%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO198+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 : n018.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 12:24:26 PM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 11 unt; 4 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 55 ~; 62 |; 17 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 57 !; 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] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(X,Z),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ~ apart_point_and_line(intersection_point(X,Z),Y) ),
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(X,Z),Y)
& ~ 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(sK0_skl,sK2_skl),sK1_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(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(sK0_skl,sK2_skl),sK1_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,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)],[f62,f51]) ).
fof(f67,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_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)],[f65,f47]) ).
fof(f88,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)
| apart_point_and_line(intersection_point(sK0_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)],[f67,f44]) ).
fof(f101,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(f102,plain,
( ~ sQ4_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f114,definition,
( sQ8_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ8_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f128,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK0_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)],[f88,f49]) ).
fof(f131,definition,
( sQ10_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ10_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f138,definition,
( sQ12_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ12_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( sQ10_spl
| sQ12_spl
| sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f128,f114,f101,f138,f131]) ).
fof(f143,plain,
( ~ sQ8_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f115,f53]) ).
fof(f145,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f49]) ).
fof(f146,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( ~ sQ4_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f102,f52]) ).
fof(f149,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f49]) ).
fof(f150,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( ~ sQ12_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f139,f53]) ).
fof(f154,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f47]) ).
fof(f155,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f50]) ).
fof(f157,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
$false,
inference(sat_refutation,[status(thm)],[f141,f146,f150,f155,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n018.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 13:20:03 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.42 % Elapsed time: 0.039597 seconds
% 0.14/5.42 % CPU time: 0.116647 seconds
% 0.14/5.42 % Total memory used: 17.231 MB
% 0.14/5.42 % Net memory used: 16.830 MB
%------------------------------------------------------------------------------