TSTP Solution File: SET101-6 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET101-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:32:39 EDT 2022
% Result : Unsatisfiable 30.21s 30.38s
% Output : CNFRefutation 30.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 13 unt; 0 nHn; 7 RR)
% Number of literals : 27 ( 6 equ; 9 neg)
% Maximal clause size : 3 ( 1 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 : 26 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair2,axiom,
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X,Y),universal_class) ).
cnf(singleton_set,axiom,
unordered_pair(X,X) = singleton(X) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ).
cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
~ member(singleton(x),ordered_pair(x,y)) ).
cnf(refute_0_0,plain,
member(unordered_pair(X_14,X_14),universal_class),
inference(subst,[],[unordered_pairs_in_universal:[bind(X,$fot(X_14)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_1,plain,
unordered_pair(X_14,X_14) = singleton(X_14),
inference(subst,[],[singleton_set:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
( unordered_pair(X_14,X_14) != singleton(X_14)
| ~ member(unordered_pair(X_14,X_14),universal_class)
| member(singleton(X_14),universal_class) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(X_14,X_14),universal_class) ),[0],$fot(singleton(X_14))]]) ).
cnf(refute_0_3,plain,
( ~ member(unordered_pair(X_14,X_14),universal_class)
| member(singleton(X_14),universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_14,X_14),singleton(X_14)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
member(singleton(X_14),universal_class),
inference(resolve,[$cnf( member(unordered_pair(X_14,X_14),universal_class) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ member(singleton(X_14),universal_class)
| member(singleton(X_14),unordered_pair(singleton(X_14),X_270)) ),
inference(subst,[],[unordered_pair2:[bind(X,$fot(singleton(X_14))),bind(Y,$fot(X_270))]]) ).
cnf(refute_0_6,plain,
member(singleton(X_14),unordered_pair(singleton(X_14),X_270)),
inference(resolve,[$cnf( member(singleton(X_14),universal_class) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y)))),
inference(subst,[],[refute_0_6:[bind(X_14,$fot(X_649)),bind(X_270,$fot(unordered_pair(X_649,singleton(Y))))]]) ).
cnf(refute_0_8,plain,
unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))) = ordered_pair(X_649,Y),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_649))]]) ).
cnf(refute_0_9,plain,
( unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))) != ordered_pair(X_649,Y)
| ~ member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))))
| member(singleton(X_649),ordered_pair(X_649,Y)) ),
introduced(tautology,[equality,[$cnf( member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y)))) ),[1],$fot(ordered_pair(X_649,Y))]]) ).
cnf(refute_0_10,plain,
( ~ member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))))
| member(singleton(X_649),ordered_pair(X_649,Y)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))),ordered_pair(X_649,Y)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
member(singleton(X_649),ordered_pair(X_649,Y)),
inference(resolve,[$cnf( member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y)))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
member(singleton(x),ordered_pair(x,y)),
inference(subst,[],[refute_0_11:[bind(Y,$fot(y)),bind(X_649,$fot(x))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( member(singleton(x),ordered_pair(x,y)) )],[refute_0_12,prove_singleton_member_of_ordered_pair_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET101-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 18:37:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.21/30.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.21/30.38
% 30.21/30.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.21/30.38
%------------------------------------------------------------------------------