%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:24:36 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 8 unt; 2 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 123 ( 56 ~; 44 |; 15 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 59 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> point(intersection_point(L,M)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [L,A] :
( ( point(A)
& line(L) )
=> line(orthogonal_through_point(L,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y] :
( ( line(Y)
& point(X) )
=> ? [Z] :
( incident_point_and_line(Z,Y)
& point(Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y] :
( ( line(Y)
& point(X) )
=> ? [Z] :
( incident_point_and_line(Z,Y)
& point(Z) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f56,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f76,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f83,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f101,plain,
! [L,M] :
( point(intersection_point(L,M))
| ~ convergent_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f102,plain,
! [X0,X1] :
( point(intersection_point(X0,X1))
| ~ convergent_lines(X0,X1)
| ~ line(X1)
| ~ line(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f105,plain,
! [L,A] :
( line(orthogonal_through_point(L,A))
| ~ point(A)
| ~ line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f106,plain,
! [X0,X1] :
( line(orthogonal_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f119,plain,
! [X,Y] :
( ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f120,plain,
( ! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) )
& ! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f127,plain,
? [X,Y] :
( ! [Z] :
( ~ incident_point_and_line(Z,Y)
| ~ point(Z) )
& line(Y)
& point(X) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [Y] :
( ! [Z] :
( ~ incident_point_and_line(Z,Y)
| ~ point(Z) )
& line(Y)
& ? [X] : point(X) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ! [Z] :
( ~ incident_point_and_line(Z,sK0_skl)
| ~ point(Z) )
& line(sK0_skl)
& point(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f128]) ).
fof(f130,plain,
point(sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
line(sK0_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK0_skl)
| ~ point(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f143,plain,
! [X0] :
( ~ point(X0)
| apart_point_and_line(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f122,f132]) ).
fof(f145,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| apart_point_and_line(intersection_point(X0,X1),sK0_skl) ),
inference(resolution,[status(thm)],[f143,f102]) ).
fof(f147,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[status(thm)],[f76,f83]) ).
fof(f150,plain,
! [X0,X1] :
( ~ line(X0)
| ~ line(orthogonal_through_point(X0,X1))
| apart_point_and_line(intersection_point(orthogonal_through_point(X0,X1),X0),sK0_skl) ),
inference(resolution,[status(thm)],[f147,f145]) ).
fof(f151,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| ~ line(X0)
| apart_point_and_line(intersection_point(orthogonal_through_point(X0,X1),X0),sK0_skl) ),
inference(resolution,[status(thm)],[f150,f106]) ).
fof(f152,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| apart_point_and_line(intersection_point(orthogonal_through_point(X0,X1),X0),sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0] :
( ~ convergent_lines(orthogonal_through_point(sK0_skl,X0),sK0_skl)
| ~ point(X0)
| ~ line(sK0_skl) ),
inference(resolution,[status(thm)],[f152,f57]) ).
fof(f154,definition,
( sQ0_spl
<=> line(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ0_spl
| ~ line(sK0_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X0] :
( sQ1_spl
<=> ( ~ convergent_lines(orthogonal_through_point(sK0_skl,X0),sK0_skl)
| ~ point(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ1_spl
| ~ convergent_lines(orthogonal_through_point(sK0_skl,X0),sK0_skl)
| ~ point(X0) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f153,f154,f157]) ).
fof(f161,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f131]) ).
fof(f162,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
! [X0] :
( ~ sQ1_spl
| ~ point(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f147]) ).
fof(f165,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f130,f163]) ).
fof(f166,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
$false,
inference(sat_refutation,[status(thm)],[f160,f162,f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:55:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.048303 seconds
% 0.12/0.41 % CPU time: 0.123434 seconds
% 0.12/0.41 % Total memory used: 18.109 MB
% 0.12/0.41 % Net memory used: 18.020 MB
%------------------------------------------------------------------------------