%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO176+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 12:24:17 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 63 ( 25 ~; 20 |; 13 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 33 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f36,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(f37,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)],[f36]) ).
fof(f54,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,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(f61,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f127,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)],[f37]) ).
fof(f128,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)],[f127]) ).
fof(f129,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)],[f128]) ).
fof(f131,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
( apart_point_and_line(sK0_skl,sK2_skl)
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f164,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK1_skl,sK2_skl),X0)
| ~ apart_point_and_line(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f62,f133]) ).
fof(f206,plain,
( ~ convergent_lines(sK1_skl,sK2_skl)
| ~ apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f164,f57]) ).
fof(f207,plain,
( ~ convergent_lines(sK1_skl,sK2_skl)
| ~ apart_point_and_line(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f164,f55]) ).
fof(f212,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f206,f131]) ).
fof(f213,plain,
~ apart_point_and_line(sK0_skl,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f207,f131]) ).
fof(f214,plain,
apart_point_and_line(sK0_skl,sK1_skl),
inference(backward_subsumption_resolution,[status(thm)],[f132,f212]) ).
fof(f217,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f214,f213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO176+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n006.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 12:56:57 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.072013 seconds
% 0.17/0.50 % CPU time: 0.211311 seconds
% 0.17/0.50 % Total memory used: 13.858 MB
% 0.17/0.50 % Net memory used: 13.720 MB
%------------------------------------------------------------------------------