%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO194+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:24:24 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 47 ~; 69 |; 13 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 92 ( 89 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_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(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(X,Z),Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(X,Z),Y) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f18,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
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(f56,plain,
! [X0] :
( apart_point_and_line(X0,sK2_skl)
| distinct_points(intersection_point(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f41,f53]) ).
fof(f58,plain,
! [X0,X1] :
( distinct_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f47,f19]) ).
fof(f59,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f58,f25]) ).
fof(f62,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f59,f18]) ).
fof(f65,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X2)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f56,f38]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X2,sK2_skl)
| apart_point_and_line(intersection_point(X2,sK2_skl),X1)
| apart_point_and_line(intersection_point(X2,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f65,f36]) ).
fof(f190,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f78,f52]) ).
fof(f375,plain,
! [X0] :
( ~ convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| ~ distinct_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f190,f36]) ).
fof(f381,plain,
! [X0] :
( ~ convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| ~ distinct_lines(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f54]) ).
fof(f383,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| ~ distinct_lines(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f50]) ).
fof(f385,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)
| ~ distinct_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f383,f34]) ).
fof(f390,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f62]) ).
fof(f391,plain,
apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f390,f50]) ).
fof(f392,plain,
~ convergent_lines(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f391,f34]) ).
fof(f395,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f392,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO194+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:20:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.45 % Refutation found
% 0.13/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.103260 seconds
% 0.13/0.46 % CPU time: 0.646795 seconds
% 0.13/0.46 % Total memory used: 22.770 MB
% 0.13/0.46 % Net memory used: 21.338 MB
%------------------------------------------------------------------------------