TSTP Solution File: SET117+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET117+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:32:50 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : CNFRefutation 0.18s
% 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 : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 5 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class) ).
fof(ordered_pair_defn,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) ).
fof(corollary_1_to_ordered_pairs_are_sets,conjecture,
! [X] :
( ordered_pair(first(X),second(X)) = X
=> member(X,universal_class) ) ).
fof(subgoal_0,plain,
! [X] :
( ordered_pair(first(X),second(X)) = X
=> member(X,universal_class) ),
inference(strip,[],[corollary_1_to_ordered_pairs_are_sets]) ).
fof(negate_0_0,plain,
~ ! [X] :
( ordered_pair(first(X),second(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,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(canonicalize,[],[ordered_pair_defn]) ).
fof(normalize_0_3,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X] :
( ~ member(X,universal_class)
& ordered_pair(first(X),second(X)) = X ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ member(skolemFOFtoCNF_X_2,universal_class)
& ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2 ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
ordered_pair(first(skolemFOFtoCNF_X_2),second(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(singleton(X_22),unordered_pair(X_22,singleton(X_23))),universal_class),
inference(subst,[],[refute_0_0:[bind(X,$fot(singleton(X_22))),bind(Y,$fot(unordered_pair(X_22,singleton(X_23))))]]) ).
cnf(refute_0_2,plain,
ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
ordered_pair(X_22,X_23) = unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_22)),bind(Y,$fot(X_23))]]) ).
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( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ordered_pair(X_22,X_23) != unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23)))
| unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))) = ordered_pair(X_22,X_23) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(ordered_pair(X_22,X_23))),bind(Y0,$fot(unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23)))))]]) ).
cnf(refute_0_8,plain,
unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))) = ordered_pair(X_22,X_23),
inference(resolve,[$cnf( $equal(ordered_pair(X_22,X_23),unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23)))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))) != ordered_pair(X_22,X_23)
| ~ member(unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))),universal_class)
| member(ordered_pair(X_22,X_23),universal_class) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))),universal_class) ),[0],$fot(ordered_pair(X_22,X_23))]]) ).
cnf(refute_0_10,plain,
( ~ member(unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))),universal_class)
| member(ordered_pair(X_22,X_23),universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))),ordered_pair(X_22,X_23)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
member(ordered_pair(X_22,X_23),universal_class),
inference(resolve,[$cnf( member(unordered_pair(singleton(X_22),unordered_pair(X_22,singleton(X_23))),universal_class) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
member(ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)),universal_class),
inference(subst,[],[refute_0_11:[bind(X_22,$fot(first(skolemFOFtoCNF_X_2))),bind(X_23,$fot(second(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_0_13,plain,
ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)) = skolemFOFtoCNF_X_2,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_14,plain,
( ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)) != skolemFOFtoCNF_X_2
| ~ member(ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)),universal_class)
| member(skolemFOFtoCNF_X_2,universal_class) ),
introduced(tautology,[equality,[$cnf( member(ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)),universal_class) ),[0],$fot(skolemFOFtoCNF_X_2)]]) ).
cnf(refute_0_15,plain,
( ~ member(ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)),universal_class)
| member(skolemFOFtoCNF_X_2,universal_class) ),
inference(resolve,[$cnf( $equal(ordered_pair(first(skolemFOFtoCNF_X_2),second(skolemFOFtoCNF_X_2)),skolemFOFtoCNF_X_2) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
member(skolemFOFtoCNF_X_2,universal_class),
inference(resolve,[$cnf( member(ordered_pair(first(skolemFOFtoCNF_X_2),second(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
% 0.06/0.12 % Problem : SET117+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.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 05:44:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42
% 0.18/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.42
%------------------------------------------------------------------------------