%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO173+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 : n009.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 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 9 unt; 4 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 40 ~; 39 |; 17 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 34 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,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(f15,conjecture,
! [X,Y,U,V] :
( ( distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X,Y,U,V] :
( ( distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f29,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
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(f48,plain,
? [X,Y,U,V] :
( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& distinct_lines(U,line_connecting(X,Y))
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
? [X,Y,U] :
( ~ apart_point_and_line(Y,U)
& ~ apart_point_and_line(X,U)
& distinct_lines(U,line_connecting(X,Y))
& ? [V] : convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ apart_point_and_line(sK1_skl,sK2_skl)
& ~ apart_point_and_line(sK0_skl,sK2_skl)
& distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))
& convergent_lines(sK2_skl,sK3_skl)
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f49]) ).
fof(f51,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
~ apart_point_and_line(sK0_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
~ apart_point_and_line(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f68,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X1,sK2_skl)
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,sK2_skl)
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f73,plain,
( apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,sK2_skl)
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f68,f51]) ).
fof(f74,definition,
( sQ0_spl
<=> apart_point_and_line(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ0_spl
| apart_point_and_line(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ1_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f84,definition,
( sQ3_spl
<=> apart_point_and_line(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ3_spl
| apart_point_and_line(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,definition,
( sQ4_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ4_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ1_spl
| sQ0_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f73,f84,f87,f74,f77]) ).
fof(f93,plain,
( ~ sQ1_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f78,f32]) ).
fof(f96,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f51]) ).
fof(f97,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f98,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f55]) ).
fof(f99,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f98]) ).
fof(f100,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f54]) ).
fof(f101,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f156,plain,
( ~ sQ4_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f88,f30]) ).
fof(f159,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f51]) ).
fof(f160,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f161,plain,
$false,
inference(sat_refutation,[status(thm)],[f90,f97,f99,f101,f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO173+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 % Computer : n009.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sun Sep 20 12:56:42 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.50 % Drodi V4.1.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.58 % Elapsed time: 0.081808 seconds
% 0.22/0.58 % CPU time: 0.080403 seconds
% 0.22/0.58 % Total memory used: 2.882 MB
% 0.22/0.58 % Net memory used: 2.854 MB
%------------------------------------------------------------------------------