%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO195+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 : n011.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 12:24:25 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 13 unt; 6 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 59 ~; 81 |; 15 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 84 !; 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(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(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(f9,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(f10,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(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,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(Y,X),Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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(Y,X),Z) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
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(f35,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)],[f9]) ).
fof(f36,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)],[f35]) ).
fof(f37,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)],[f10]) ).
fof(f38,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,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)],[f38]) ).
fof(f43,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(intersection_point(Y,X),Z)
& 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)],[f14]) ).
fof(f46,plain,
( ~ apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_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)],[f45]) ).
fof(f47,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
~ apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f54,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f26,f47]) ).
fof(f60,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK1_skl,X1)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f54,f26]) ).
fof(f71,plain,
! [X0] :
( convergent_lines(X0,sK1_skl)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f60,f17]) ).
fof(f72,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK0_skl,X1)
| convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f71,f26]) ).
fof(f78,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f34]) ).
fof(f79,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f33]) ).
fof(f91,plain,
distinct_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f44,f47]) ).
fof(f115,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK1_skl)
| apart_point_and_line(X1,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f91]) ).
fof(f152,plain,
! [X0] :
( convergent_lines(X0,sK0_skl)
| convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f72,f17]) ).
fof(f155,plain,
convergent_lines(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f152,f17]) ).
fof(f181,plain,
! [X0] :
( apart_point_and_line(X0,sK2_skl)
| distinct_points(intersection_point(sK0_skl,sK1_skl),X0) ),
inference(resolution,[status(thm)],[f39,f50]) ).
fof(f231,plain,
! [X0] :
( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)
| apart_point_and_line(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f181,f115]) ).
fof(f234,definition,
! [X0] :
( sQ0_spl
<=> ( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK2_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f235,plain,
! [X0] :
( ~ sQ0_spl
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK2_skl) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,definition,
( sQ1_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ1_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
( sQ2_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ2_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f231,f234,f237,f240]) ).
fof(f253,definition,
( sQ4_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ4_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f261,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f47]) ).
fof(f262,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f275,plain,
( ~ sQ1_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f238,f79]) ).
fof(f278,plain,
( ~ sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f275,f253,f237]) ).
fof(f301,plain,
( ~ sQ2_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f241,f78]) ).
fof(f304,plain,
( ~ sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f301,f253,f240]) ).
fof(f410,plain,
( ~ sQ0_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f235,f51]) ).
fof(f415,definition,
( sQ15_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( ~ sQ15_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f418,definition,
( sQ16_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( ~ sQ16_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( ~ sQ0_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f410,f415,f418,f234]) ).
fof(f422,plain,
( ~ sQ15_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f416,f78]) ).
fof(f425,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f155]) ).
fof(f426,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f427,plain,
( ~ sQ16_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f419,f79]) ).
fof(f430,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f155]) ).
fof(f431,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f430]) ).
fof(f432,plain,
$false,
inference(sat_refutation,[status(thm)],[f243,f262,f278,f304,f421,f426,f431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO195+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:20:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.055586 seconds
% 0.09/0.44 % CPU time: 0.300071 seconds
% 0.09/0.44 % Total memory used: 15.372 MB
% 0.09/0.44 % Net memory used: 14.856 MB
%------------------------------------------------------------------------------