TSTP Solution File: GEO176+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO176+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 05:24:54 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 12 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 40 ~; 47 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
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(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_points(X,Z)
| apart_point_and_line(Z,Y) ) ) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(X,U)
| apart_point_and_line(X,V) ) )
=> distinct_points(X,intersection_point(U,V)) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(X,U)
| apart_point_and_line(X,V) ) )
=> distinct_points(X,intersection_point(U,V)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(X,U)
| apart_point_and_line(X,V) ) )
=> distinct_points(X,intersection_point(U,V)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,V,X,Y] :
( ~ distinct_points(X,intersection_point(U,V))
& convergent_lines(U,V)
& distinct_points(X,Y)
& ( apart_point_and_line(X,U)
| apart_point_and_line(X,V) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
& convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,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_4,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_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_5]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(X_74,skolemFOFtoCNF_U)
| ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_points(X_74,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(X_74,skolemFOFtoCNF_U)
| distinct_points(X_74,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_3:[bind(X_74,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_5,plain,
~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| apart_point_and_line(X_47,skolemFOFtoCNF_V)
| distinct_points(skolemFOFtoCNF_X,X_47) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(X_47,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_X,X_47) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_9:[bind(X_47,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_10,refute_0_5]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(X_81,skolemFOFtoCNF_V)
| ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_points(X_81,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_81))]]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X_81,skolemFOFtoCNF_V)
| distinct_points(X_81,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V)
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_14:[bind(X_81,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(subst,[],[refute_0_17:[bind(X,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_19,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_19,refute_0_4]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_20,refute_0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO176+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % 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 : Sat Jun 18 01:45:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.41
% 0.21/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.42
%------------------------------------------------------------------------------