%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO198+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 : n019.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 0.15s 5.65s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 12 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 233 ( 107 ~; 102 |; 15 &)
% ( 0 <=>; 9 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 112 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
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(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
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,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(X,Z),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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(X,Z),Y) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f26,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
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(f39,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
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,Z] :
( apart_point_and_line(intersection_point(X,Z),Y)
& ~ 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)],[f16]) ).
fof(f49,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_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)],[f48]) ).
fof(f50,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
convergent_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f28,f19]) ).
fof(f57,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f22,f17]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(intersection_point(X0,X1),X3)
| ~ distinct_lines(X1,X3)
| ~ distinct_points(intersection_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f38,f36]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1)
| ~ distinct_lines(X1,X0)
| ~ distinct_points(intersection_point(X0,X1),X2) ),
inference(resolution,[status(thm)],[f63,f34]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1)
| ~ distinct_lines(X1,X0)
| ~ distinct_points(intersection_point(X0,X1),X2) ),
inference(duplicate_literals_removal,[status(thm)],[f85]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(X1,X2),X0)
| ~ distinct_lines(X1,X0)
| ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X2)) ),
inference(resolution,[status(thm)],[f90,f34]) ).
fof(f258,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| ~ convergent_lines(sK2_skl,sK0_skl)
| ~ distinct_lines(sK0_skl,sK2_skl)
| ~ distinct_points(intersection_point(sK2_skl,sK0_skl),intersection_point(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f93,f53]) ).
fof(f259,plain,
! [X0,X1] :
( ~ convergent_lines(X1,X0)
| ~ convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1)
| ~ distinct_lines(X1,X0)
| ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(resolution,[status(thm)],[f93,f36]) ).
fof(f266,plain,
( ~ convergent_lines(sK2_skl,sK0_skl)
| ~ distinct_lines(sK0_skl,sK2_skl)
| ~ distinct_points(intersection_point(sK2_skl,sK0_skl),intersection_point(sK0_skl,sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f50]) ).
fof(f267,plain,
! [X0,X1] :
( ~ convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1)
| ~ distinct_lines(X1,X0)
| ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f259]) ).
fof(f268,plain,
! [X0,X1] :
( ~ convergent_lines(X1,X0)
| ~ distinct_lines(X1,X0)
| ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f55]) ).
fof(f273,plain,
! [X0,X1] :
( ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
| ~ convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f268,f57]) ).
fof(f281,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X1,X0))
| ~ distinct_points(intersection_point(X0,X1),X2)
| ~ convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f273,f22]) ).
fof(f681,plain,
( ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK2_skl,sK0_skl))
| ~ convergent_lines(sK2_skl,sK0_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f266,f57]) ).
fof(f858,plain,
( ~ distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl))
| ~ convergent_lines(sK0_skl,sK2_skl)
| ~ distinct_lines(sK0_skl,sK2_skl)
| ~ convergent_lines(sK2_skl,sK0_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f681,f281]) ).
fof(f863,plain,
( ~ distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl))
| ~ convergent_lines(sK0_skl,sK2_skl)
| ~ convergent_lines(sK2_skl,sK0_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f858]) ).
fof(f864,plain,
( ~ distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl))
| ~ convergent_lines(sK0_skl,sK2_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f863,f55]) ).
fof(f873,plain,
( ~ distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl))
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f864,f52]) ).
fof(f878,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| ~ apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f873,f41]) ).
fof(f908,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| ~ apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f878,f36]) ).
fof(f914,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f908,f54]) ).
fof(f920,plain,
~ distinct_lines(sK0_skl,sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f914,f50]) ).
fof(f921,plain,
! [X0] :
( convergent_lines(X0,sK2_skl)
| ~ convergent_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f920,f47]) ).
fof(f929,plain,
~ convergent_lines(sK2_skl,sK0_skl),
inference(resolution,[status(thm)],[f921,f19]) ).
fof(f956,plain,
~ convergent_lines(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f929,f55]) ).
fof(f958,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f956,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n019.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 13:17:55 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.15/5.65 % Refutation found
% 0.15/5.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.67 % Elapsed time: 0.280536 seconds
% 0.15/5.67 % CPU time: 2.037020 seconds
% 0.15/5.67 % Total memory used: 33.903 MB
% 0.15/5.67 % Net memory used: 29.777 MB
%------------------------------------------------------------------------------