%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO215+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 : n015.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 12:24:33 PM UTC 2026
% Result : Theorem 0.09s 0.52s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 15 unt; 4 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 150 ( 55 ~; 75 |; 8 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 92 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : ~ distinct_lines(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(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
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(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f39,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(f40,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)],[f39]) ).
fof(f41,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)],[f40]) ).
fof(f42,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)],[f40]) ).
fof(f51,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f67,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f68,plain,
! [L,M] :
( ! [N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| ! [A] :
( apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) )
| ~ distinct_lines(L,M) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N)
& convergent_lines(L,M) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f71,plain,
? [L,M] :
( ? [N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N) )
& convergent_lines(L,M) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f72,plain,
( ~ unorthogonal_lines(sK1_skl,sK2_skl)
& ~ unorthogonal_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(L,sK0_skl),skolemize(M,sK1_skl),skolemize(N,sK2_skl)],[f71]) ).
fof(f73,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
~ unorthogonal_lines(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
~ unorthogonal_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f83,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f34,f73]) ).
fof(f86,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK1_skl,X1)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f83,f34]) ).
fof(f89,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f41,f23]) ).
fof(f91,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f42,f23]) ).
fof(f97,plain,
! [X0] :
( convergent_lines(X0,sK1_skl)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f86,f25]) ).
fof(f98,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK0_skl,X1)
| convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f97,f34]) ).
fof(f107,plain,
! [X0] :
( convergent_lines(X0,sK0_skl)
| convergent_lines(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f98,f25]) ).
fof(f121,plain,
distinct_lines(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f52,f73]) ).
fof(f137,plain,
! [X0] :
( distinct_lines(sK1_skl,X0)
| distinct_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f121,f31]) ).
fof(f138,definition,
! [X0] :
( sQ2_spl
<=> ( apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f139,plain,
! [X0] :
( ~ sQ2_spl
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f161,definition,
( sQ6_spl
<=> convergent_lines(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ6_spl
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f184,plain,
! [X0,X1,X2] :
( distinct_lines(sK0_skl,X1)
| unorthogonal_lines(X1,X2)
| unorthogonal_lines(sK1_skl,X2)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f69,f137]) ).
fof(f201,plain,
! [X0] :
( ~ sQ2_spl
| apart_point_and_line(intersection_point(sK1_skl,X0),sK0_skl)
| ~ convergent_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f89,f139]) ).
fof(f248,definition,
( sQ13_spl
<=> distinct_lines(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( ~ sQ13_spl
| distinct_lines(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f315,plain,
convergent_lines(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f107,f25]) ).
fof(f436,plain,
! [X0] :
( distinct_lines(sK0_skl,sK0_skl)
| unorthogonal_lines(sK1_skl,sK2_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f184,f74]) ).
fof(f454,definition,
( sQ30_spl
<=> unorthogonal_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ30_spl
| unorthogonal_lines(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f458,plain,
( sQ13_spl
| sQ30_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f436,f138,f454,f248]) ).
fof(f463,plain,
( ~ sQ2_spl
| ~ convergent_lines(sK1_skl,sK0_skl)
| ~ convergent_lines(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f201,f91]) ).
fof(f466,plain,
( ~ sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f463,f161,f138]) ).
fof(f467,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f24]) ).
fof(f468,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f469,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f315]) ).
fof(f470,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f471,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f75]) ).
fof(f472,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f473,plain,
$false,
inference(sat_refutation,[status(thm)],[f458,f466,f468,f470,f472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO215+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 : n015.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 13:32:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.52 % Refutation found
% 0.09/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.54 % Elapsed time: 0.160090 seconds
% 0.09/0.54 % CPU time: 1.020019 seconds
% 0.09/0.54 % Total memory used: 27.201 MB
% 0.09/0.54 % Net memory used: 24.981 MB
%------------------------------------------------------------------------------