TSTP Solution File: SET060+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET060+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Tue Jul 19 03:31:57 EDT 2022
% Result : Theorem 44.19s 44.39s
% Output : CNFRefutation 44.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 36 ~; 21 |; 6 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection,axiom,
! [X,Y,Z] :
( member(Z,intersection(X,Y))
<=> ( member(Z,X)
& member(Z,Y) ) ) ).
fof(complement,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( member(Z,universal_class)
& ~ member(Z,X) ) ) ).
fof(special_classes_lemma,conjecture,
! [X,Y] : ~ member(Y,intersection(complement(X),X)) ).
fof(subgoal_0,plain,
! [X,Y] : ~ member(Y,intersection(complement(X),X)),
inference(strip,[],[special_classes_lemma]) ).
fof(negate_0_0,plain,
~ ! [X,Y] : ~ member(Y,intersection(complement(X),X)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y] : member(Y,intersection(complement(X),X)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
member(skolemFOFtoCNF_Y_1,intersection(complement(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_2)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ member(Z,intersection(X,Y))
<=> ( ~ member(Z,X)
| ~ member(Z,Y) ) ),
inference(canonicalize,[],[intersection]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ member(Z,intersection(X,Y))
<=> ( ~ member(Z,X)
| ~ member(Z,Y) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ( ~ member(Z,intersection(X,Y))
| member(Z,X) )
& ( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
& ( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Z] :
( ~ member(Z,complement(X))
<=> ( ~ member(Z,universal_class)
| member(Z,X) ) ),
inference(canonicalize,[],[complement]) ).
fof(normalize_0_7,plain,
! [X,Z] :
( ~ member(Z,complement(X))
<=> ( ~ member(Z,universal_class)
| member(Z,X) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Z] :
( ( ~ member(Z,X)
| ~ member(Z,complement(X)) )
& ( ~ member(Z,complement(X))
| member(Z,universal_class) )
& ( ~ member(Z,universal_class)
| member(Z,X)
| member(Z,complement(X)) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Z] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
member(skolemFOFtoCNF_Y_1,intersection(complement(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_2)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ member(skolemFOFtoCNF_Y_1,intersection(complement(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_2))
| member(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(complement(skolemFOFtoCNF_X_2))),bind(Y,$fot(skolemFOFtoCNF_X_2)),bind(Z,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_3,plain,
member(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,intersection(complement(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_2)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_Y_1,complement(skolemFOFtoCNF_X_2))
| ~ member(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Z,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_6,plain,
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ member(skolemFOFtoCNF_Y_1,intersection(complement(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_2))
| member(skolemFOFtoCNF_Y_1,complement(skolemFOFtoCNF_X_2)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(complement(skolemFOFtoCNF_X_2))),bind(Y,$fot(skolemFOFtoCNF_X_2)),bind(Z,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_8,plain,
member(skolemFOFtoCNF_Y_1,complement(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,intersection(complement(skolemFOFtoCNF_X_2),skolemFOFtoCNF_X_2)) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
~ member(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,complement(skolemFOFtoCNF_X_2)) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_2) )],[refute_0_3,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET060+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 9 16:04:26 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 44.19/44.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.19/44.39
% 44.19/44.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.19/44.40
%------------------------------------------------------------------------------