TSTP Solution File: GEO201+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GEO201+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 : Tue Apr 30 20:17:29 EDT 2024
% Result : Theorem 0.18s 0.39s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 68 ( 15 unt; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 57 ~; 70 |; 5 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 65 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ distinct_points(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : ~ distinct_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_lines(U,V) )
=> ( apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f16,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ! [Z] :
( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f31,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) )
| distinct_points(Z,intersection_point(X,Y)) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f32,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ! [Z] :
( ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) )
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
! [X,Y,U,V] :
( ~ distinct_points(X,Y)
| ~ distinct_lines(U,V)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f43,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
? [X,Y] :
( convergent_lines(X,Y)
& distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f46,plain,
( convergent_lines(sk0_0,sk0_1)
& distinct_points(intersection_point(sk0_0,sk0_1),intersection_point(sk0_1,sk0_0)) ),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
convergent_lines(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
distinct_points(intersection_point(sk0_0,sk0_1),intersection_point(sk0_1,sk0_0)),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f49,plain,
! [X0] :
( ~ apart_point_and_line(X0,sk0_0)
| distinct_points(X0,intersection_point(sk0_0,sk0_1)) ),
inference(resolution,[status(thm)],[f33,f47]) ).
fof(f50,plain,
! [X0] :
( ~ apart_point_and_line(X0,sk0_1)
| distinct_points(X0,intersection_point(sk0_0,sk0_1)) ),
inference(resolution,[status(thm)],[f34,f47]) ).
fof(f52,plain,
! [X0] :
( convergent_lines(sk0_0,X0)
| convergent_lines(sk0_1,X0) ),
inference(resolution,[status(thm)],[f26,f47]) ).
fof(f54,plain,
! [X0,X1] :
( convergent_lines(sk0_0,X0)
| ~ apart_point_and_line(X1,X0)
| distinct_points(X1,intersection_point(sk0_1,X0)) ),
inference(resolution,[status(thm)],[f52,f34]) ).
fof(f55,plain,
! [X0,X1] :
( convergent_lines(sk0_0,X0)
| ~ apart_point_and_line(X1,sk0_1)
| distinct_points(X1,intersection_point(sk0_1,X0)) ),
inference(resolution,[status(thm)],[f52,f33]) ).
fof(f104,plain,
( spl0_7
<=> convergent_lines(sk0_0,sk0_0) ),
introduced(split_symbol_definition) ).
fof(f105,plain,
( convergent_lines(sk0_0,sk0_0)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f130,plain,
distinct_lines(sk0_0,sk0_1),
inference(resolution,[status(thm)],[f44,f47]) ).
fof(f166,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| apart_point_and_line(intersection_point(sk0_0,sk0_1),X0)
| apart_point_and_line(intersection_point(sk0_0,sk0_1),X1)
| apart_point_and_line(intersection_point(sk0_1,sk0_0),X0)
| apart_point_and_line(intersection_point(sk0_1,sk0_0),X1) ),
inference(resolution,[status(thm)],[f36,f48]) ).
fof(f167,plain,
( spl0_10
<=> apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_0) ),
introduced(split_symbol_definition) ).
fof(f168,plain,
( apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_0)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( spl0_11
<=> apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f171,plain,
( apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_1)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( spl0_12
<=> apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_0) ),
introduced(split_symbol_definition) ).
fof(f174,plain,
( apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_0)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( spl0_13
<=> apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f177,plain,
( apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_1)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_0)
| apart_point_and_line(intersection_point(sk0_0,sk0_1),sk0_1)
| apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_0)
| apart_point_and_line(intersection_point(sk0_1,sk0_0),sk0_1) ),
inference(resolution,[status(thm)],[f166,f130]) ).
fof(f180,plain,
( spl0_10
| spl0_11
| spl0_12
| spl0_13 ),
inference(split_clause,[status(thm)],[f179,f167,f170,f173,f176]) ).
fof(f195,plain,
! [X0] :
( convergent_lines(sk0_0,X0)
| distinct_points(intersection_point(sk0_1,sk0_0),intersection_point(sk0_1,X0))
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f177,f55]) ).
fof(f220,plain,
( distinct_points(intersection_point(sk0_0,sk0_1),intersection_point(sk0_0,sk0_1))
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f171,f50]) ).
fof(f221,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f15]) ).
fof(f222,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f223,plain,
( distinct_points(intersection_point(sk0_0,sk0_1),intersection_point(sk0_0,sk0_1))
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f168,f49]) ).
fof(f224,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f15]) ).
fof(f225,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f229,plain,
( spl0_20
<=> distinct_points(intersection_point(sk0_1,sk0_0),intersection_point(sk0_1,sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f230,plain,
( distinct_points(intersection_point(sk0_1,sk0_0),intersection_point(sk0_1,sk0_0))
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( convergent_lines(sk0_0,sk0_0)
| distinct_points(intersection_point(sk0_1,sk0_0),intersection_point(sk0_1,sk0_0))
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f174,f54]) ).
fof(f233,plain,
( spl0_7
| spl0_20
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f232,f104,f229,f173]) ).
fof(f244,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f17]) ).
fof(f245,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f15]) ).
fof(f247,plain,
~ spl0_20,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f263,plain,
( spl0_23
<=> distinct_lines(sk0_1,sk0_1) ),
introduced(split_symbol_definition) ).
fof(f264,plain,
( distinct_lines(sk0_1,sk0_1)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f287,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f16]) ).
fof(f288,plain,
~ spl0_23,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f294,plain,
( convergent_lines(sk0_0,sk0_0)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f195,f15]) ).
fof(f295,plain,
( spl0_7
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f294,f104,f176]) ).
fof(f296,plain,
$false,
inference(sat_refutation,[status(thm)],[f180,f222,f225,f233,f245,f247,f288,f295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO201+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 30 01:19:19 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.18/0.39 % Refutation found
% 0.18/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.40 % Elapsed time: 0.056422 seconds
% 0.18/0.40 % CPU time: 0.364205 seconds
% 0.18/0.40 % Total memory used: 12.380 MB
% 0.18/0.40 % Net memory used: 11.988 MB
%------------------------------------------------------------------------------