TSTP Solution File: GEO225+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO225+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 05:25:37 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 41 ~; 48 |; 21 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 42 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(X,Z)
| distinct_points(Y,Z) ) ) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ) ) ).
fof(con,conjecture,
! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(A,X)
& ~ apart_point_and_line(B,X) ) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(A,X)
& ~ apart_point_and_line(B,X) ) ) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(A,X)
& ~ apart_point_and_line(B,X) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [A,B] :
( distinct_points(A,B)
& point(A)
& point(B)
& ! [X] : line(X)
& ! [X] :
( apart_point_and_line(A,X)
| apart_point_and_line(B,X) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
& point(skolemFOFtoCNF_A)
& point(skolemFOFtoCNF_B)
& ! [X] : line(X)
& ! [X] :
( apart_point_and_line(skolemFOFtoCNF_A,X)
| apart_point_and_line(skolemFOFtoCNF_B,X) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_6,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( apart_point_and_line(skolemFOFtoCNF_A,X)
| apart_point_and_line(skolemFOFtoCNF_B,X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_8,plain,
! [X] :
( apart_point_and_line(skolemFOFtoCNF_A,X)
| apart_point_and_line(skolemFOFtoCNF_B,X) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(canonicalize,[],[con1]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) )
& ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ distinct_points(skolemFOFtoCNF_B,X_26)
| distinct_points(X_26,Z)
| distinct_points(skolemFOFtoCNF_B,Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_2,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| distinct_points(skolemFOFtoCNF_A,X_24)
| distinct_points(skolemFOFtoCNF_B,X_24) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_B)),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_4,plain,
( distinct_points(skolemFOFtoCNF_A,X_24)
| distinct_points(skolemFOFtoCNF_B,X_24) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( distinct_points(skolemFOFtoCNF_A,X_26)
| distinct_points(skolemFOFtoCNF_B,X_26) ),
inference(subst,[],[refute_0_4:[bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_6,plain,
( distinct_points(X_26,Z)
| distinct_points(skolemFOFtoCNF_A,X_26)
| distinct_points(skolemFOFtoCNF_B,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_B,X_26) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A)
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_6:[bind(Z,$fot(skolemFOFtoCNF_A)),bind(X_26,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_8,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_10,plain,
distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(skolemFOFtoCNF_A,X)
| apart_point_and_line(skolemFOFtoCNF_B,X) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
( apart_point_and_line(skolemFOFtoCNF_A,line_connecting(X_33,X_34))
| apart_point_and_line(skolemFOFtoCNF_B,line_connecting(X_33,X_34)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(line_connecting(X_33,X_34)))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_B,line_connecting(X_33,X_34))
| ~ distinct_points(X_33,X_34)
| distinct_points(skolemFOFtoCNF_B,X_33) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_33)),bind(Y,$fot(X_34)),bind(Z,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_15,plain,
( ~ distinct_points(X_33,X_34)
| apart_point_and_line(skolemFOFtoCNF_A,line_connecting(X_33,X_34))
| distinct_points(skolemFOFtoCNF_B,X_33) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_B,line_connecting(X_33,X_34)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_15:[bind(X_33,$fot(skolemFOFtoCNF_B)),bind(X_34,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
~ distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_19,plain,
apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
| ~ distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(skolemFOFtoCNF_A)),bind(Z,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_22,plain,
( ~ distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_10,refute_0_22]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_A) )],[refute_0_23,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO225+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 21:27:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------