TSTP Solution File: SET077-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET077-7 : 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 03:32:17 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 3 equ; 4 neg)
% Maximal clause size : 3 ( 1 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 : 8 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X,Y),universal_class) ).
cnf(singleton_set,axiom,
unordered_pair(X,X) = singleton(X) ).
cnf(prove_singletons_are_sets_1,negated_conjecture,
~ member(singleton(x),universal_class) ).
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),universal_class),
inference(subst,[],[refute_0_4:[bind(X_14,$fot(x))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( member(singleton(x),universal_class) )],[refute_0_5,prove_singletons_are_sets_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET077-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % 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 : Sun Jul 10 04:17:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44
% 0.20/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.44
%------------------------------------------------------------------------------