TSTP Solution File: GEO226+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GEO226+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 20:17:39 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 43 ~; 31 |; 20 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(f9,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [L,M] :
( ( line(L)
& line(M)
& convergent_lines(L,M) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,L)
& incident_point_and_line(X,M) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [L,M] :
( ( line(L)
& line(M)
& convergent_lines(L,M) )
=> ? [X] :
( point(X)
=> ( incident_point_and_line(X,L)
& incident_point_and_line(X,M) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f47,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f48,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ! [Z] :
( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f54,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ apart_point_and_line(intersection_point(X,Y),X) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| ~ apart_point_and_line(intersection_point(X,Y),Y) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f57,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f71,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f119,plain,
! [X,Y] :
( ( ~ incident_point_and_line(X,Y)
| ~ apart_point_and_line(X,Y) )
& ( incident_point_and_line(X,Y)
| apart_point_and_line(X,Y) ) ),
inference(NNF_transformation,[status(esa)],[f34]) ).
fof(f120,plain,
( ! [X,Y] :
( ~ incident_point_and_line(X,Y)
| ~ apart_point_and_line(X,Y) )
& ! [X,Y] :
( incident_point_and_line(X,Y)
| apart_point_and_line(X,Y) ) ),
inference(miniscoping,[status(esa)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f127,plain,
? [L,M] :
( line(L)
& line(M)
& convergent_lines(L,M)
& ! [X] :
( point(X)
& ( ~ incident_point_and_line(X,L)
| ~ incident_point_and_line(X,M) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f128,plain,
? [L,M] :
( line(L)
& line(M)
& convergent_lines(L,M)
& ! [X] : point(X)
& ! [X] :
( ~ incident_point_and_line(X,L)
| ~ incident_point_and_line(X,M) ) ),
inference(miniscoping,[status(esa)],[f127]) ).
fof(f129,plain,
( line(sk0_0)
& line(sk0_1)
& convergent_lines(sk0_0,sk0_1)
& ! [X] : point(X)
& ! [X] :
( ~ incident_point_and_line(X,sk0_0)
| ~ incident_point_and_line(X,sk0_1) ) ),
inference(skolemization,[status(esa)],[f128]) ).
fof(f132,plain,
convergent_lines(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f134,plain,
! [X0] :
( ~ incident_point_and_line(X0,sk0_0)
| ~ incident_point_and_line(X0,sk0_1) ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f142,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X0) ),
inference(resolution,[status(thm)],[f49,f40]) ).
fof(f145,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f71,f142]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,parallel_through_point(X1,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f71,f49]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X2,X0)
| convergent_lines(X2,parallel_through_point(X1,X3)) ),
inference(resolution,[status(thm)],[f147,f49]) ).
fof(f165,plain,
! [X0,X1] :
( convergent_lines(sk0_1,X0)
| convergent_lines(sk0_0,parallel_through_point(X0,X1)) ),
inference(resolution,[status(thm)],[f157,f132]) ).
fof(f179,plain,
convergent_lines(sk0_1,sk0_0),
inference(resolution,[status(thm)],[f165,f145]) ).
fof(f431,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| incident_point_and_line(intersection_point(X0,X1),X0) ),
inference(resolution,[status(thm)],[f55,f122]) ).
fof(f432,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| incident_point_and_line(intersection_point(X0,X1),X1) ),
inference(resolution,[status(thm)],[f57,f122]) ).
fof(f433,plain,
! [X0] :
( ~ convergent_lines(sk0_1,X0)
| ~ incident_point_and_line(intersection_point(sk0_1,X0),sk0_0) ),
inference(resolution,[status(thm)],[f431,f134]) ).
fof(f444,plain,
( spl0_0
<=> convergent_lines(sk0_1,sk0_0) ),
introduced(split_symbol_definition) ).
fof(f446,plain,
( ~ convergent_lines(sk0_1,sk0_0)
| spl0_0 ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( ~ convergent_lines(sk0_1,sk0_0)
| ~ convergent_lines(sk0_1,sk0_0) ),
inference(resolution,[status(thm)],[f433,f432]) ).
fof(f448,plain,
~ spl0_0,
inference(split_clause,[status(thm)],[f447,f444]) ).
fof(f449,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f179]) ).
fof(f450,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f451,plain,
$false,
inference(sat_refutation,[status(thm)],[f448,f450]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO226+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 01:19:50 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42 % Elapsed time: 0.065111 seconds
% 0.21/0.42 % CPU time: 0.428406 seconds
% 0.21/0.42 % Total memory used: 13.362 MB
% 0.21/0.42 % Net memory used: 12.996 MB
%------------------------------------------------------------------------------