TSTP Solution File: GEO215+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO215+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 05:25:29 EDT 2022
% Result : Theorem 0.73s 0.90s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 21 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 60 ~; 77 |; 9 &)
% ( 0 <=>; 8 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 60 !; 3 ?)
% 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(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ) ).
fof(con,conjecture,
! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( convergent_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> unorthogonal_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( convergent_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> unorthogonal_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [L,M,N] :
( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(M,N)
& convergent_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
& ~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_6,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_points(X,X),
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)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,L,M,N] :
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[ouo1]) ).
fof(normalize_0_18,plain,
! [A,L,M,N] :
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,X_22)
| convergent_lines(X_22,Z)
| convergent_lines(skolemFOFtoCNF_M,Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_2,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_21)
| convergent_lines(skolemFOFtoCNF_M,X_21) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_4,plain,
( convergent_lines(skolemFOFtoCNF_L,X_21)
| convergent_lines(skolemFOFtoCNF_M,X_21) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( convergent_lines(skolemFOFtoCNF_L,X_22)
| convergent_lines(skolemFOFtoCNF_M,X_22) ),
inference(subst,[],[refute_0_4:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_6,plain,
( convergent_lines(X_22,Z)
| convergent_lines(skolemFOFtoCNF_L,X_22)
| convergent_lines(skolemFOFtoCNF_M,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,X_22) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_6:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_22,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_8,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_10,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(X_93,skolemFOFtoCNF_L)
| ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| distinct_points(X_93,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_L)),bind(Z,$fot(X_93))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(X_93,skolemFOFtoCNF_L)
| distinct_points(X_93,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,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_13:[bind(X_93,$fot(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)))]]) ).
cnf(refute_0_15,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)),
inference(subst,[],[refute_0_15:[bind(X,$fot(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)))]]) ).
cnf(refute_0_17,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( ~ apart_point_and_line(X_108,skolemFOFtoCNF_M)
| ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| distinct_points(X_108,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_L)),bind(Z,$fot(X_108))]]) ).
cnf(refute_0_19,plain,
( ~ apart_point_and_line(X_108,skolemFOFtoCNF_M)
| distinct_points(X_108,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ apart_point_and_line(X_799,skolemFOFtoCNF_M)
| distinct_points(X_799,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_19:[bind(X_108,$fot(X_799))]]) ).
cnf(refute_0_21,plain,
~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_22,plain,
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_23,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_24,plain,
distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_26,plain,
( ~ distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| apart_point_and_line(X_783,skolemFOFtoCNF_L)
| apart_point_and_line(X_783,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,X_786)
| unorthogonal_lines(skolemFOFtoCNF_M,X_786) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_783)),bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M)),bind(N,$fot(X_786))]]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(X_783,skolemFOFtoCNF_L)
| apart_point_and_line(X_783,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,X_786)
| unorthogonal_lines(skolemFOFtoCNF_M,X_786) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(X_797,skolemFOFtoCNF_L)
| apart_point_and_line(X_797,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_27:[bind(X_783,$fot(X_797)),bind(X_786,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(X_797,skolemFOFtoCNF_L)
| apart_point_and_line(X_797,skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_28,refute_0_21]) ).
cnf(refute_0_30,plain,
~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_31,plain,
( apart_point_and_line(X_797,skolemFOFtoCNF_L)
| apart_point_and_line(X_797,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( apart_point_and_line(X_799,skolemFOFtoCNF_L)
| apart_point_and_line(X_799,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_31:[bind(X_797,$fot(X_799))]]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(X_799,skolemFOFtoCNF_L)
| distinct_points(X_799,intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(resolve,[$cnf( apart_point_and_line(X_799,skolemFOFtoCNF_M) )],[refute_0_32,refute_0_20]) ).
cnf(refute_0_34,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L)
| distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) ),
inference(subst,[],[refute_0_33:[bind(X_799,$fot(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)))]]) ).
cnf(refute_0_35,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) )],[refute_0_34,refute_0_16]) ).
cnf(refute_0_36,plain,
distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),skolemFOFtoCNF_L) )],[refute_0_35,refute_0_14]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L),intersection_point(skolemFOFtoCNF_M,skolemFOFtoCNF_L)) )],[refute_0_36,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO215+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jun 18 14:12:59 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.73/0.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.73/0.90
% 0.73/0.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.73/0.90
%------------------------------------------------------------------------------