%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:24:28 PM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 9 unt; 4 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 43 ~; 41 |; 11 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f29,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
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(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(f48,plain,
? [X,Y,Z] :
( distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( distinct_lines(line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),sK0_skl)
& distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
& convergent_lines(sK0_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)],[f48]) ).
fof(f50,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
convergent_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
distinct_lines(line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),sK0_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f66,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)],[f38,f52]) ).
fof(f72,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))) ),
inference(resolution,[status(thm)],[f66,f53]) ).
fof(f79,definition,
( sQ0_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ0_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,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(f83,plain,
( ~ sQ1_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ2_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ2_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ3_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f79,f82,f85,f88]) ).
fof(f100,plain,
( ~ sQ3_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f89,f34]) ).
fof(f103,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f51]) ).
fof(f104,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( ~ sQ2_spl
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f86,f32]) ).
fof(f108,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f52]) ).
fof(f109,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( ~ sQ0_spl
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f80,f30]) ).
fof(f113,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f52]) ).
fof(f114,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( ~ sQ1_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f83,f34]) ).
fof(f118,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f50]) ).
fof(f119,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f120,plain,
$false,
inference(sat_refutation,[status(thm)],[f91,f104,f109,f114,f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:26:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.030687 seconds
% 0.15/0.41 % CPU time: 0.070914 seconds
% 0.15/0.41 % Total memory used: 4.230 MB
% 0.15/0.41 % Net memory used: 4.173 MB
%------------------------------------------------------------------------------