%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO203+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 : n007.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 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 63 ( 10 unt; 7 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 187 ( 68 ~; 88 |; 16 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 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(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
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(f13,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(f14,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)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f27,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X,Y] :
( ! [Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y)) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
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(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(f45,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)],[f14]) ).
fof(f46,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)],[f45]) ).
fof(f47,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
convergent_lines(sK0_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)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
distinct_lines(line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f53,plain,
! [X0,X1] :
( distinct_points(X1,X0)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f59,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK0_skl)
| apart_point_and_line(X1,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f50]) ).
fof(f64,plain,
! [X0,X1,X2] :
( distinct_points(X1,intersection_point(sK0_skl,X2))
| ~ convergent_lines(sK0_skl,X2)
| apart_point_and_line(X1,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f59,f33]) ).
fof(f68,plain,
! [X0,X1] :
( ~ convergent_lines(sK0_skl,X1)
| apart_point_and_line(intersection_point(sK0_skl,X1),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,intersection_point(sK0_skl,X1)) ),
inference(resolution,[status(thm)],[f64,f15]) ).
fof(f70,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,intersection_point(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f68,f47]) ).
fof(f75,definition,
( sQ1_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,[sQ1_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ1_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)],[f75]) ).
fof(f79,definition,
! [X0] :
( sQ2_spl
<=> ( apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,intersection_point(sK0_skl,sK1_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f80,plain,
! [X0] :
( ~ sQ2_spl
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,intersection_point(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,definition,
( sQ3_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,[sQ3_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ3_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)],[f82]) ).
fof(f85,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f70,f79,f82]) ).
fof(f88,plain,
! [X0,X1] :
( ~ sQ2_spl
| distinct_points(X0,intersection_point(sK0_skl,X1))
| ~ convergent_lines(sK0_skl,X1)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(X0,intersection_point(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f80,f33]) ).
fof(f97,plain,
! [X0] :
( ~ sQ2_spl
| ~ convergent_lines(sK0_skl,X0)
| apart_point_and_line(intersection_point(sK0_skl,X0),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))
| ~ distinct_points(intersection_point(sK0_skl,X0),intersection_point(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f88,f15]) ).
fof(f98,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)))
| ~ distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f97,f48]) ).
fof(f101,definition,
( sQ4_spl
<=> distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( sQ4_spl
| ~ distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f98,f101,f75,f79]) ).
fof(f105,definition,
( sQ5_spl
<=> distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ5_spl
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f110,plain,
( ~ sQ3_spl
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f83,f29]) ).
fof(f114,definition,
( sQ6_spl
<=> distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ6_spl
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f118,plain,
( ~ sQ3_spl
| sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f110,f114,f105,f82]) ).
fof(f119,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f49]) ).
fof(f120,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f121,plain,
( ~ sQ1_spl
| distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f76,f30]) ).
fof(f126,definition,
( sQ7_spl
<=> distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ7_spl
| distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f121,f114,f126,f75]) ).
fof(f132,plain,
( sQ4_spl
| ~ distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(resolution,[status(thm)],[f103,f53]) ).
fof(f141,plain,
( sQ4_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f132,f114,f101]) ).
fof(f142,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f15]) ).
fof(f143,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f144,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f15]) ).
fof(f145,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f104,f118,f120,f129,f141,f143,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO203+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.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
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:21:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.047198 seconds
% 0.11/0.40 % CPU time: 0.140793 seconds
% 0.11/0.40 % Total memory used: 17.669 MB
% 0.11/0.40 % Net memory used: 17.267 MB
%------------------------------------------------------------------------------