TSTP Solution File: SET024-6 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET024-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:31:24 EDT 2022
% Result : Unsatisfiable 0.81s 0.99s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 17 ( 3 equ; 6 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 : 5 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair3,axiom,
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ) ).
cnf(singleton_set,axiom,
unordered_pair(X,X) = singleton(X) ).
cnf(prove_set_in_its_singleton_1,negated_conjecture,
member(x,universal_class) ).
cnf(prove_set_in_its_singleton_2,negated_conjecture,
~ member(x,singleton(x)) ).
cnf(refute_0_0,plain,
( ~ member(x,universal_class)
| member(x,unordered_pair(X_110,x)) ),
inference(subst,[],[unordered_pair3:[bind(X,$fot(X_110)),bind(Y,$fot(x))]]) ).
cnf(refute_0_1,plain,
member(x,unordered_pair(X_110,x)),
inference(resolve,[$cnf( member(x,universal_class) )],[prove_set_in_its_singleton_1,refute_0_0]) ).
cnf(refute_0_2,plain,
member(x,unordered_pair(x,x)),
inference(subst,[],[refute_0_1:[bind(X_110,$fot(x))]]) ).
cnf(refute_0_3,plain,
unordered_pair(x,x) = singleton(x),
inference(subst,[],[singleton_set:[bind(X,$fot(x))]]) ).
cnf(refute_0_4,plain,
( unordered_pair(x,x) != singleton(x)
| ~ member(x,unordered_pair(x,x))
| member(x,singleton(x)) ),
introduced(tautology,[equality,[$cnf( member(x,unordered_pair(x,x)) ),[1],$fot(singleton(x))]]) ).
cnf(refute_0_5,plain,
( ~ member(x,unordered_pair(x,x))
| member(x,singleton(x)) ),
inference(resolve,[$cnf( $equal(unordered_pair(x,x),singleton(x)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
member(x,singleton(x)),
inference(resolve,[$cnf( member(x,unordered_pair(x,x)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
$false,
inference(resolve,[$cnf( member(x,singleton(x)) )],[refute_0_6,prove_set_in_its_singleton_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET024-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 15:14:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.81/0.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.81/0.99
% 0.81/0.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.81/0.99
%------------------------------------------------------------------------------