%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO185+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 12:24:21 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 6 unt; 2 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 41 ~; 40 |; 19 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 54 !; 8 ?)
% 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(f12,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,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,
! [X,Y,U,V] :
( ( equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(X,V)
& incident_point_and_line(X,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,U,V] :
( ( equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( incident_point_and_line(X,V)
& incident_point_and_line(X,U) ) ),
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(f60,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f107,plain,
! [X,Y] :
( ( distinct_points(X,Y)
| equal_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f108,plain,
( ! [X,Y] :
( distinct_points(X,Y)
| equal_points(X,Y) )
& ! [X,Y] :
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
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,U,V] :
( ( ~ incident_point_and_line(X,V)
| ~ incident_point_and_line(X,U) )
& equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [X,U,V] :
( ( ~ incident_point_and_line(X,V)
| ~ incident_point_and_line(X,U) )
& equal_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& ? [Y] : distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ( ~ incident_point_and_line(sK0_skl,sK2_skl)
| ~ incident_point_and_line(sK0_skl,sK1_skl) )
& equal_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))
& convergent_lines(sK1_skl,sK2_skl)
& distinct_points(sK0_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(Y,sK3_skl)],[f128]) ).
fof(f131,plain,
convergent_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
equal_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
( ~ incident_point_and_line(sK0_skl,sK2_skl)
| ~ incident_point_and_line(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f144,definition,
( sQ0_spl
<=> incident_point_and_line(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ0_spl
| ~ incident_point_and_line(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ1_spl
<=> incident_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ1_spl
| ~ incident_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f133,f144,f147]) ).
fof(f152,plain,
~ distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(resolution,[status(thm)],[f109,f132]) ).
fof(f154,plain,
( sQ0_spl
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f122,f146]) ).
fof(f161,plain,
! [X0] :
( sQ0_spl
| apart_point_and_line(X0,sK1_skl)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f62,f154]) ).
fof(f167,plain,
( sQ0_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f161,f152]) ).
fof(f170,plain,
( sQ0_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f167,f55]) ).
fof(f172,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f131]) ).
fof(f173,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( sQ1_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f149,f122]) ).
fof(f176,plain,
! [X0] :
( sQ1_spl
| apart_point_and_line(X0,sK2_skl)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f174,f62]) ).
fof(f179,plain,
( sQ1_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f176,f152]) ).
fof(f185,plain,
( sQ1_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f179,f57]) ).
fof(f187,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f131]) ).
fof(f188,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
$false,
inference(sat_refutation,[status(thm)],[f150,f173,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.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 13:11:58 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
% 0.10/0.42 % Elapsed time: 0.043345 seconds
% 0.10/0.42 % CPU time: 0.188045 seconds
% 0.10/0.42 % Total memory used: 16.485 MB
% 0.10/0.42 % Net memory used: 16.294 MB
%------------------------------------------------------------------------------