%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO193+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 12:24:24 PM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 14 unt; 7 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 194 ( 71 ~; 93 |; 15 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 67 ( 64 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,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(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(Z,Y),X) ) ),
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(Z,Y),X) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(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(Z,Y),X)
& 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(sK2_skl,sK1_skl),sK0_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(f48,plain,
convergent_lines(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
convergent_lines(sK0_skl,sK2_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(sK2_skl,sK1_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f34]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f33]) ).
fof(f62,plain,
! [X0,X1,X2,X3,X4] :
( ~ apart_point_and_line(X2,X4)
| ~ convergent_lines(X3,X4)
| apart_point_and_line(intersection_point(X3,X4),X1)
| apart_point_and_line(intersection_point(X3,X4),X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f36,f34]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X2,sK2_skl)
| apart_point_and_line(intersection_point(X2,sK2_skl),X1)
| apart_point_and_line(intersection_point(X2,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)],[f62,f50]) ).
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)],[f65,f49]) ).
fof(f73,plain,
! [X0,X1] :
( ~ convergent_lines(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) ),
inference(resolution,[status(thm)],[f66,f44]) ).
fof(f84,plain,
( 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)],[f73,f47]) ).
fof(f89,definition,
( sQ3_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
( sQ4_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ4_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ5_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f99,definition,
( sQ6_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ6_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ7_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ7_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f106,plain,
( sQ5_spl
| sQ7_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f84,f99,f89,f102,f95]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ convergent_lines(X2,sK1_skl)
| apart_point_and_line(intersection_point(X2,sK1_skl),X1)
| apart_point_and_line(intersection_point(X2,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f96,f62]) ).
fof(f108,plain,
( ~ sQ7_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f103,f53]) ).
fof(f110,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f49]) ).
fof(f111,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( ~ sQ3_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f90,f52]) ).
fof(f114,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f47]) ).
fof(f115,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
( ~ sQ6_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f100,f53]) ).
fof(f118,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f47]) ).
fof(f119,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)
| ~ distinct_lines(X0,X1) ),
inference(resolution,[status(thm)],[f107,f48]) ).
fof(f128,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X0)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0) ),
inference(resolution,[status(thm)],[f120,f44]) ).
fof(f138,plain,
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f128,f49]) ).
fof(f141,definition,
( sQ10_spl
<=> apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ10_spl
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f148,definition,
( sQ12_spl
<=> apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( ~ sQ12_spl
| apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ sQ5_spl
| sQ10_spl
| sQ12_spl
| sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f138,f102,f92,f148,f141,f95]) ).
fof(f153,plain,
( ~ sQ4_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f93,f52]) ).
fof(f155,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f49]) ).
fof(f156,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f51]) ).
fof(f158,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
( ~ sQ10_spl
| ~ convergent_lines(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f142,f53]) ).
fof(f161,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f48]) ).
fof(f162,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f111,f115,f119,f151,f156,f158,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO193+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n007.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 20 13:13:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Drodi V4.1.1
% 0.16/0.44 % Refutation found
% 0.16/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.47 % Elapsed time: 0.048899 seconds
% 0.16/0.47 % CPU time: 0.143225 seconds
% 0.16/0.47 % Total memory used: 7.567 MB
% 0.16/0.47 % Net memory used: 7.461 MB
%------------------------------------------------------------------------------