%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO202+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 : 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 12:24:28 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 12 unt; 5 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 52 ~; 58 |; 11 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(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(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(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(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(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
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(f45,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
? [X,Y,Z] :
( distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)
& convergent_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl)
& convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
& distinct_points(sK0_skl,sK2_skl)
& distinct_points(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,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
distinct_points(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f67,plain,
! [X0,X1] :
( apart_point_and_line(sK0_skl,X1)
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X1)
| apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f53,f38]) ).
fof(f77,plain,
! [X0] :
( ~ convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X0)
| ~ distinct_lines(X0,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f67,f34]) ).
fof(f85,definition,
( sQ1_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ2_spl
<=> convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ2_spl
| ~ convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f92,definition,
! [X0] :
( sQ3_spl
<=> ( apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X0)
| ~ distinct_lines(X0,line_connecting(sK0_skl,sK1_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f93,plain,
! [X0] :
( ~ sQ3_spl
| apart_point_and_line(sK0_skl,X0)
| apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X0)
| ~ distinct_lines(X0,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ4_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ4_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( ~ sQ2_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f77,f92,f95,f88]) ).
fof(f99,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f52]) ).
fof(f100,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f108,plain,
! [X0] :
( convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)
| distinct_lines(line_connecting(sK0_skl,sK2_skl),X0) ),
inference(resolution,[status(thm)],[f47,f52]) ).
fof(f114,plain,
distinct_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f108,f19]) ).
fof(f149,plain,
( ~ sQ1_spl
| ~ distinct_points(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f86,f30]) ).
fof(f152,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f51]) ).
fof(f153,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ sQ4_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f96,f30]) ).
fof(f157,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f50]) ).
fof(f158,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f231,plain,
( ~ sQ3_spl
| ~ convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))
| ~ distinct_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f93,f36]) ).
fof(f237,definition,
( sQ19_spl
<=> distinct_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ19_spl
| ~ distinct_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ1_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f231,f237,f85,f88,f92]) ).
fof(f245,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f114]) ).
fof(f246,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f245]) ).
fof(f247,plain,
$false,
inference(sat_refutation,[status(thm)],[f98,f100,f153,f158,f240,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 20 13:22:26 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.075033 seconds
% 0.11/0.44 % CPU time: 0.328981 seconds
% 0.11/0.44 % Total memory used: 20.001 MB
% 0.11/0.44 % Net memory used: 19.301 MB
%------------------------------------------------------------------------------