TSTP Solution File: SET102-6 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET102-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 03:32:40 EDT 2022
% Result : Unsatisfiable 40.79s 40.99s
% Output : CNFRefutation 40.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 5 RR)
% Number of literals : 18 ( 3 equ; 6 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 : 22 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair3,axiom,
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X,Y),universal_class) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ).
cnf(prove_unordered_pair_member_of_ordered_pair_1,negated_conjecture,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)) ).
cnf(refute_0_0,plain,
( ~ member(unordered_pair(X,Y),universal_class)
| member(unordered_pair(X,Y),unordered_pair(X_107,unordered_pair(X,Y))) ),
inference(subst,[],[unordered_pair3:[bind(X,$fot(X_107)),bind(Y,$fot(unordered_pair(X,Y)))]]) ).
cnf(refute_0_1,plain,
member(unordered_pair(X,Y),unordered_pair(X_107,unordered_pair(X,Y))),
inference(resolve,[$cnf( member(unordered_pair(X,Y),universal_class) )],[unordered_pairs_in_universal,refute_0_0]) ).
cnf(refute_0_2,plain,
member(unordered_pair(X_560,singleton(Y)),unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y)))),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_560)),bind(Y,$fot(singleton(Y))),bind(X_107,$fot(singleton(X_560)))]]) ).
cnf(refute_0_3,plain,
unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y))) = ordered_pair(X_560,Y),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_560))]]) ).
cnf(refute_0_4,plain,
( unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y))) != ordered_pair(X_560,Y)
| ~ member(unordered_pair(X_560,singleton(Y)),unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y))))
| member(unordered_pair(X_560,singleton(Y)),ordered_pair(X_560,Y)) ),
introduced(tautology,[equality,[$cnf( member(unordered_pair(X_560,singleton(Y)),unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y)))) ),[1],$fot(ordered_pair(X_560,Y))]]) ).
cnf(refute_0_5,plain,
( ~ member(unordered_pair(X_560,singleton(Y)),unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y))))
| member(unordered_pair(X_560,singleton(Y)),ordered_pair(X_560,Y)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y))),ordered_pair(X_560,Y)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
member(unordered_pair(X_560,singleton(Y)),ordered_pair(X_560,Y)),
inference(resolve,[$cnf( member(unordered_pair(X_560,singleton(Y)),unordered_pair(singleton(X_560),unordered_pair(X_560,singleton(Y)))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(subst,[],[refute_0_6:[bind(Y,$fot(y)),bind(X_560,$fot(x))]]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( member(unordered_pair(x,singleton(y)),ordered_pair(x,y)) )],[refute_0_7,prove_unordered_pair_member_of_ordered_pair_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET102-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 00:21:58 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 40.79/40.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.79/40.99
% 40.79/40.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.79/40.99
%------------------------------------------------------------------------------