%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO225+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:24:36 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 1 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 57 ( 20 ~; 12 |; 18 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f33,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f60,plain,
? [A,B] :
( ! [X] :
( ( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& line(X) )
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
? [A,B] :
( ! [X] :
( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& ! [X] : line(X)
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [X] :
( apart_point_and_line(sK1_skl,X)
| apart_point_and_line(sK0_skl,X) )
& ! [X] : line(X)
& distinct_points(sK0_skl,sK1_skl)
& point(sK1_skl)
& point(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f61]) ).
fof(f65,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f67,plain,
! [X0] :
( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f76,plain,
! [X0] :
( apart_point_and_line(sK0_skl,line_connecting(X0,sK1_skl))
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f36,f67]) ).
fof(f83,plain,
( ~ distinct_points(sK0_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f76,f34]) ).
fof(f84,definition,
( sQ1_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ1_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
~ sQ1_spl,
inference(split_clause,[status(thm)],[f83,f84]) ).
fof(f88,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f65]) ).
fof(f89,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f90,plain,
$false,
inference(sat_refutation,[status(thm)],[f87,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 13:59:27 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.50 % Refutation found
% 0.18/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.56 % Elapsed time: 0.091460 seconds
% 0.18/0.56 % CPU time: 0.089595 seconds
% 0.18/0.56 % Total memory used: 3.266 MB
% 0.18/0.56 % Net memory used: 3.235 MB
%------------------------------------------------------------------------------