TSTP Solution File: SET073-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET073-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 03:32:13 EDT 2022
% Result : Unsatisfiable 1.16s 1.34s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 15 unt; 0 nHn; 20 RR)
% Number of literals : 38 ( 9 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 5 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(existence_of_null_class,axiom,
~ member(Z,null_class) ).
cnf(corollary_of_null_class_is_subclass,axiom,
( ~ subclass(X,null_class)
| X = null_class ) ).
cnf(singleton_in_unordered_pair1,axiom,
subclass(singleton(X),unordered_pair(X,Y)) ).
cnf(prove_corollary_to_unordered_pair_axiom1_1,negated_conjecture,
member(x,universal_class) ).
cnf(prove_corollary_to_unordered_pair_axiom1_2,negated_conjecture,
unordered_pair(x,y) = null_class ).
cnf(refute_0_0,plain,
( ~ member(x,universal_class)
| member(x,unordered_pair(X_138,x)) ),
inference(subst,[],[unordered_pair3:[bind(X,$fot(X_138)),bind(Y,$fot(x))]]) ).
cnf(refute_0_1,plain,
member(x,unordered_pair(X_138,x)),
inference(resolve,[$cnf( member(x,universal_class) )],[prove_corollary_to_unordered_pair_axiom1_1,refute_0_0]) ).
cnf(refute_0_2,plain,
member(x,unordered_pair(x,x)),
inference(subst,[],[refute_0_1:[bind(X_138,$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,
subclass(singleton(x),unordered_pair(x,y)),
inference(subst,[],[singleton_in_unordered_pair1:[bind(X,$fot(x)),bind(Y,$fot(y))]]) ).
cnf(refute_0_8,plain,
( unordered_pair(x,y) != null_class
| ~ subclass(singleton(x),unordered_pair(x,y))
| subclass(singleton(x),null_class) ),
introduced(tautology,[equality,[$cnf( subclass(singleton(x),unordered_pair(x,y)) ),[1],$fot(null_class)]]) ).
cnf(refute_0_9,plain,
( ~ subclass(singleton(x),unordered_pair(x,y))
| subclass(singleton(x),null_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(x,y),null_class) )],[prove_corollary_to_unordered_pair_axiom1_2,refute_0_8]) ).
cnf(refute_0_10,plain,
subclass(singleton(x),null_class),
inference(resolve,[$cnf( subclass(singleton(x),unordered_pair(x,y)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ subclass(singleton(x),null_class)
| singleton(x) = null_class ),
inference(subst,[],[corollary_of_null_class_is_subclass:[bind(X,$fot(singleton(x)))]]) ).
cnf(refute_0_12,plain,
singleton(x) = null_class,
inference(resolve,[$cnf( subclass(singleton(x),null_class) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( singleton(x) != null_class
| ~ member(x,singleton(x))
| member(x,null_class) ),
introduced(tautology,[equality,[$cnf( member(x,singleton(x)) ),[1],$fot(null_class)]]) ).
cnf(refute_0_14,plain,
( ~ member(x,singleton(x))
| member(x,null_class) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
member(x,null_class),
inference(resolve,[$cnf( member(x,singleton(x)) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
~ member(x,null_class),
inference(subst,[],[existence_of_null_class:[bind(Z,$fot(x))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( member(x,null_class) )],[refute_0_15,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET073-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n006.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 10:49:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.16/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.16/1.34
% 1.16/1.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.16/1.34
%------------------------------------------------------------------------------