%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO226+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 : n002.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 12:24:37 PM UTC 2026
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 4 unt; 1 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 30 ~; 19 |; 20 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 35 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,M)
& incident_point_and_line(X,L) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,M)
& incident_point_and_line(X,L) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f54,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
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(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,
? [L,M] :
( ! [X] :
( ( ~ incident_point_and_line(X,M)
| ~ incident_point_and_line(X,L) )
& point(X) )
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [L,M] :
( ! [X] :
( ~ incident_point_and_line(X,M)
| ~ incident_point_and_line(X,L) )
& ! [X] : point(X)
& convergent_lines(L,M)
& line(M)
& line(L) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ! [X] :
( ~ incident_point_and_line(X,sK1_skl)
| ~ incident_point_and_line(X,sK0_skl) )
& ! [X] : point(X)
& convergent_lines(sK0_skl,sK1_skl)
& line(sK1_skl)
& line(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f128]) ).
fof(f132,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK1_skl)
| ~ incident_point_and_line(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f148,plain,
! [X0] :
( ~ incident_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f122,f134]) ).
fof(f150,plain,
! [X0] :
( apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f148,f122]) ).
fof(f151,plain,
! [X0] :
( ~ convergent_lines(X0,sK1_skl)
| apart_point_and_line(intersection_point(X0,sK1_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f150,f57]) ).
fof(f153,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f151,f55]) ).
fof(f154,definition,
( sQ0_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ0_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
~ sQ0_spl,
inference(split_clause,[status(thm)],[f153,f154]) ).
fof(f158,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f132]) ).
fof(f159,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f160,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO226+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n002.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 14:00:16 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 0.20/0.50 % Refutation found
% 0.20/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.56 % Elapsed time: 0.092561 seconds
% 0.23/0.56 % CPU time: 0.115290 seconds
% 0.23/0.56 % Total memory used: 5.788 MB
% 0.23/0.56 % Net memory used: 5.757 MB
%------------------------------------------------------------------------------