%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 11 unt; 4 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 49 ~; 54 |; 5 &)
% ( 5 <=>; 6 =>; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 57 !; 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] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y] :
( distinct_points(X,Y)
=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y] :
( distinct_points(X,Y)
=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f50,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
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(f111,plain,
! [X,Y] :
( ( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f112,plain,
( ! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) )
& ! [X,Y] :
( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f127,plain,
? [X,Y] :
( ~ equal_lines(line_connecting(X,Y),line_connecting(Y,X))
& distinct_points(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ~ equal_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)],[f127]) ).
fof(f129,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
~ equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f141,plain,
! [X0] :
( distinct_points(sK1_skl,X0)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f43,f129]) ).
fof(f142,plain,
distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)),
inference(resolution,[status(thm)],[f114,f130]) ).
fof(f144,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| distinct_points(sK1_skl,X1)
| distinct_points(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f141,f43]) ).
fof(f150,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)],[f142,f59]) ).
fof(f153,plain,
distinct_points(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f144,f38]) ).
fof(f212,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)],[f150,f153]) ).
fof(f236,definition,
( sQ5_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( ~ sQ5_spl
| apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ6_spl
<=> apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ6_spl
| apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ7_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ7_spl
| apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ8_spl
<=> apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ8_spl
| apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f212,f236,f239,f242,f245]) ).
fof(f354,plain,
( ~ sQ6_spl
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f240,f51]) ).
fof(f357,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f354,f153]) ).
fof(f358,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( ~ sQ8_spl
| ~ distinct_points(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f246,f53]) ).
fof(f362,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f153]) ).
fof(f363,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f422,plain,
( ~ sQ5_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f237,f53]) ).
fof(f425,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f129]) ).
fof(f426,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f427,plain,
( ~ sQ7_spl
| ~ distinct_points(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f243,f51]) ).
fof(f430,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f129]) ).
fof(f431,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f430]) ).
fof(f432,plain,
$false,
inference(sat_refutation,[status(thm)],[f248,f358,f363,f426,f431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:16:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.046205 seconds
% 0.09/0.42 % CPU time: 0.143982 seconds
% 0.09/0.42 % Total memory used: 18.703 MB
% 0.09/0.42 % Net memory used: 18.574 MB
%------------------------------------------------------------------------------