TSTP Solution File: SET101-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET101-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 0.80s 0.99s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 10 RR)
% Number of literals : 31 ( 15 equ; 11 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X) ).
cnf(corollary_1_to_singletons_are_sets,axiom,
member(singleton(Y),unordered_pair(X,singleton(Y))) ).
cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
~ member(singleton(x),ordered_pair(x,y)) ).
cnf(refute_0_0,plain,
member(singleton(X_41),unordered_pair(X_40,singleton(X_41))),
inference(subst,[],[corollary_1_to_singletons_are_sets:[bind(X,$fot(X_40)),bind(Y,$fot(X_41))]]) ).
cnf(refute_0_1,plain,
unordered_pair(singleton(X_41),X_40) = unordered_pair(X_40,singleton(X_41)),
inference(subst,[],[commutativity_of_unordered_pair:[bind(X,$fot(singleton(X_41))),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( unordered_pair(singleton(X_41),X_40) != unordered_pair(X_40,singleton(X_41))
| unordered_pair(X_40,singleton(X_41)) = unordered_pair(singleton(X_41),X_40) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(unordered_pair(singleton(X_41),X_40))),bind(Y0,$fot(unordered_pair(X_40,singleton(X_41))))]]) ).
cnf(refute_0_6,plain,
unordered_pair(X_40,singleton(X_41)) = unordered_pair(singleton(X_41),X_40),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_41),X_40),unordered_pair(X_40,singleton(X_41))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( unordered_pair(X_40,singleton(X_41)) != unordered_pair(singleton(X_41),X_40)
| ~ member(singleton(X_41),unordered_pair(X_40,singleton(X_41)))
| member(singleton(X_41),unordered_pair(singleton(X_41),X_40)) ),
introduced(tautology,[equality,[$cnf( member(singleton(X_41),unordered_pair(X_40,singleton(X_41))) ),[1],$fot(unordered_pair(singleton(X_41),X_40))]]) ).
cnf(refute_0_8,plain,
( ~ member(singleton(X_41),unordered_pair(X_40,singleton(X_41)))
| member(singleton(X_41),unordered_pair(singleton(X_41),X_40)) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_40,singleton(X_41)),unordered_pair(singleton(X_41),X_40)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
member(singleton(X_41),unordered_pair(singleton(X_41),X_40)),
inference(resolve,[$cnf( member(singleton(X_41),unordered_pair(X_40,singleton(X_41))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
member(singleton(X_41),unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163)))),
inference(subst,[],[refute_0_9:[bind(X_40,$fot(unordered_pair(X_41,singleton(X_163))))]]) ).
cnf(refute_0_11,plain,
unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163))) = ordered_pair(X_41,X_163),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_41)),bind(Y,$fot(X_163))]]) ).
cnf(refute_0_12,plain,
( unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163))) != ordered_pair(X_41,X_163)
| ~ member(singleton(X_41),unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163))))
| member(singleton(X_41),ordered_pair(X_41,X_163)) ),
introduced(tautology,[equality,[$cnf( member(singleton(X_41),unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163)))) ),[1],$fot(ordered_pair(X_41,X_163))]]) ).
cnf(refute_0_13,plain,
( ~ member(singleton(X_41),unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163))))
| member(singleton(X_41),ordered_pair(X_41,X_163)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163))),ordered_pair(X_41,X_163)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
member(singleton(X_41),ordered_pair(X_41,X_163)),
inference(resolve,[$cnf( member(singleton(X_41),unordered_pair(singleton(X_41),unordered_pair(X_41,singleton(X_163)))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
member(singleton(x),ordered_pair(x,y)),
inference(subst,[],[refute_0_14:[bind(X_163,$fot(y)),bind(X_41,$fot(x))]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( member(singleton(x),ordered_pair(x,y)) )],[refute_0_15,prove_singleton_member_of_ordered_pair_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET101-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 : Sat Jul 9 17:07:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.80/0.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/0.99
% 0.80/0.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.80/0.99
%------------------------------------------------------------------------------