%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO225+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 : n018.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 12:24:37 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 66 ( 21 ~; 18 |; 21 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
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(f17,conjecture,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,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(f32,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)],[f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,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)],[f32]) ).
fof(f57,plain,
? [A,B] :
( ! [X] :
( ( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& line(X) )
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
? [A,B] :
( ! [X] :
( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& ! [X] : line(X)
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [X] :
( apart_point_and_line(sK1_skl,X)
| apart_point_and_line(sK0_skl,X) )
& ! [X] : line(X)
& distinct_points(sK0_skl,sK1_skl)
& point(sK1_skl)
& point(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f58]) ).
fof(f62,plain,
distinct_points(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
! [X0] :
( apart_point_and_line(sK1_skl,X0)
| apart_point_and_line(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f66,plain,
! [X0,X1] :
( distinct_points(sK1_skl,X1)
| ~ distinct_points(X0,X1)
| apart_point_and_line(sK0_skl,line_connecting(X0,X1)) ),
inference(resolution,[status(thm)],[f64,f34]) ).
fof(f68,plain,
! [X0] :
( ~ distinct_points(X0,sK1_skl)
| apart_point_and_line(sK0_skl,line_connecting(X0,sK1_skl)) ),
inference(resolution,[status(thm)],[f66,f19]) ).
fof(f70,plain,
! [X0] :
( distinct_points(sK0_skl,X0)
| ~ distinct_points(X0,sK1_skl)
| ~ distinct_points(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f68,f33]) ).
fof(f78,plain,
! [X0] :
( distinct_points(sK0_skl,X0)
| ~ distinct_points(X0,sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f70]) ).
fof(f80,plain,
~ distinct_points(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f78,f19]) ).
fof(f81,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f80,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 20 13:57:42 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.40 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.043137 seconds
% 0.13/0.44 % CPU time: 0.108177 seconds
% 0.13/0.44 % Total memory used: 15.068 MB
% 0.13/0.44 % Net memory used: 14.750 MB
%------------------------------------------------------------------------------