%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO197+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:24:26 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 116 ( 40 ~; 53 |; 17 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(Z,Y),X) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,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(f32,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)],[f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,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)],[f32]) ).
fof(f35,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f43,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
? [X,Y,Z] :
( apart_point_and_line(intersection_point(Z,Y),X)
& ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl)
& ~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
& convergent_lines(sK0_skl,sK2_skl)
& convergent_lines(sK2_skl,sK1_skl)
& convergent_lines(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f45]) ).
fof(f47,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
convergent_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f34]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f33]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4] :
( ~ apart_point_and_line(X2,X3)
| ~ convergent_lines(X3,X4)
| apart_point_and_line(intersection_point(X3,X4),X1)
| apart_point_and_line(intersection_point(X3,X4),X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f36,f33]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ convergent_lines(sK0_skl,X2)
| apart_point_and_line(intersection_point(sK0_skl,X2),X1)
| apart_point_and_line(intersection_point(sK0_skl,X2),X0)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f65,f51]) ).
fof(f72,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f69,f47]) ).
fof(f90,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f72,f44]) ).
fof(f96,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f90,f48]) ).
fof(f101,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f50]) ).
fof(f102,plain,
( ~ convergent_lines(sK2_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f101,f54]) ).
fof(f105,plain,
( ~ convergent_lines(sK2_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f53]) ).
fof(f106,plain,
apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f105,f48]) ).
fof(f107,plain,
~ convergent_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f106,f53]) ).
fof(f110,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f107,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO197+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:19:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.046045 seconds
% 0.11/0.43 % CPU time: 0.166848 seconds
% 0.11/0.43 % Total memory used: 18.250 MB
% 0.11/0.43 % Net memory used: 17.817 MB
%------------------------------------------------------------------------------