%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:24:21 PM UTC 2026
% Result : Theorem 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 13 unt; 4 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 149 ( 57 ~; 57 |; 23 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 69 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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(f14,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,U,V] :
( ( incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> equal_points(X,intersection_point(U,V)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f58,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)],[f11]) ).
fof(f59,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)],[f58]) ).
fof(f66,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f67,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
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(f110,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(f121,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] :
( ~ equal_points(X,intersection_point(U,V))
& incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
? [X,U,V] :
( ~ equal_points(X,intersection_point(U,V))
& incident_point_and_line(X,V)
& incident_point_and_line(X,U)
& convergent_lines(U,V)
& ? [Y] : distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ equal_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))
& incident_point_and_line(sK0_skl,sK2_skl)
& incident_point_and_line(sK0_skl,sK1_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,
incident_point_and_line(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
incident_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
~ equal_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f150,plain,
distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)),
inference(resolution,[status(thm)],[f134,f110]) ).
fof(f190,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f68,f131]) ).
fof(f198,plain,
distinct_lines(sK2_skl,sK1_skl),
inference(resolution,[status(thm)],[f190,f40]) ).
fof(f199,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK1_skl)
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,sK1_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f198,f59]) ).
fof(f798,plain,
( apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)
| apart_point_and_line(sK0_skl,sK1_skl)
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f199,f150]) ).
fof(f812,definition,
( sQ39_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f813,plain,
( ~ sQ39_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f812]) ).
fof(f815,definition,
( sQ40_spl
<=> apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f816,plain,
( ~ sQ40_spl
| apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f815]) ).
fof(f828,definition,
( sQ44_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ44_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,definition,
( sQ45_spl
<=> apart_point_and_line(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( ~ sQ45_spl
| apart_point_and_line(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f846,plain,
( sQ40_spl
| sQ39_spl
| sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f798,f828,f831,f812,f815]) ).
fof(f877,plain,
( ~ sQ45_spl
| ~ incident_point_and_line(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f832,f121]) ).
fof(f878,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f877,f132]) ).
fof(f879,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f878]) ).
fof(f882,plain,
( ~ sQ44_spl
| ~ incident_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f829,f121]) ).
fof(f883,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f882,f133]) ).
fof(f884,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f883]) ).
fof(f889,plain,
( ~ sQ39_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f813,f57]) ).
fof(f893,plain,
( ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f889,f131]) ).
fof(f894,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f893]) ).
fof(f1094,plain,
( ~ sQ40_spl
| ~ convergent_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f816,f55]) ).
fof(f1098,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1094,f131]) ).
fof(f1099,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1098]) ).
fof(f1100,plain,
$false,
inference(sat_refutation,[status(thm)],[f846,f879,f884,f894,f1099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 13:15:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48 % Elapsed time: 0.111232 seconds
% 0.13/0.48 % CPU time: 0.600220 seconds
% 0.13/0.48 % Total memory used: 23.792 MB
% 0.13/0.48 % Net memory used: 22.874 MB
%------------------------------------------------------------------------------