TSTP Solution File: SET077+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET077+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:32:17 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 21 unt; 0 def)
% Number of atoms : 33 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 28 ( 3 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X) ).
fof(singletons_are_sets,conjecture,
! [X] : member(singleton(X),universal_class) ).
fof(subgoal_0,plain,
! [X] : member(singleton(X),universal_class),
inference(strip,[],[singletons_are_sets]) ).
fof(negate_0_0,plain,
~ ! [X] : member(singleton(X),universal_class),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] : ~ member(singleton(X),universal_class),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ member(singleton(skolemFOFtoCNF_X_2),universal_class),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(canonicalize,[],[unordered_pair]) ).
fof(normalize_0_3,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[singleton_set_defn]) ).
fof(normalize_0_5,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ member(singleton(skolemFOFtoCNF_X_2),universal_class),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
member(unordered_pair(X,Y),universal_class),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
member(unordered_pair(X_8,X_8),universal_class),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_8)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_3,plain,
singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
singleton(X_8) = unordered_pair(X_8,X_8),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( singleton(X_8) != unordered_pair(X_8,X_8)
| unordered_pair(X_8,X_8) = singleton(X_8) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(singleton(X_8))),bind(Y0,$fot(unordered_pair(X_8,X_8)))]]) ).
cnf(refute_0_9,plain,
unordered_pair(X_8,X_8) = singleton(X_8),
inference(resolve,[$cnf( $equal(singleton(X_8),unordered_pair(X_8,X_8)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( unordered_pair(X_8,X_8) != singleton(X_8)
| ~ member(unordered_pair(X_8,X_8),universal_class)
| member(singleton(X_8),universal_class) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(X_8,X_8),universal_class) ),[0],$fot(singleton(X_8))]]) ).
cnf(refute_0_11,plain,
( ~ member(unordered_pair(X_8,X_8),universal_class)
| member(singleton(X_8),universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_8,X_8),singleton(X_8)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
member(singleton(X_8),universal_class),
inference(resolve,[$cnf( member(unordered_pair(X_8,X_8),universal_class) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
member(singleton(skolemFOFtoCNF_X_2),universal_class),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(skolemFOFtoCNF_X_2))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( member(singleton(skolemFOFtoCNF_X_2),universal_class) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET077+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 00:12:17 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41
% 0.19/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.41
%------------------------------------------------------------------------------