ).

fof(f790,plain,
    ! [X0,X1,X2] :
      ( ~ unequally_directed_lines(line_connecting(X0,X1),X2)
      | ~ unequally_directed_lines(X2,line_connecting(X1,X0)) ),
    inference(resolution,[status(thm)],[f267,f157]) ).

fof(f808,plain,
    ! [X0,X1,X2] :
      ( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
      | ~ unequally_directed_lines(X0,line_connecting(X2,X1)) ),
    inference(resolution,[status(thm)],[f790,f192]) ).

fof(f833,plain,
    ! [X0,X1,X2] :
      ( ~ unequally_directed_lines(X0,X1)
      | unequally_directed_lines(X1,line_connecting(X2,X2)) ),
    inference(resolution,[status(thm)],[f808,f81]) ).

fof(f842,plain,
    ! [X0,X1] : ~ unequally_directed_lines(X0,line_connecting(X1,X1)),
    inference(factoring,[status(esa)],[f808]) ).

fof(f843,plain,
    ! [X0,X1] : ~ unequally_directed_lines(X0,X1),
    inference(backward_subsumption_resolution,[status(thm)],[f833,f842]) ).

fof(f847,plain,
    ! [X0,X1,X2] :
      ( before_on_line(X0,X1,X2)
      | ~ distinct_points(X1,X2)
      | left_apart_point(X2,X0)
      | left_apart_point(X2,reverse_line(X0)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f148,f843]) ).

fof(f848,plain,
    ! [X0,X1,X2] :
      ( before_on_line(X0,X1,X2)
      | ~ distinct_points(X1,X2)
      | left_apart_point(X2,reverse_line(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f847,f94]) ).

fof(f1152,plain,
    ! [X0,X1,X2] :
      ( before_on_line(X0,X1,X2)
      | ~ distinct_points(X1,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f848,f94]) ).

fof(f1201,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f141,f1152]) ).

fof(f1202,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1201,f132]) ).

fof(f1203,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f1202]) ).

fof(f1209,plain,
    ( ~ distinct_points(sk0_1,sk0_0)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f144,f1152]) ).

fof(f1218,plain,
    ( ~ distinct_points(sk0_0,sk0_1)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f1209,f159]) ).

fof(f1219,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1218,f132]) ).

fof(f1220,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f1219]) ).

fof(f1221,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f145,f1203,f1220]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : GEO254+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.02/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.27  % Computer : n032.cluster.edu
% 0.09/0.27  % Model    : x86_64 x86_64
% 0.09/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27  % Memory   : 8042.1875MB
% 0.09/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27  % CPULimit : 300
% 0.09/0.27  % WCLimit  : 300
% 0.09/0.27  % DateTime : Tue Apr 30 01:47:36 EDT 2024
% 0.09/0.27  % CPUTime  : 
% 0.09/0.28  % Drodi V3.6.0
% 0.13/0.39  % Refutation found
% 0.13/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40  % Elapsed time: 0.120823 seconds
% 0.13/0.40  % CPU time: 0.887274 seconds
% 0.13/0.40  % Total memory used: 21.150 MB
% 0.13/0.40  % Net memory used: 19.836 MB
%------------------------------------------------------------------------------