%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO176+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 5 unt; 2 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 75 ( 28 ~; 26 |; 15 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 25 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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/sandbox2/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(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(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,sK2_skl)
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,definition,
( sQ0_spl
<=> apart_point_and_line(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f52,f55]) ).
fof(f65,plain,
! [X0] :
( ~ sQ0_spl
| distinct_points(sK0_skl,intersection_point(sK1_skl,X0))
| ~ convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f33,f53]) ).
fof(f132,plain,
( ~ sQ0_spl
| distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f65,f49]) ).
fof(f134,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f51]) ).
fof(f135,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f137,plain,
! [X0] :
( ~ sQ1_spl
| distinct_points(sK0_skl,intersection_point(X0,sK2_skl))
| ~ convergent_lines(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f56,f34]) ).
fof(f168,plain,
( ~ sQ1_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f137,f51]) ).
fof(f171,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f49]) ).
fof(f172,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f135,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO176+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 12:58:43 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 0.20/0.48 % Refutation found
% 0.20/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.54 % Elapsed time: 0.076132 seconds
% 0.24/0.54 % CPU time: 0.100195 seconds
% 0.24/0.54 % Total memory used: 3.401 MB
% 0.24/0.54 % Net memory used: 3.351 MB
%------------------------------------------------------------------------------