%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO172+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 : n017.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 12:24:16 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 11 unt; 4 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 54 ~; 53 |; 13 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 52 ( 49 !; 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(Z,Y)
& ~ apart_point_and_line(Z,X)
& convergent_lines(X,Y) )
=> ~ distinct_points(Z,intersection_point(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X)
& convergent_lines(X,Y) )
=> ~ distinct_points(Z,intersection_point(X,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] :
( 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)],[f14]) ).
fof(f46,plain,
( distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl))
& ~ apart_point_and_line(sK2_skl,sK1_skl)
& ~ apart_point_and_line(sK2_skl,sK0_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,
~ apart_point_and_line(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
~ apart_point_and_line(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(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_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f44]) ).
fof(f73,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK1_skl)
| apart_point_and_line(X1,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f72,f47]) ).
fof(f79,plain,
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)
| apart_point_and_line(sK2_skl,sK1_skl)
| apart_point_and_line(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f73,f50]) ).
fof(f85,definition,
( sQ0_spl
<=> apart_point_and_line(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ0_spl
| apart_point_and_line(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ1_spl
<=> apart_point_and_line(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ1_spl
| apart_point_and_line(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,definition,
( sQ2_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ2_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,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(f95,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f85,f88,f91,f94]) ).
fof(f108,plain,
! [X0] :
( ~ sQ3_spl
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(X0,sK1_skl))
| ~ convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f95,f34]) ).
fof(f111,plain,
( ~ sQ3_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f108,f15]) ).
fof(f116,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f47]) ).
fof(f117,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f121,plain,
! [X0] :
( ~ sQ2_spl
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,X0))
| ~ convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f92,f33]) ).
fof(f128,plain,
( ~ sQ2_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f121,f15]) ).
fof(f133,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f47]) ).
fof(f134,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f48]) ).
fof(f136,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f49]) ).
fof(f138,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
$false,
inference(sat_refutation,[status(thm)],[f97,f117,f134,f136,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 12:52:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.036254 seconds
% 0.09/0.41 % CPU time: 0.097182 seconds
% 0.09/0.41 % Total memory used: 10.825 MB
% 0.09/0.41 % Net memory used: 10.622 MB
%------------------------------------------------------------------------------