%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:24:24 PM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 8 unt; 6 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 147 ( 57 ~; 64 |; 10 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 80 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X,Y] :
( ! [Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z) )
| ~ distinct_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X,Y] :
( ! [Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) ) )
| ~ convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f40,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)],[f11]) ).
fof(f41,plain,
! [X,Y] :
( ! [Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) )
| ~ apart_point_and_line(X,Y) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f43,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
? [X,Y] :
( ? [Z] :
( ( ~ distinct_lines(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z) )
& convergent_lines(X,Y) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ( ~ distinct_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) )
& apart_point_and_line(intersection_point(sK0_skl,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)],[f46]) ).
fof(f48,plain,
convergent_lines(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ distinct_lines(sK1_skl,sK2_skl)
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,definition,
( sQ0_spl
<=> distinct_lines(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ0_spl
| ~ distinct_lines(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> distinct_lines(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f51,f54]) ).
fof(f62,plain,
! [X0] :
( convergent_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f26,f48]) ).
fof(f63,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f34]) ).
fof(f64,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f15,f33]) ).
fof(f65,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK1_skl,X1)
| convergent_lines(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f62,f26]) ).
fof(f75,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f130,plain,
! [X0] :
( distinct_lines(sK1_skl,X0)
| convergent_lines(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f65,f44]) ).
fof(f145,definition,
( sQ9_spl
<=> convergent_lines(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f152,definition,
! [X0] :
( sQ11_spl
<=> distinct_lines(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f153,plain,
! [X0] :
( ~ sQ11_spl
| distinct_lines(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f130,f145,f152]) ).
fof(f196,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| distinct_lines(sK2_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f75,f64]) ).
fof(f197,plain,
( ~ convergent_lines(sK0_skl,sK1_skl)
| distinct_lines(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f75,f63]) ).
fof(f204,definition,
( sQ14_spl
<=> distinct_lines(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ14_spl
| distinct_lines(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( ~ sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f196,f204,f145]) ).
fof(f208,definition,
( sQ15_spl
<=> distinct_lines(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ15_spl
| distinct_lines(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f197,f208,f145]) ).
fof(f213,plain,
( ~ sQ11_spl
| $false ),
inference(resolution,[status(thm)],[f153,f16]) ).
fof(f214,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,plain,
! [X0] :
( ~ sQ14_spl
| distinct_lines(sK0_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f205,f23]) ).
fof(f237,plain,
( ~ sQ14_spl
| distinct_lines(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f215,f16]) ).
fof(f238,plain,
( ~ sQ14_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f53]) ).
fof(f239,plain,
( ~ sQ14_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f241,plain,
! [X0] :
( ~ sQ15_spl
| distinct_lines(sK1_skl,X0)
| distinct_lines(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f209,f23]) ).
fof(f245,plain,
( ~ sQ15_spl
| distinct_lines(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f241,f16]) ).
fof(f246,plain,
( ~ sQ15_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f245,f54,f208]) ).
fof(f247,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f155,f207,f211,f214,f239,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 13:19:13 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.41 % Elapsed time: 0.038977 seconds
% 0.13/5.41 % CPU time: 0.120937 seconds
% 0.13/5.41 % Total memory used: 9.609 MB
% 0.13/5.41 % Net memory used: 9.383 MB
%------------------------------------------------------------------------------