TSTP Solution File: GEO225+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GEO225+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:08:25 EDT 2023
% Result : Theorem 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 24 ~; 18 |; 21 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 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/sandbox2/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,X)
& distinct_points(Z,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(A,X)
& ~ apart_point_and_line(B,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(A,X)
& ~ apart_point_and_line(B,X) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f31,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f32,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
| ! [Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f57,plain,
? [A,B] :
( point(A)
& point(B)
& distinct_points(A,B)
& ! [X] :
( line(X)
& ( apart_point_and_line(A,X)
| apart_point_and_line(B,X) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f58,plain,
? [A,B] :
( point(A)
& point(B)
& distinct_points(A,B)
& ! [X] : line(X)
& ! [X] :
( apart_point_and_line(A,X)
| apart_point_and_line(B,X) ) ),
inference(miniscoping,[status(esa)],[f57]) ).
fof(f59,plain,
( point(sk0_0)
& point(sk0_1)
& distinct_points(sk0_0,sk0_1)
& ! [X] : line(X)
& ! [X] :
( apart_point_and_line(sk0_0,X)
| apart_point_and_line(sk0_1,X) ) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f62,plain,
distinct_points(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f64,plain,
! [X0] :
( apart_point_and_line(sk0_0,X0)
| apart_point_and_line(sk0_1,X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(resolution,[status(thm)],[f33,f19]) ).
fof(f75,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(resolution,[status(thm)],[f34,f19]) ).
fof(f81,plain,
! [X0] :
( ~ distinct_points(X0,sk0_1)
| apart_point_and_line(sk0_0,line_connecting(X0,sk0_1)) ),
inference(resolution,[status(thm)],[f75,f64]) ).
fof(f84,plain,
( spl0_1
<=> distinct_points(sk0_0,sk0_1) ),
introduced(split_symbol_definition) ).
fof(f86,plain,
( ~ distinct_points(sk0_0,sk0_1)
| spl0_1 ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( ~ distinct_points(sk0_0,sk0_1)
| ~ distinct_points(sk0_0,sk0_1) ),
inference(resolution,[status(thm)],[f81,f71]) ).
fof(f88,plain,
~ spl0_1,
inference(split_clause,[status(thm)],[f87,f84]) ).
fof(f89,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f62]) ).
fof(f90,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO225+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 12:10:27 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.56 % Elapsed time: 0.014286 seconds
% 0.18/0.56 % CPU time: 0.015246 seconds
% 0.18/0.56 % Memory used: 526.333 KB
%------------------------------------------------------------------------------