TSTP Solution File: GEO225+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 5 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 41 ~; 26 |; 18 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 55 ( 0 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ) ).
fof(con,conjecture,
! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( incident_point_and_line(A,X)
& incident_point_and_line(B,X) ) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ( point(A)
& point(B)
& distinct_points(A,B) )
=> ? [X] :
( line(X)
=> ( incident_point_and_line(A,X)
& incident_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)
=> ( incident_point_and_line(A,X)
& incident_point_and_line(B,X) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [A,B] :
( distinct_points(A,B)
& point(A)
& point(B)
& ! [X] : line(X)
& ! [X] :
( ~ incident_point_and_line(A,X)
| ~ incident_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] :
( ~ incident_point_and_line(skolemFOFtoCNF_A,X)
| ~ incident_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,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(canonicalize,[],[a4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,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_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ incident_point_and_line(skolemFOFtoCNF_A,X)
| ~ incident_point_and_line(skolemFOFtoCNF_B,X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ incident_point_and_line(skolemFOFtoCNF_A,X)
| ~ incident_point_and_line(skolemFOFtoCNF_B,X) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
| ~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( apart_point_and_line(skolemFOFtoCNF_A,X_37)
| incident_point_and_line(skolemFOFtoCNF_A,X_37) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_5,plain,
( ~ incident_point_and_line(skolemFOFtoCNF_A,X)
| ~ incident_point_and_line(skolemFOFtoCNF_B,X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ incident_point_and_line(skolemFOFtoCNF_A,X_36)
| ~ incident_point_and_line(skolemFOFtoCNF_B,X_36) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_7,plain,
( apart_point_and_line(skolemFOFtoCNF_B,X_36)
| incident_point_and_line(skolemFOFtoCNF_B,X_36) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_8,plain,
( ~ incident_point_and_line(skolemFOFtoCNF_A,X_36)
| apart_point_and_line(skolemFOFtoCNF_B,X_36) ),
inference(resolve,[$cnf( incident_point_and_line(skolemFOFtoCNF_B,X_36) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ incident_point_and_line(skolemFOFtoCNF_A,X_37)
| apart_point_and_line(skolemFOFtoCNF_B,X_37) ),
inference(subst,[],[refute_0_8:[bind(X_36,$fot(X_37))]]) ).
cnf(refute_0_10,plain,
( apart_point_and_line(skolemFOFtoCNF_A,X_37)
| apart_point_and_line(skolemFOFtoCNF_B,X_37) ),
inference(resolve,[$cnf( incident_point_and_line(skolemFOFtoCNF_A,X_37) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(skolemFOFtoCNF_A,line_connecting(X_52,skolemFOFtoCNF_B))
| apart_point_and_line(skolemFOFtoCNF_B,line_connecting(X_52,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_10:[bind(X_37,$fot(line_connecting(X_52,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_B,line_connecting(X_52,skolemFOFtoCNF_B))
| ~ distinct_points(X_52,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_52)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_points(X_52,skolemFOFtoCNF_B)
| apart_point_and_line(skolemFOFtoCNF_A,line_connecting(X_52,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_B,line_connecting(X_52,skolemFOFtoCNF_B)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_14:[bind(X_52,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_16,plain,
apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.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 : Sat Jun 18 10:36:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------