TSTP Solution File: SET085-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 03:32:24 EDT 2022
% Result : Unsatisfiable 169.50s 169.68s
% Output : CNFRefutation 169.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 50 ( 12 unt; 18 nHn; 39 RR)
% Number of literals : 96 ( 57 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair2,axiom,
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ).
cnf(regularity1,axiom,
( X = null_class
| member(regular(X),X) ) ).
cnf(unordered_pair_equals_singleton2,axiom,
( member(X,universal_class)
| unordered_pair(X,Y) = singleton(Y) ) ).
cnf(corollary_to_set_in_its_singleton,axiom,
( ~ member(X,universal_class)
| singleton(X) != null_class ) ).
cnf(only_member_in_singleton,axiom,
( ~ member(Y,singleton(X))
| Y = X ) ).
cnf(prove_singleton_in_unordered_pair3_1,negated_conjecture,
unordered_pair(y,z) = singleton(x) ).
cnf(prove_singleton_in_unordered_pair3_2,negated_conjecture,
member(x,universal_class) ).
cnf(prove_singleton_in_unordered_pair3_3,negated_conjecture,
x != y ).
cnf(prove_singleton_in_unordered_pair3_4,negated_conjecture,
x != z ).
cnf(refute_0_0,plain,
( ~ member(z,singleton(x))
| z = x ),
inference(subst,[],[only_member_in_singleton:[bind(X,$fot(x)),bind(Y,$fot(z))]]) ).
cnf(refute_0_1,plain,
( singleton(X_93) = null_class
| member(regular(singleton(X_93)),singleton(X_93)) ),
inference(subst,[],[regularity1:[bind(X,$fot(singleton(X_93)))]]) ).
cnf(refute_0_2,plain,
( singleton(X_91) = null_class
| member(regular(singleton(X_91)),singleton(X_91)) ),
inference(subst,[],[regularity1:[bind(X,$fot(singleton(X_91)))]]) ).
cnf(refute_0_3,plain,
( ~ member(regular(singleton(X_91)),singleton(X_91))
| regular(singleton(X_91)) = X_91 ),
inference(subst,[],[only_member_in_singleton:[bind(X,$fot(X_91)),bind(Y,$fot(regular(singleton(X_91))))]]) ).
cnf(refute_0_4,plain,
( regular(singleton(X_91)) = X_91
| singleton(X_91) = null_class ),
inference(resolve,[$cnf( member(regular(singleton(X_91)),singleton(X_91)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( regular(singleton(X_93)) = X_93
| singleton(X_93) = null_class ),
inference(subst,[],[refute_0_4:[bind(X_91,$fot(X_93))]]) ).
cnf(refute_0_6,plain,
( regular(singleton(X_93)) != X_93
| ~ member(regular(singleton(X_93)),singleton(X_93))
| member(X_93,singleton(X_93)) ),
introduced(tautology,[equality,[$cnf( member(regular(singleton(X_93)),singleton(X_93)) ),[0],$fot(X_93)]]) ).
cnf(refute_0_7,plain,
( ~ member(regular(singleton(X_93)),singleton(X_93))
| singleton(X_93) = null_class
| member(X_93,singleton(X_93)) ),
inference(resolve,[$cnf( $equal(regular(singleton(X_93)),X_93) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( singleton(X_93) = null_class
| member(X_93,singleton(X_93)) ),
inference(resolve,[$cnf( member(regular(singleton(X_93)),singleton(X_93)) )],[refute_0_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( singleton(z) = null_class
| member(z,singleton(z)) ),
inference(subst,[],[refute_0_8:[bind(X_93,$fot(z))]]) ).
cnf(refute_0_10,plain,
( ~ member(y,singleton(x))
| y = x ),
inference(subst,[],[only_member_in_singleton:[bind(X,$fot(x)),bind(Y,$fot(y))]]) ).
cnf(refute_0_11,plain,
( ~ member(y,universal_class)
| member(y,unordered_pair(y,Y)) ),
inference(subst,[],[unordered_pair2:[bind(X,$fot(y))]]) ).
cnf(refute_0_12,plain,
( unordered_pair(y,z) = singleton(z)
| member(y,universal_class) ),
inference(subst,[],[unordered_pair_equals_singleton2:[bind(X,$fot(y)),bind(Y,$fot(z))]]) ).
cnf(refute_0_13,plain,
( unordered_pair(y,z) != singleton(x)
| unordered_pair(y,z) != singleton(z)
| singleton(z) = singleton(x) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(y,z),singleton(x)) ),[0],$fot(singleton(z))]]) ).
cnf(refute_0_14,plain,
( unordered_pair(y,z) != singleton(x)
| singleton(z) = singleton(x)
| member(y,universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(y,z),singleton(z)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( singleton(z) = singleton(x)
| member(y,universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(y,z),singleton(x)) )],[prove_singleton_in_unordered_pair3_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( singleton(z) = singleton(x)
| member(y,unordered_pair(y,Y)) ),
inference(resolve,[$cnf( member(y,universal_class) )],[refute_0_15,refute_0_11]) ).
cnf(refute_0_17,plain,
( singleton(z) = singleton(x)
| member(y,unordered_pair(y,z)) ),
inference(subst,[],[refute_0_16:[bind(Y,$fot(z))]]) ).
cnf(refute_0_18,plain,
( unordered_pair(y,z) != singleton(x)
| ~ member(y,unordered_pair(y,z))
| member(y,singleton(x)) ),
introduced(tautology,[equality,[$cnf( member(y,unordered_pair(y,z)) ),[1],$fot(singleton(x))]]) ).
cnf(refute_0_19,plain,
( ~ member(y,unordered_pair(y,z))
| member(y,singleton(x)) ),
inference(resolve,[$cnf( $equal(unordered_pair(y,z),singleton(x)) )],[prove_singleton_in_unordered_pair3_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( singleton(z) = singleton(x)
| member(y,singleton(x)) ),
inference(resolve,[$cnf( member(y,unordered_pair(y,z)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( singleton(z) = singleton(x)
| y = x ),
inference(resolve,[$cnf( member(y,singleton(x)) )],[refute_0_20,refute_0_10]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( y != x
| x = y ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(y)),bind(Y0,$fot(x))]]) ).
cnf(refute_0_26,plain,
y != x,
inference(resolve,[$cnf( $equal(x,y) )],[refute_0_25,prove_singleton_in_unordered_pair3_3]) ).
cnf(refute_0_27,plain,
singleton(z) = singleton(x),
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
( singleton(z) != singleton(x)
| ~ member(z,singleton(z))
| member(z,singleton(x)) ),
introduced(tautology,[equality,[$cnf( member(z,singleton(z)) ),[1],$fot(singleton(x))]]) ).
cnf(refute_0_29,plain,
( ~ member(z,singleton(z))
| member(z,singleton(x)) ),
inference(resolve,[$cnf( $equal(singleton(z),singleton(x)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( singleton(z) = null_class
| member(z,singleton(x)) ),
inference(resolve,[$cnf( member(z,singleton(z)) )],[refute_0_9,refute_0_29]) ).
cnf(refute_0_31,plain,
( singleton(z) != null_class
| singleton(z) != singleton(x)
| singleton(x) = null_class ),
introduced(tautology,[equality,[$cnf( $equal(singleton(z),null_class) ),[0],$fot(singleton(x))]]) ).
cnf(refute_0_32,plain,
( singleton(z) != null_class
| singleton(x) = null_class ),
inference(resolve,[$cnf( $equal(singleton(z),singleton(x)) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( singleton(x) = null_class
| member(z,singleton(x)) ),
inference(resolve,[$cnf( $equal(singleton(z),null_class) )],[refute_0_30,refute_0_32]) ).
cnf(refute_0_34,plain,
( singleton(x) != null_class
| ~ member(x,universal_class) ),
inference(subst,[],[corollary_to_set_in_its_singleton:[bind(X,$fot(x))]]) ).
cnf(refute_0_35,plain,
singleton(x) != null_class,
inference(resolve,[$cnf( member(x,universal_class) )],[prove_singleton_in_unordered_pair3_2,refute_0_34]) ).
cnf(refute_0_36,plain,
member(z,singleton(x)),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_33,refute_0_35]) ).
cnf(refute_0_37,plain,
z = x,
inference(resolve,[$cnf( member(z,singleton(x)) )],[refute_0_36,refute_0_0]) ).
cnf(refute_0_38,plain,
( z != x
| x = z ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(z)),bind(Y0,$fot(x))]]) ).
cnf(refute_0_39,plain,
z != x,
inference(resolve,[$cnf( $equal(x,z) )],[refute_0_38,prove_singleton_in_unordered_pair3_4]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( $equal(z,x) )],[refute_0_37,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 06:33:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 169.50/169.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 169.50/169.68
% 169.50/169.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 169.50/169.68
%------------------------------------------------------------------------------