%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO172+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 : n008.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 12:24:16 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 16 unt; 4 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 61 ~; 67 |; 15 &)
% ( 6 <=>; 7 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 84 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(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(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
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,Z] :
( ( incident_point_and_line(Z,Y)
& incident_point_and_line(Z,X)
& convergent_lines(X,Y) )
=> equal_points(Z,intersection_point(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,Z] :
( ( incident_point_and_line(Z,Y)
& incident_point_and_line(Z,X)
& convergent_lines(X,Y) )
=> equal_points(Z,intersection_point(X,Y)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
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,Z] :
( ~ equal_points(Z,intersection_point(X,Y))
& incident_point_and_line(Z,Y)
& incident_point_and_line(Z,X)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_points(sK2_skl,intersection_point(sK0_skl,sK1_skl))
& incident_point_and_line(sK2_skl,sK1_skl)
& incident_point_and_line(sK2_skl,sK0_skl)
& convergent_lines(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f127]) ).
fof(f129,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
incident_point_and_line(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
incident_point_and_line(sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f132,plain,
~ equal_points(sK2_skl,intersection_point(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f143,plain,
distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl)),
inference(resolution,[status(thm)],[f110,f132]) ).
fof(f148,plain,
! [X0] :
( distinct_points(intersection_point(sK0_skl,sK1_skl),X0)
| distinct_points(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f43,f143]) ).
fof(f151,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(intersection_point(sK0_skl,sK1_skl),X1)
| distinct_points(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f148,f43]) ).
fof(f180,plain,
distinct_points(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(resolution,[status(thm)],[f151,f38]) ).
fof(f316,plain,
! [X0] :
( convergent_lines(sK0_skl,X0)
| distinct_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f68,f129]) ).
fof(f329,plain,
distinct_lines(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f316,f40]) ).
fof(f332,plain,
! [X0,X1] :
( apart_point_and_line(X1,sK0_skl)
| apart_point_and_line(X1,sK1_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK1_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f329,f59]) ).
fof(f968,plain,
( apart_point_and_line(sK2_skl,sK0_skl)
| apart_point_and_line(sK2_skl,sK1_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f332,f180]) ).
fof(f978,definition,
( sQ40_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f979,plain,
( ~ sQ40_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f978]) ).
fof(f981,definition,
( sQ41_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f982,plain,
( ~ sQ41_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f981]) ).
fof(f984,definition,
( sQ42_spl
<=> apart_point_and_line(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f985,plain,
( ~ sQ42_spl
| apart_point_and_line(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f984]) ).
fof(f987,definition,
( sQ43_spl
<=> apart_point_and_line(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f988,plain,
( ~ sQ43_spl
| apart_point_and_line(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f987]) ).
fof(f990,plain,
( sQ43_spl
| sQ42_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f968,f978,f981,f984,f987]) ).
fof(f1050,plain,
( ~ sQ43_spl
| ~ incident_point_and_line(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f988,f121]) ).
fof(f1051,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1050,f130]) ).
fof(f1052,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f1051]) ).
fof(f1055,plain,
( ~ sQ42_spl
| ~ incident_point_and_line(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f985,f121]) ).
fof(f1056,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1055,f131]) ).
fof(f1057,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f1056]) ).
fof(f1058,plain,
( ~ sQ40_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f979,f57]) ).
fof(f1062,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1058,f129]) ).
fof(f1063,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1062]) ).
fof(f1064,plain,
( ~ sQ41_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f982,f55]) ).
fof(f1068,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1064,f129]) ).
fof(f1069,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1068]) ).
fof(f1070,plain,
$false,
inference(sat_refutation,[status(thm)],[f990,f1052,f1057,f1063,f1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO172+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 12:56:54 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.089193 seconds
% 0.14/0.47 % CPU time: 0.444724 seconds
% 0.14/0.47 % Total memory used: 21.699 MB
% 0.14/0.47 % Net memory used: 20.982 MB
%------------------------------------------------------------------------------