TSTP Solution File: GEO226+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO226+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 05:25:38 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 16 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 48 ~; 49 |; 20 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 45 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(con2,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)) ) ) ).
fof(con,conjecture,
! [L,M] :
( ( line(L)
& line(M)
& convergent_lines(L,M) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,L)
& ~ apart_point_and_line(X,M) ) ) ) ).
fof(subgoal_0,plain,
! [L,M] :
( ( line(L)
& line(M)
& convergent_lines(L,M) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,L)
& ~ apart_point_and_line(X,M) ) ) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M] :
( ( line(L)
& line(M)
& convergent_lines(L,M) )
=> ? [X] :
( point(X)
=> ( ~ apart_point_and_line(X,L)
& ~ apart_point_and_line(X,M) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_1,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [L,M] :
( convergent_lines(L,M)
& line(L)
& line(M)
& ! [X] : point(X)
& ! [X] :
( apart_point_and_line(X,L)
| apart_point_and_line(X,M) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& line(skolemFOFtoCNF_L)
& line(skolemFOFtoCNF_M)
& ! [X] : point(X)
& ! [X] :
( apart_point_and_line(X,skolemFOFtoCNF_L)
| apart_point_and_line(X,skolemFOFtoCNF_M) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( apart_point_and_line(X,skolemFOFtoCNF_L)
| apart_point_and_line(X,skolemFOFtoCNF_M) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( apart_point_and_line(X,skolemFOFtoCNF_L)
| apart_point_and_line(X,skolemFOFtoCNF_M) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_10,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)),
inference(subst,[],[refute_0_0:[bind(X,$fot(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)))]]) ).
cnf(refute_0_2,plain,
( apart_point_and_line(X,skolemFOFtoCNF_L)
| apart_point_and_line(X,skolemFOFtoCNF_M) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( apart_point_and_line(X_552,skolemFOFtoCNF_L)
| apart_point_and_line(X_552,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_552))]]) ).
cnf(refute_0_4,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,X_289)
| convergent_lines(X_289,Z)
| convergent_lines(skolemFOFtoCNF_M,Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(X_289))]]) ).
cnf(refute_0_6,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_288)
| convergent_lines(skolemFOFtoCNF_M,X_288) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M)),bind(Z,$fot(X_288))]]) ).
cnf(refute_0_8,plain,
( convergent_lines(skolemFOFtoCNF_L,X_288)
| convergent_lines(skolemFOFtoCNF_M,X_288) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( convergent_lines(skolemFOFtoCNF_L,X_289)
| convergent_lines(skolemFOFtoCNF_M,X_289) ),
inference(subst,[],[refute_0_8:[bind(X_288,$fot(X_289))]]) ).
cnf(refute_0_10,plain,
( convergent_lines(X_289,Z)
| convergent_lines(skolemFOFtoCNF_L,X_289)
| convergent_lines(skolemFOFtoCNF_M,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,X_289) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_10:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_289,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_12,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_14,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(X_550,skolemFOFtoCNF_M)
| ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| distinct_points(X_550,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_L)),bind(Z,$fot(X_550))]]) ).
cnf(refute_0_17,plain,
( ~ apart_point_and_line(X_550,skolemFOFtoCNF_M)
| distinct_points(X_550,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ apart_point_and_line(X_552,skolemFOFtoCNF_M)
| distinct_points(X_552,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_17:[bind(X_550,$fot(X_552))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(X_552,skolemFOFtoCNF_L)
| distinct_points(X_552,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(resolve,[$cnf( apart_point_and_line(X_552,skolemFOFtoCNF_M) )],[refute_0_3,refute_0_18]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L)
| distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_19:[bind(X_552,$fot(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)))]]) ).
cnf(refute_0_21,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) )],[refute_0_20,refute_0_1]) ).
cnf(refute_0_22,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
( ~ apart_point_and_line(X_563,skolemFOFtoCNF_L)
| ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| distinct_points(X_563,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_L)),bind(Z,$fot(X_563))]]) ).
cnf(refute_0_24,plain,
( ~ apart_point_and_line(X_563,skolemFOFtoCNF_L)
| distinct_points(X_563,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_14,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L)
| distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_24:[bind(X_563,$fot(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)))]]) ).
cnf(refute_0_26,plain,
distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) )],[refute_0_26,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO226+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n009.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 20:22:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45
% 0.21/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.46
%------------------------------------------------------------------------------