TSTP Solution File: GEO196+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:08:13 EDT 2023
% Result : Theorem 3.01s 0.79s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 12 unt; 0 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 42 ~; 55 |; 18 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 107 (; 103 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ convergent_lines(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [X,Y,U,V] :
( ( convergent_lines(X,Y)
& convergent_lines(U,V)
& incident_point_and_line(intersection_point(X,Y),U)
& incident_point_and_line(intersection_point(X,Y),V) )
=> ( incident_point_and_line(intersection_point(U,V),X)
& incident_point_and_line(intersection_point(U,V),Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [X,Y,U,V] :
( ( convergent_lines(X,Y)
& convergent_lines(U,V)
& incident_point_and_line(intersection_point(X,Y),U)
& incident_point_and_line(intersection_point(X,Y),V) )
=> ( incident_point_and_line(intersection_point(U,V),X)
& incident_point_and_line(intersection_point(U,V),Y) ) ),
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(f63,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f64,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
| ! [Z] :
( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ),
inference(miniscoping,[status(esa)],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f69,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f70,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f72,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[status(esa)],[f17]) ).
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,
? [X,Y,U,V] :
( convergent_lines(X,Y)
& convergent_lines(U,V)
& incident_point_and_line(intersection_point(X,Y),U)
& incident_point_and_line(intersection_point(X,Y),V)
& ( ~ incident_point_and_line(intersection_point(U,V),X)
| ~ incident_point_and_line(intersection_point(U,V),Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f128,plain,
( convergent_lines(sk0_0,sk0_1)
& convergent_lines(sk0_2,sk0_3)
& incident_point_and_line(intersection_point(sk0_0,sk0_1),sk0_2)
& incident_point_and_line(intersection_point(sk0_0,sk0_1),sk0_3)
& ( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
| ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1) ) ),
inference(skolemization,[status(esa)],[f127]) ).
fof(f133,plain,
( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
| ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1) ),
inference(cnf_transformation,[status(esa)],[f128]) ).
fof(f140,plain,
( spl0_0
<=> incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
| spl0_0 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( spl0_1
<=> incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( ~ incident_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1)
| spl0_1 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f133,f140,f143]) ).
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(f148,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(f151,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| ~ convergent_lines(parallel_through_point(X1,X2),X0) ),
inference(resolution,[status(thm)],[f148,f40]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X2,parallel_through_point(X1,X3))
| convergent_lines(X2,X0) ),
inference(resolution,[status(thm)],[f151,f49]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( convergent_lines(X0,X1)
| convergent_lines(X2,X0)
| convergent_lines(X3,X1)
| ~ convergent_lines(X2,X3) ),
inference(resolution,[status(thm)],[f153,f148]) ).
fof(f170,plain,
( apart_point_and_line(intersection_point(sk0_2,sk0_3),sk0_0)
| spl0_0 ),
inference(resolution,[status(thm)],[f142,f122]) ).
fof(f202,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| convergent_lines(X2,X0)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[status(thm)],[f156,f40]) ).
fof(f354,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
| ~ convergent_lines(parallel_through_point(X0,X2),X1) ),
inference(resolution,[status(thm)],[f202,f71]) ).
fof(f362,plain,
! [X0,X1,X2] : ~ convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f354,f71]) ).
fof(f374,plain,
! [X0,X1,X2,X3] :
( ~ convergent_lines(X0,parallel_through_point(parallel_through_point(X1,X2),X3))
| convergent_lines(X0,X1) ),
inference(resolution,[status(thm)],[f362,f49]) ).
fof(f426,plain,
! [X0,X1,X2] : ~ convergent_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)),
inference(resolution,[status(thm)],[f374,f40]) ).
fof(f472,plain,
! [X0,X1,X2] :
( convergent_lines(X0,parallel_through_point(X1,X2))
| ~ convergent_lines(X1,X0) ),
inference(resolution,[status(thm)],[f426,f148]) ).
fof(f495,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[status(thm)],[f472,f40]) ).
fof(f610,plain,
! [X0] :
( distinct_lines(sk0_0,X0)
| apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f65,f170]) ).
fof(f618,plain,
! [X0] :
( apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
| convergent_lines(sk0_0,X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f610,f70]) ).
fof(f623,plain,
! [X0] :
( apart_point_and_line(intersection_point(sk0_2,sk0_3),parallel_through_point(sk0_0,X0))
| spl0_0 ),
inference(resolution,[status(thm)],[f618,f495]) ).
fof(f628,plain,
( $false
| spl0_0 ),
inference(resolution,[status(thm)],[f623,f72]) ).
fof(f629,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f630,plain,
( apart_point_and_line(intersection_point(sk0_2,sk0_3),sk0_1)
| spl0_1 ),
inference(resolution,[status(thm)],[f145,f122]) ).
fof(f631,plain,
! [X0] :
( distinct_lines(sk0_1,X0)
| apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
| spl0_1 ),
inference(resolution,[status(thm)],[f630,f65]) ).
fof(f635,plain,
! [X0] :
( apart_point_and_line(intersection_point(sk0_2,sk0_3),X0)
| convergent_lines(sk0_1,X0)
| spl0_1 ),
inference(resolution,[status(thm)],[f631,f70]) ).
fof(f640,plain,
! [X0] :
( apart_point_and_line(intersection_point(sk0_2,sk0_3),parallel_through_point(sk0_1,X0))
| spl0_1 ),
inference(resolution,[status(thm)],[f635,f495]) ).
fof(f645,plain,
( $false
| spl0_1 ),
inference(resolution,[status(thm)],[f640,f72]) ).
fof(f646,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f645]) ).
fof(f647,plain,
$false,
inference(sat_refutation,[status(thm)],[f146,f629,f646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 12:03:31 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 3.01/0.79 % Refutation found
% 3.01/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.01/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.01/0.80 % Elapsed time: 0.502430 seconds
% 3.01/0.80 % CPU time: 3.376402 seconds
% 3.01/0.80 % Memory used: 23.048 MB
%------------------------------------------------------------------------------