%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO205+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 : n002.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 12:24:29 PM UTC 2026
% Result : Theorem 0.16s 15.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 11 unt; 7 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 69 ~; 79 |; 11 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 74 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(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(f11,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,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] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f40,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
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] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( ( distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
| ~ convergent_lines(sK0_skl,sK2_skl) )
& ~ distinct_lines(sK1_skl,sK2_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(f48,plain,
~ distinct_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
( distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,definition,
( sQ0_spl
<=> convergent_lines(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( sQ0_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ1_spl
<=> distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f50,f53]) ).
fof(f57,plain,
distinct_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f44,f47]) ).
fof(f65,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f26,f47]) ).
fof(f67,plain,
! [X0] :
( distinct_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f65,f44]) ).
fof(f69,plain,
convergent_lines(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f67,f48]) ).
fof(f72,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f52]) ).
fof(f73,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f80,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f33,f15]) ).
fof(f82,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f34,f15]) ).
fof(f118,definition,
( sQ4_spl
<=> distinct_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ4_spl
| distinct_lines(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f143,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,f57]) ).
fof(f355,plain,
( ~ sQ1_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),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) ),
inference(resolution,[status(thm)],[f143,f54]) ).
fof(f360,definition,
( sQ16_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ16_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ17_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( ~ sQ17_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f370,definition,
( sQ19_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( ~ sQ19_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,definition,
( sQ20_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( ~ sQ20_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,plain,
( ~ sQ1_spl
| sQ17_spl
| sQ16_spl
| sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f355,f370,f373,f360,f363,f53]) ).
fof(f387,plain,
! [X0] :
( ~ sQ17_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| distinct_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f364,f42]) ).
fof(f395,plain,
( ~ sQ17_spl
| ~ convergent_lines(sK0_skl,sK2_skl)
| distinct_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f387,f82]) ).
fof(f401,plain,
( ~ sQ17_spl
| ~ sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f395,f118,f50,f363]) ).
fof(f406,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f48]) ).
fof(f407,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( ~ sQ16_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f361,f80]) ).
fof(f411,plain,
( ~ sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f408,f50,f360]) ).
fof(f415,plain,
( ~ sQ19_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f371,f80]) ).
fof(f418,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f47]) ).
fof(f419,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f420,plain,
( ~ sQ20_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f374,f82]) ).
fof(f423,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f47]) ).
fof(f424,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f425,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f73,f376,f401,f407,f411,f419,f424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/15.39 % Computer : n002.cluster.edu
% 0.12/15.39 % Model : x86_64 x86_64
% 0.12/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.39 % Memory : 8046.5625MB
% 0.12/15.39 % OS : Linux 6.8.0-71-generic
% 0.12/15.39 % CPULimit : 300
% 0.12/15.39 % WCLimit : 300
% 0.12/15.39 % DateTime : Sun Sep 20 13:24:49 UTC 2026
% 0.12/15.39 % CPUTime :
% 0.16/15.40 % Drodi V4.1.1
% 0.16/15.50 % Refutation found
% 0.16/15.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/15.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/15.53 % Elapsed time: 0.118649 seconds
% 0.16/15.53 % CPU time: 0.679683 seconds
% 0.16/15.53 % Total memory used: 23.708 MB
% 0.16/15.53 % Net memory used: 22.197 MB
%------------------------------------------------------------------------------