%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:24:29 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 93 ( 13 unt; 10 def)
% Number of atoms : 230 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 230 ( 93 ~; 110 |; 9 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 86 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : ~ distinct_lines(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(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(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(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
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(f15,conjecture,
! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f18,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f33,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,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(f38,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)],[f37]) ).
fof(f42,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
? [X,Y,Z] :
( ( distinct_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& ~ distinct_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( ( distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
| ~ convergent_lines(sK0_skl,sK2_skl) )
& ~ distinct_lines(sK1_skl,sK2_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)],[f48]) ).
fof(f50,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
~ distinct_lines(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,definition,
( sQ0_spl
<=> convergent_lines(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ0_spl
| convergent_lines(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( sQ0_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ1_spl
| distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56]) ).
fof(f64,plain,
! [X0] :
( convergent_lines(sK0_skl,X0)
| distinct_lines(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f47,f50]) ).
fof(f65,plain,
( sQ0_spl
| distinct_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f64,f55]) ).
fof(f69,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f51]) ).
fof(f70,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f69]) ).
fof(f73,plain,
! [X0] :
( ~ sQ0_spl
| convergent_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f54,f47]) ).
fof(f78,plain,
( ~ sQ0_spl
| distinct_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f73,f19]) ).
fof(f82,plain,
! [X0,X1] :
( ~ sQ0_spl
| apart_point_and_line(X1,sK0_skl)
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,sK0_skl)
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f78,f38]) ).
fof(f119,definition,
! [X0] :
( sQ4_spl
<=> ( convergent_lines(sK0_skl,X0)
| convergent_lines(sK0_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f120,plain,
! [X0] :
( ~ sQ4_spl
| convergent_lines(sK0_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f146,definition,
( sQ8_spl
<=> convergent_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ8_spl
| convergent_lines(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f207,definition,
! [X0,X1] :
( sQ13_spl
<=> ( convergent_lines(sK0_skl,X1)
| distinct_lines(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f208,plain,
! [X0,X1] :
( ~ sQ13_spl
| convergent_lines(sK0_skl,X1)
| distinct_lines(X0,X1) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f402,definition,
( sQ33_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ33_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f417,definition,
( sQ37_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( ~ sQ37_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f419,plain,
( sQ37_spl
| ~ apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,definition,
( sQ38_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ38_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f437,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f82,f57]) ).
fof(f442,definition,
( sQ41_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ41_spl
| apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f457,definition,
( sQ45_spl
<=> apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ45_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| sQ33_spl
| sQ41_spl
| sQ38_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f437,f457,f420,f442,f402,f53,f56]) ).
fof(f477,plain,
( ~ sQ38_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f421,f34]) ).
fof(f480,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f50]) ).
fof(f481,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( ~ sQ33_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f403,f34]) ).
fof(f485,plain,
( ~ sQ33_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f482,f53,f402]) ).
fof(f486,plain,
( ~ sQ37_spl
| ~ convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f418,f36]) ).
fof(f489,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f50]) ).
fof(f490,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f491,plain,
! [X0] :
( ~ sQ45_spl
| apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f458,f44]) ).
fof(f495,plain,
( ~ sQ41_spl
| ~ convergent_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f443,f36]) ).
fof(f498,plain,
( ~ sQ41_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f495,f53,f442]) ).
fof(f594,plain,
! [X0] :
( ~ sQ4_spl
| convergent_lines(sK0_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f120]) ).
fof(f597,plain,
( ~ sQ4_spl
| $false ),
inference(resolution,[status(thm)],[f594,f19]) ).
fof(f598,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f599,plain,
! [X0] :
( ~ sQ8_spl
| convergent_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f147,f47]) ).
fof(f608,plain,
! [X0] :
( ~ sQ13_spl
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f208,f18]) ).
fof(f614,plain,
( ~ sQ13_spl
| $false ),
inference(resolution,[status(thm)],[f608,f19]) ).
fof(f615,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f652,plain,
( ~ sQ8_spl
| distinct_lines(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f599,f19]) ).
fof(f654,plain,
! [X0] :
( ~ sQ8_spl
| distinct_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f652,f25]) ).
fof(f660,plain,
( ~ sQ8_spl
| distinct_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f654,f18]) ).
fof(f661,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f51]) ).
fof(f662,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f1230,plain,
( sQ37_spl
| ~ sQ45_spl
| distinct_lines(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f491,f419]) ).
fof(f1241,plain,
! [X0] :
( sQ37_spl
| ~ sQ45_spl
| distinct_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f1230,f25]) ).
fof(f1244,plain,
( sQ37_spl
| ~ sQ45_spl
| distinct_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f1241,f18]) ).
fof(f1245,plain,
( sQ37_spl
| ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1244,f51]) ).
fof(f1246,plain,
( sQ37_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f1245]) ).
fof(f1247,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f70,f460,f481,f485,f490,f498,f598,f615,f662,f1246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 13:25:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.46 % Refutation found
% 0.12/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.50 % Elapsed time: 0.133167 seconds
% 0.12/0.50 % CPU time: 0.820746 seconds
% 0.12/0.50 % Total memory used: 24.217 MB
% 0.12/0.50 % Net memory used: 22.661 MB
%------------------------------------------------------------------------------