TSTP Solution File: SET093+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET093+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 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 03:32:30 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 20 unt; 0 def)
% Number of atoms : 47 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 10 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 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(corollary_2_to_singletons_are_sets,conjecture,
! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ) ).
fof(subgoal_0,plain,
! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
inference(strip,[],[corollary_2_to_singletons_are_sets]) ).
fof(negate_0_0,plain,
~ ! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(canonicalize,[],[unordered_pair]) ).
fof(normalize_0_1,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[singleton_set_defn]) ).
fof(normalize_0_3,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X] :
( ~ member(X,universal_class)
& singleton(member_of(X)) = X ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ member(skolemFOFtoCNF_X_2,universal_class)
& singleton(member_of(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2 ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
singleton(member_of(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
~ member(skolemFOFtoCNF_X_2,universal_class),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
member(unordered_pair(X,Y),universal_class),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
member(unordered_pair(X_10,X_10),universal_class),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_10)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
singleton(X) = unordered_pair(X,X),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
singleton(X_10) = unordered_pair(X_10,X_10),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( singleton(X_10) != unordered_pair(X_10,X_10)
| unordered_pair(X_10,X_10) = singleton(X_10) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(singleton(X_10))),bind(Y0,$fot(unordered_pair(X_10,X_10)))]]) ).
cnf(refute_0_8,plain,
unordered_pair(X_10,X_10) = singleton(X_10),
inference(resolve,[$cnf( $equal(singleton(X_10),unordered_pair(X_10,X_10)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( unordered_pair(X_10,X_10) != singleton(X_10)
| ~ member(unordered_pair(X_10,X_10),universal_class)
| member(singleton(X_10),universal_class) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(X_10,X_10),universal_class) ),[0],$fot(singleton(X_10))]]) ).
cnf(refute_0_10,plain,
( ~ member(unordered_pair(X_10,X_10),universal_class)
| member(singleton(X_10),universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_10,X_10),singleton(X_10)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
member(singleton(X_10),universal_class),
inference(resolve,[$cnf( member(unordered_pair(X_10,X_10),universal_class) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
member(singleton(member_of(skolemFOFtoCNF_X_2)),universal_class),
inference(subst,[],[refute_0_11:[bind(X_10,$fot(member_of(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_0_13,plain,
singleton(member_of(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_14,plain,
( singleton(member_of(skolemFOFtoCNF_X_2)) != skolemFOFtoCNF_X_2
| ~ member(singleton(member_of(skolemFOFtoCNF_X_2)),universal_class)
| member(skolemFOFtoCNF_X_2,universal_class) ),
introduced(tautology,[equality,[$cnf( member(singleton(member_of(skolemFOFtoCNF_X_2)),universal_class) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_15,plain,
( ~ member(singleton(member_of(skolemFOFtoCNF_X_2)),universal_class)
| member(skolemFOFtoCNF_X_2,universal_class) ),
inference(resolve,[$cnf( $equal(singleton(member_of(skolemFOFtoCNF_X_2)),skolemFOFtoCNF_X_2) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
member(skolemFOFtoCNF_X_2,universal_class),
inference(resolve,[$cnf( member(singleton(member_of(skolemFOFtoCNF_X_2)),universal_class) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
~ member(skolemFOFtoCNF_X_2,universal_class),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_X_2,universal_class) )],[refute_0_16,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET093+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 01:24:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.44
% 0.21/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.44
%------------------------------------------------------------------------------