%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO186+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 : n005.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 12:24:21 PM UTC 2026
% Result : Theorem 0.18s 0.56s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 62 ~; 50 |; 21 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 67 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,U,V] :
( ( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ~ distinct_points(X,intersection_point(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ~ distinct_points(X,intersection_point(U,V)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
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,U,V] :
( distinct_points(X,intersection_point(U,V))
& ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,U,V] :
( distinct_points(X,intersection_point(U,V))
& ~ apart_point_and_line(X,V)
& ~ apart_point_and_line(X,U)
& convergent_lines(U,V)
& ? [Y] : distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))
& ~ apart_point_and_line(sK0_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK1_skl)
& convergent_lines(sK1_skl,sK2_skl)
& distinct_points(sK0_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(Y,sK3_skl)],[f46]) ).
fof(f49,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f58,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f33,f15]) ).
fof(f59,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f34,f15]) ).
fof(f61,plain,
! [X0,X1] :
( distinct_lines(X1,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f23,f16]) ).
fof(f68,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,sK2_skl)
| apart_point_and_line(sK0_skl,X1)
| ~ distinct_lines(sK2_skl,X1)
| ~ distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f36,f51]) ).
fof(f73,plain,
! [X0] :
( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_lines(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f68,f50]) ).
fof(f77,plain,
! [X0] :
( ~ convergent_lines(X0,sK2_skl)
| apart_point_and_line(intersection_point(X0,sK2_skl),sK1_skl)
| ~ distinct_lines(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,intersection_point(X0,sK2_skl)) ),
inference(resolution,[status(thm)],[f73,f59]) ).
fof(f88,plain,
( ~ convergent_lines(sK1_skl,sK2_skl)
| ~ convergent_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f77,f58]) ).
fof(f89,plain,
( ~ convergent_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK2_skl,sK1_skl)
| ~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f88]) ).
fof(f90,plain,
( ~ convergent_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK2_skl,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f52]) ).
fof(f91,plain,
~ distinct_lines(sK2_skl,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f90,f49]) ).
fof(f93,plain,
~ distinct_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f91,f61]) ).
fof(f99,plain,
~ convergent_lines(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f93,f44]) ).
fof(f100,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f99,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n005.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 13:07:03 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.56 % Refutation found
% 0.18/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.60 % Elapsed time: 0.125867 seconds
% 0.18/0.60 % CPU time: 0.599448 seconds
% 0.18/0.60 % Total memory used: 17.395 MB
% 0.18/0.60 % Net memory used: 16.686 MB
%------------------------------------------------------------------------------