TSTP Solution File: SET079+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET079+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 03:32:18 EDT 2022
% Result : Theorem 9.27s 9.52s
% Output : CNFRefutation 9.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 22 unt; 0 def)
% Number of atoms : 85 ( 37 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 83 ( 41 ~; 28 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 6 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X) ).
fof(null_class_defn,axiom,
! [X] : ~ member(X,null_class) ).
fof(corollary_to_set_in_its_singleton,conjecture,
! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ) ).
fof(subgoal_0,plain,
! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ),
inference(strip,[],[corollary_to_set_in_its_singleton]) ).
fof(negate_0_0,plain,
~ ! [X] :
( member(X,universal_class)
=> singleton(X) != null_class ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( singleton(X) = null_class
& member(X,universal_class) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( singleton(skolemFOFtoCNF_X_2) = null_class
& member(skolemFOFtoCNF_X_2,universal_class) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
member(skolemFOFtoCNF_X_2,universal_class),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
<=> ( ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(canonicalize,[],[unordered_pair_defn]) ).
fof(normalize_0_4,plain,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
<=> ( ~ member(U,universal_class)
| ( U != X
& U != Y ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [U,X,Y] :
( ( ~ member(U,unordered_pair(X,Y))
| member(U,universal_class) )
& ( U != X
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( U != Y
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [U,X,Y] :
( U != X
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[singleton_set_defn]) ).
fof(normalize_0_8,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
singleton(skolemFOFtoCNF_X_2) = null_class,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [X] : ~ member(X,null_class),
inference(canonicalize,[],[null_class_defn]) ).
fof(normalize_0_11,plain,
! [X] : ~ member(X,null_class),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
member(skolemFOFtoCNF_X_2,universal_class),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( U != X
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( X != X
| ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(X))]]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_X_2,universal_class)
| member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,X_267)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(X_267))]]) ).
cnf(refute_0_6,plain,
member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,X_267)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_2,universal_class) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)),
inference(subst,[],[refute_0_6:[bind(X_267,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_8,plain,
singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
singleton(skolemFOFtoCNF_X_2) = unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_10,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_11,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_12,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( singleton(skolemFOFtoCNF_X_2) != unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)
| unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) = singleton(skolemFOFtoCNF_X_2) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(singleton(skolemFOFtoCNF_X_2))),bind(Y0,$fot(unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_0_14,plain,
unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) = singleton(skolemFOFtoCNF_X_2),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_X_2),unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2) != singleton(skolemFOFtoCNF_X_2)
| ~ member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2))
| member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)) ),[1],$fot(singleton(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2))
| member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),singleton(skolemFOFtoCNF_X_2)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2)) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
singleton(skolemFOFtoCNF_X_2) = null_class,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_19,plain,
( singleton(skolemFOFtoCNF_X_2) != null_class
| ~ member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2))
| member(skolemFOFtoCNF_X_2,null_class) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)) ),[1],$fot(null_class)]]) ).
cnf(refute_0_20,plain,
( ~ member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2))
| member(skolemFOFtoCNF_X_2,null_class) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_X_2),null_class) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
member(skolemFOFtoCNF_X_2,null_class),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
~ member(X,null_class),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_23,plain,
~ member(skolemFOFtoCNF_X_2,null_class),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_2,null_class) )],[refute_0_21,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET079+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 05:31:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.27/9.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.27/9.52
% 9.27/9.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.27/9.52
%------------------------------------------------------------------------------