TSTP Solution File: SET024+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET024+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 03:31:23 EDT 2022
% Result : Theorem 1.27s 1.50s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 74 ( 29 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 73 ( 34 ~; 25 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 5 sgn 21 !; 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(set_in_its_singleton,conjecture,
! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ) ).
fof(subgoal_0,plain,
! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
inference(strip,[],[set_in_its_singleton]) ).
fof(negate_0_0,plain,
~ ! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ member(X,singleton(X))
& member(X,universal_class) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2))
& 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,
~ member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)),
inference(conjunct,[],[normalize_0_1]) ).
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( $equal(X,X) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_X_2,universal_class)
| member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,X_101)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(X_101))]]) ).
cnf(refute_0_6,plain,
member(skolemFOFtoCNF_X_2,unordered_pair(skolemFOFtoCNF_X_2,X_101)),
inference(resolve,[$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_101,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_8,plain,
singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
singleton(skolemFOFtoCNF_X_2) = unordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_X_2),
inference(subst,[],[refute_0_8:[bind(X,$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,
~ member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_2,singleton(skolemFOFtoCNF_X_2)) )],[refute_0_17,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET024+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 10 09:09:38 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.27/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.27/1.50
% 1.27/1.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.27/1.50
%------------------------------------------------------------------------------