%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:24:37 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 63 ( 20 ~; 17 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,M)
& ~ apart_point_and_line(X,L) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,M)
& ~ apart_point_and_line(X,L) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) ) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f57,plain,
? [L,M] :
( ! [X] :
( ( apart_point_and_line(X,M)
| apart_point_and_line(X,L) )
& point(X) )
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
? [L,M] :
( ! [X] :
( apart_point_and_line(X,M)
| apart_point_and_line(X,L) )
& ! [X] : point(X)
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [X] :
( apart_point_and_line(X,sK1_skl)
| apart_point_and_line(X,sK0_skl) )
& ! [X] : point(X)
& convergent_lines(sK0_skl,sK1_skl)
& line(sK1_skl)
& line(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f58]) ).
fof(f62,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
! [X0] :
( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f69,plain,
! [X0,X1] :
( distinct_points(X0,intersection_point(X1,sK1_skl))
| ~ convergent_lines(X1,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f64,f38]) ).
fof(f71,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f69,f62]) ).
fof(f72,plain,
apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl),
inference(resolution,[status(thm)],[f71,f19]) ).
fof(f74,plain,
! [X0] :
( distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,X0))
| ~ convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f72,f37]) ).
fof(f75,plain,
~ convergent_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f74,f19]) ).
fof(f76,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f75,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n017.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 20 13:57:12 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.40 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.032535 seconds
% 0.10/0.43 % CPU time: 0.070910 seconds
% 0.10/0.43 % Total memory used: 7.543 MB
% 0.10/0.43 % Net memory used: 7.390 MB
%------------------------------------------------------------------------------