%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO201+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 : n014.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 12:24:27 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 11 unt; 4 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 61 ~; 68 |; 5 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 63 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
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] :
( convergent_lines(X,Y)
=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
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] :
( distinct_points(intersection_point(X,Y),intersection_point(Y,X))
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl))
& convergent_lines(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f45]) ).
fof(f47,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f55,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f26,f17]) ).
fof(f65,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_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)],[f36,f48]) ).
fof(f80,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)
| apart_point_and_line(intersection_point(sK1_skl,sK0_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)],[f65,f44]) ).
fof(f89,plain,
( apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK0_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)],[f80,f47]) ).
fof(f95,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(f96,plain,
( ~ sQ2_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,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(f99,plain,
( ~ sQ3_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,definition,
( sQ4_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ4_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,definition,
( sQ5_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ5_spl
| apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f95,f98,f101,f104]) ).
fof(f116,plain,
! [X0] :
( ~ sQ5_spl
| distinct_points(intersection_point(sK1_skl,sK0_skl),intersection_point(sK1_skl,X0))
| ~ convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f105,f33]) ).
fof(f140,plain,
( ~ sQ5_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f116,f15]) ).
fof(f141,plain,
( ~ sQ5_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f140,f55]) ).
fof(f146,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f47]) ).
fof(f147,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f150,plain,
! [X0] :
( ~ sQ4_spl
| distinct_points(intersection_point(sK1_skl,sK0_skl),intersection_point(X0,sK0_skl))
| ~ convergent_lines(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f102,f34]) ).
fof(f166,plain,
( ~ sQ4_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f150,f15]) ).
fof(f167,plain,
( ~ sQ4_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f166,f55]) ).
fof(f172,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f47]) ).
fof(f173,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f177,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)],[f96,f33]) ).
fof(f189,plain,
( ~ sQ2_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f177,f15]) ).
fof(f190,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f47]) ).
fof(f191,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f194,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)],[f99,f34]) ).
fof(f201,plain,
( ~ sQ3_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f194,f15]) ).
fof(f202,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f47]) ).
fof(f203,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
$false,
inference(sat_refutation,[status(thm)],[f107,f147,f173,f191,f203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:21:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.052536 seconds
% 0.10/0.43 % CPU time: 0.176567 seconds
% 0.10/0.43 % Total memory used: 17.846 MB
% 0.10/0.43 % Net memory used: 17.389 MB
%------------------------------------------------------------------------------