%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO200+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 : n014.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 12:24:27 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 10 unt; 8 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 49 ~; 69 |; 6 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y] :
( distinct_points(X,Y)
=> ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y] :
( distinct_points(X,Y)
=> ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X,Y] :
( ! [Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f27,plain,
! [X,Y,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X,Y] :
( ! [Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y)) )
| ~ distinct_points(X,Y) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f35,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)],[f9]) ).
fof(f36,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)],[f35]) ).
fof(f45,plain,
? [X,Y] :
( distinct_lines(line_connecting(X,Y),line_connecting(Y,X))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl))
& distinct_points(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f45]) ).
fof(f47,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f20,f47]) ).
fof(f50,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f49,f20]) ).
fof(f55,plain,
distinct_points(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f50,f15]) ).
fof(f63,definition,
( sQ0_spl
<=> distinct_points(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ0_spl
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f70,definition,
( sQ2_spl
<=> distinct_points(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ2_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f109,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))
| ~ distinct_points(X0,X1) ),
inference(resolution,[status(thm)],[f36,f48]) ).
fof(f132,plain,
( apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f109,f55]) ).
fof(f164,definition,
( sQ6_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ6_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,definition,
( sQ7_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ7_spl
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,definition,
( sQ8_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ8_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ9_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ9_spl
| apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ9_spl
| sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f132,f164,f167,f170,f173]) ).
fof(f241,plain,
( ~ sQ9_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f174,f30]) ).
fof(f247,definition,
( sQ21_spl
<=> distinct_points(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ21_spl
| distinct_points(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( ~ sQ9_spl
| sQ21_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f241,f63,f247,f173]) ).
fof(f253,plain,
( ~ sQ8_spl
| distinct_points(sK0_skl,sK0_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f171,f29]) ).
fof(f259,plain,
( ~ sQ8_spl
| sQ21_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f253,f70,f247,f170]) ).
fof(f261,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f47]) ).
fof(f262,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f264,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f55]) ).
fof(f265,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f248,f15]) ).
fof(f267,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( ~ sQ6_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f165,f30]) ).
fof(f274,definition,
( sQ22_spl
<=> distinct_points(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ22_spl
| distinct_points(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,plain,
( ~ sQ6_spl
| sQ22_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f268,f70,f274,f164]) ).
fof(f280,plain,
( ~ sQ7_spl
| distinct_points(sK1_skl,sK1_skl)
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f168,f29]) ).
fof(f286,plain,
( ~ sQ7_spl
| sQ22_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f280,f63,f274,f167]) ).
fof(f287,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f15]) ).
fof(f288,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
$false,
inference(sat_refutation,[status(thm)],[f176,f250,f259,f262,f265,f267,f277,f286,f288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.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 13:19:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.037463 seconds
% 0.12/0.39 % CPU time: 0.100908 seconds
% 0.12/0.39 % Total memory used: 12.392 MB
% 0.12/0.39 % Net memory used: 12.145 MB
%------------------------------------------------------------------------------