TSTP Solution File: GEO197+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO197+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 : 600s
% DateTime : Sat Jul 16 05:25:13 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 25 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 38 ~; 36 |; 18 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 12 sgn 58 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z)
& incident_point_and_line(intersection_point(X,Y),Z) )
=> incident_point_and_line(intersection_point(Z,Y),X) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z)
& incident_point_and_line(intersection_point(X,Y),Z) )
=> incident_point_and_line(intersection_point(Z,Y),X) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(Z,Y)
& convergent_lines(X,Z)
& incident_point_and_line(intersection_point(X,Y),Z) )
=> incident_point_and_line(intersection_point(Z,Y),X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_7,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [X,Y,Z] :
( ~ incident_point_and_line(intersection_point(Z,Y),X)
& convergent_lines(X,Y)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& incident_point_and_line(intersection_point(X,Y),Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ incident_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& convergent_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
& incident_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ incident_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(canonicalize,[],[a4]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) )
& ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq2]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_18,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X),
inference(subst,[],[refute_0_0:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ distinct_lines(parallel_through_point(X_101,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X)
| convergent_lines(parallel_through_point(X_101,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(parallel_through_point(X_101,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),X_99)
| distinct_lines(X_99,Z)
| distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))),bind(Y,$fot(X_99))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(skolemFOFtoCNF_X,parallel_through_point(X_82,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))
| distinct_lines(parallel_through_point(X_82,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_X,Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(parallel_through_point(X_82,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))))]]) ).
cnf(refute_0_7,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),
inference(subst,[],[refute_0_7:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_9,plain,
~ incident_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| incident_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_12,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
inference(resolve,[$cnf( incident_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_11,refute_0_9]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_79)
| distinct_lines(skolemFOFtoCNF_X,X_79) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(X_79))]]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_79)
| distinct_lines(skolemFOFtoCNF_X,X_79) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))
| distinct_lines(skolemFOFtoCNF_X,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))) ),
inference(subst,[],[refute_0_15:[bind(X_79,$fot(parallel_through_point(Y,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))))]]) ).
cnf(refute_0_17,plain,
distinct_lines(skolemFOFtoCNF_X,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))) )],[refute_0_16,refute_0_8]) ).
cnf(refute_0_18,plain,
distinct_lines(skolemFOFtoCNF_X,parallel_through_point(X_82,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_82))]]) ).
cnf(refute_0_19,plain,
( distinct_lines(parallel_through_point(X_82,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_X,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,parallel_through_point(X_82,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))) )],[refute_0_18,refute_0_6]) ).
cnf(refute_0_20,plain,
( distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),X_99)
| distinct_lines(skolemFOFtoCNF_X,X_99) ),
inference(subst,[],[refute_0_19:[bind(Z,$fot(X_99)),bind(X_82,$fot(X_100))]]) ).
cnf(refute_0_21,plain,
( distinct_lines(X_99,Z)
| distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),Z)
| distinct_lines(skolemFOFtoCNF_X,X_99) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),X_99) )],[refute_0_20,refute_0_5]) ).
cnf(refute_0_22,plain,
( distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_21:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_99,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_23,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_24,plain,
~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_25,plain,
distinct_lines(parallel_through_point(X_100,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
distinct_lines(parallel_through_point(X_101,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X),
inference(subst,[],[refute_0_25:[bind(X_100,$fot(X_101))]]) ).
cnf(refute_0_27,plain,
convergent_lines(parallel_through_point(X_101,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_101,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
convergent_lines(parallel_through_point(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X),
inference(subst,[],[refute_0_27:[bind(X_101,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),skolemFOFtoCNF_X) )],[refute_0_28,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO197+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 17 17:19:47 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------