%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO186+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 : n016.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 0.15s 0.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 120 ( 47 ~; 48 |; 19 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 67 ( 59 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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)],[f15]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,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)],[f11]) ).
fof(f38,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)],[f37]) ).
fof(f45,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,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)],[f16]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f49]) ).
fof(f52,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f66,plain,
! [X0,X1] :
( distinct_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f47,f19]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(X3,X2)
| 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_points(X0,X1) ),
inference(resolution,[status(thm)],[f38,f66]) ).
fof(f73,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK1_skl)
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f69,f52]) ).
fof(f80,plain,
! [X0,X1] :
( ~ convergent_lines(X1,sK2_skl)
| apart_point_and_line(intersection_point(X1,sK2_skl),sK1_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,intersection_point(X1,sK2_skl)) ),
inference(resolution,[status(thm)],[f73,f36]) ).
fof(f98,plain,
! [X0] :
( ~ convergent_lines(sK1_skl,sK2_skl)
| ~ convergent_lines(sK1_skl,sK2_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,intersection_point(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f80,f34]) ).
fof(f101,plain,
! [X0] :
( ~ convergent_lines(sK1_skl,sK2_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,intersection_point(sK1_skl,sK2_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f98]) ).
fof(f102,plain,
! [X0] :
( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,intersection_point(sK1_skl,sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f52]) ).
fof(f176,plain,
( apart_point_and_line(sK0_skl,sK1_skl)
| ~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f102,f54]) ).
fof(f179,plain,
apart_point_and_line(sK0_skl,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f176,f55]) ).
fof(f180,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f179,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n016.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Sun Sep 20 13:11:37 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.55 % Drodi V4.1.1
% 0.15/0.58 % Refutation found
% 0.15/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.60 % Elapsed time: 0.056541 seconds
% 0.15/0.60 % CPU time: 0.215005 seconds
% 0.15/0.60 % Total memory used: 18.483 MB
% 0.15/0.60 % Net memory used: 17.993 MB
%------------------------------------------------------------------------------