TSTP Solution File: SET025+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET025+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 03:31:25 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : CNFRefutation 0.21s
% 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 : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 5 sgn 18 !; 2 ?)
% 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(ordered_pair_is_set,conjecture,
! [X,Y] : member(ordered_pair(X,Y),universal_class) ).
fof(subgoal_0,plain,
! [X,Y] : member(ordered_pair(X,Y),universal_class),
inference(strip,[],[ordered_pair_is_set]) ).
fof(negate_0_0,plain,
~ ! [X,Y] : member(ordered_pair(X,Y),universal_class),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y] : ~ member(ordered_pair(X,Y),universal_class),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ member(ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1),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,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(canonicalize,[],[ordered_pair_defn]) ).
fof(normalize_0_5,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(specialize,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ member(ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1),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(singleton(X_19),unordered_pair(X_19,singleton(X_20))),universal_class),
inference(subst,[],[refute_0_1:[bind(X,$fot(singleton(X_19))),bind(Y,$fot(unordered_pair(X_19,singleton(X_20))))]]) ).
cnf(refute_0_3,plain,
ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
ordered_pair(X_19,X_20) = unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_19)),bind(Y,$fot(X_20))]]) ).
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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ordered_pair(X_19,X_20) != unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20)))
| unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))) = ordered_pair(X_19,X_20) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(ordered_pair(X_19,X_20))),bind(Y0,$fot(unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20)))))]]) ).
cnf(refute_0_9,plain,
unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))) = ordered_pair(X_19,X_20),
inference(resolve,[$cnf( $equal(ordered_pair(X_19,X_20),unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))) != ordered_pair(X_19,X_20)
| ~ member(unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))),universal_class)
| member(ordered_pair(X_19,X_20),universal_class) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))),universal_class) ),[0],$fot(ordered_pair(X_19,X_20))]]) ).
cnf(refute_0_11,plain,
( ~ member(unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))),universal_class)
| member(ordered_pair(X_19,X_20),universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))),ordered_pair(X_19,X_20)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
member(ordered_pair(X_19,X_20),universal_class),
inference(resolve,[$cnf( member(unordered_pair(singleton(X_19),unordered_pair(X_19,singleton(X_20))),universal_class) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
member(ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1),universal_class),
inference(subst,[],[refute_0_12:[bind(X_19,$fot(skolemFOFtoCNF_X_2)),bind(X_20,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_1),universal_class) )],[refute_0_13,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET025+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.05/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n009.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 : Mon Jul 11 09:17:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43
% 0.21/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.44
%------------------------------------------------------------------------------