TSTP Solution File: SET104-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET104-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:32:42 EDT 2022
% Result : Unsatisfiable 20.38s 20.56s
% Output : CNFRefutation 20.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of clauses : 53 ( 26 unt; 7 nHn; 28 RR)
% Number of literals : 90 ( 81 equ; 33 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 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(unordered_pair_equals_singleton1,axiom,
( member(Y,universal_class)
| unordered_pair(X,Y) = singleton(X) ) ).
cnf(singleton_is_null_class,axiom,
( member(X,universal_class)
| singleton(X) = null_class ) ).
cnf(unordered_pairs_and_singletons,axiom,
unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ).
cnf(prove_property_2_of_ordered_pair_2,negated_conjecture,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y) ).
cnf(prove_property_2_of_ordered_pair_3,negated_conjecture,
~ member(x,universal_class) ).
cnf(refute_0_0,plain,
unordered_pair(singleton(X_63),unordered_pair(X_63,singleton(X_64))) = ordered_pair(X_63,X_64),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_63)),bind(Y,$fot(X_64))]]) ).
cnf(refute_0_1,plain,
unordered_pair(singleton(X_64),X_63) = unordered_pair(X_63,singleton(X_64)),
inference(subst,[],[commutativity_of_unordered_pair:[bind(X,$fot(singleton(X_64))),bind(Y,$fot(X_63))]]) ).
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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( unordered_pair(singleton(X_64),X_63) != unordered_pair(X_63,singleton(X_64))
| unordered_pair(X_63,singleton(X_64)) = unordered_pair(singleton(X_64),X_63) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(unordered_pair(singleton(X_64),X_63))),bind(Y0,$fot(unordered_pair(X_63,singleton(X_64))))]]) ).
cnf(refute_0_6,plain,
unordered_pair(X_63,singleton(X_64)) = unordered_pair(singleton(X_64),X_63),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_64),X_63),unordered_pair(X_63,singleton(X_64))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( unordered_pair(X_63,singleton(X_64)) != unordered_pair(singleton(X_64),X_63)
| unordered_pair(singleton(X_63),unordered_pair(X_63,singleton(X_64))) != ordered_pair(X_63,X_64)
| unordered_pair(singleton(X_63),unordered_pair(singleton(X_64),X_63)) = ordered_pair(X_63,X_64) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(X_63),unordered_pair(X_63,singleton(X_64))),ordered_pair(X_63,X_64)) ),[0,1],$fot(unordered_pair(singleton(X_64),X_63))]]) ).
cnf(refute_0_8,plain,
( unordered_pair(singleton(X_63),unordered_pair(X_63,singleton(X_64))) != ordered_pair(X_63,X_64)
| unordered_pair(singleton(X_63),unordered_pair(singleton(X_64),X_63)) = ordered_pair(X_63,X_64) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_63,singleton(X_64)),unordered_pair(singleton(X_64),X_63)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
unordered_pair(singleton(X_63),unordered_pair(singleton(X_64),X_63)) = ordered_pair(X_63,X_64),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_63),unordered_pair(X_63,singleton(X_64))),ordered_pair(X_63,X_64)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
unordered_pair(singleton(x),unordered_pair(singleton(X_64),x)) = ordered_pair(x,X_64),
inference(subst,[],[refute_0_9:[bind(X_63,$fot(x))]]) ).
cnf(refute_0_11,plain,
unordered_pair(X,x) = union(singleton(X),singleton(x)),
inference(subst,[],[unordered_pairs_and_singletons:[bind(Y,$fot(x))]]) ).
cnf(refute_0_12,plain,
( singleton(x) = null_class
| member(x,universal_class) ),
inference(subst,[],[singleton_is_null_class:[bind(X,$fot(x))]]) ).
cnf(refute_0_13,plain,
singleton(x) = null_class,
inference(resolve,[$cnf( member(x,universal_class) )],[refute_0_12,prove_property_2_of_ordered_pair_3]) ).
cnf(refute_0_14,plain,
( singleton(x) != null_class
| unordered_pair(X,x) != union(singleton(X),singleton(x))
| unordered_pair(X,x) = union(singleton(X),null_class) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(X,x),union(singleton(X),singleton(x))) ),[1,1],$fot(null_class)]]) ).
cnf(refute_0_15,plain,
( unordered_pair(X,x) != union(singleton(X),singleton(x))
| unordered_pair(X,x) = union(singleton(X),null_class) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
unordered_pair(X,x) = union(singleton(X),null_class),
inference(resolve,[$cnf( $equal(unordered_pair(X,x),union(singleton(X),singleton(x))) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( unordered_pair(X,x) = singleton(X)
| member(x,universal_class) ),
inference(subst,[],[unordered_pair_equals_singleton1:[bind(Y,$fot(x))]]) ).
cnf(refute_0_18,plain,
( unordered_pair(X,x) != singleton(X)
| unordered_pair(X,x) != union(singleton(X),null_class)
| singleton(X) = union(singleton(X),null_class) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(X,x),union(singleton(X),null_class)) ),[0],$fot(singleton(X))]]) ).
cnf(refute_0_19,plain,
( unordered_pair(X,x) != union(singleton(X),null_class)
| singleton(X) = union(singleton(X),null_class)
| member(x,universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(X,x),singleton(X)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( singleton(X) = union(singleton(X),null_class)
| member(x,universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(X,x),union(singleton(X),null_class)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( unordered_pair(X,x) != union(singleton(X),null_class)
| union(singleton(X),null_class) = unordered_pair(X,x) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(unordered_pair(X,x))),bind(Y0,$fot(union(singleton(X),null_class)))]]) ).
cnf(refute_0_22,plain,
union(singleton(X),null_class) = unordered_pair(X,x),
inference(resolve,[$cnf( $equal(unordered_pair(X,x),union(singleton(X),null_class)) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
( singleton(X) != union(singleton(X),null_class)
| union(singleton(X),null_class) != unordered_pair(X,x)
| singleton(X) = unordered_pair(X,x) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(X),unordered_pair(X,x)) ),[0],$fot(union(singleton(X),null_class))]]) ).
cnf(refute_0_24,plain,
( singleton(X) != union(singleton(X),null_class)
| singleton(X) = unordered_pair(X,x) ),
inference(resolve,[$cnf( $equal(union(singleton(X),null_class),unordered_pair(X,x)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( singleton(X) = unordered_pair(X,x)
| member(x,universal_class) ),
inference(resolve,[$cnf( $equal(singleton(X),union(singleton(X),null_class)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
singleton(X) = unordered_pair(X,x),
inference(resolve,[$cnf( member(x,universal_class) )],[refute_0_25,prove_property_2_of_ordered_pair_3]) ).
cnf(refute_0_27,plain,
singleton(singleton(X_64)) = unordered_pair(singleton(X_64),x),
inference(subst,[],[refute_0_26:[bind(X,$fot(singleton(X_64)))]]) ).
cnf(refute_0_28,plain,
( singleton(singleton(X_64)) != unordered_pair(singleton(X_64),x)
| unordered_pair(singleton(X_64),x) = singleton(singleton(X_64)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(singleton(singleton(X_64)))),bind(Y0,$fot(unordered_pair(singleton(X_64),x)))]]) ).
cnf(refute_0_29,plain,
unordered_pair(singleton(X_64),x) = singleton(singleton(X_64)),
inference(resolve,[$cnf( $equal(singleton(singleton(X_64)),unordered_pair(singleton(X_64),x)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( unordered_pair(singleton(X_64),x) != singleton(singleton(X_64))
| unordered_pair(singleton(x),unordered_pair(singleton(X_64),x)) != ordered_pair(x,X_64)
| unordered_pair(singleton(x),singleton(singleton(X_64))) = ordered_pair(x,X_64) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(singleton(X_64),x)),ordered_pair(x,X_64)) ),[0,1],$fot(singleton(singleton(X_64)))]]) ).
cnf(refute_0_31,plain,
( unordered_pair(singleton(x),unordered_pair(singleton(X_64),x)) != ordered_pair(x,X_64)
| unordered_pair(singleton(x),singleton(singleton(X_64))) = ordered_pair(x,X_64) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_64),x),singleton(singleton(X_64))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
unordered_pair(singleton(x),singleton(singleton(X_64))) = ordered_pair(x,X_64),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(singleton(X_64),x)),ordered_pair(x,X_64)) )],[refute_0_10,refute_0_31]) ).
cnf(refute_0_33,plain,
unordered_pair(singleton(x),singleton(singleton(X_64))) = unordered_pair(singleton(x),singleton(singleton(X_64))),
introduced(tautology,[refl,[$fot(unordered_pair(singleton(x),singleton(singleton(X_64))))]]) ).
cnf(refute_0_34,plain,
( singleton(x) != null_class
| unordered_pair(singleton(x),singleton(singleton(X_64))) != unordered_pair(singleton(x),singleton(singleton(X_64)))
| unordered_pair(singleton(x),singleton(singleton(X_64))) = unordered_pair(null_class,singleton(singleton(X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),singleton(singleton(X_64))),unordered_pair(singleton(x),singleton(singleton(X_64)))) ),[1,0],$fot(null_class)]]) ).
cnf(refute_0_35,plain,
( singleton(x) != null_class
| unordered_pair(singleton(x),singleton(singleton(X_64))) = unordered_pair(null_class,singleton(singleton(X_64))) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),singleton(singleton(X_64))),unordered_pair(singleton(x),singleton(singleton(X_64)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
unordered_pair(singleton(x),singleton(singleton(X_64))) = unordered_pair(null_class,singleton(singleton(X_64))),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_13,refute_0_35]) ).
cnf(refute_0_37,plain,
( unordered_pair(singleton(x),singleton(singleton(X_64))) != ordered_pair(x,X_64)
| unordered_pair(singleton(x),singleton(singleton(X_64))) != unordered_pair(null_class,singleton(singleton(X_64)))
| unordered_pair(null_class,singleton(singleton(X_64))) = ordered_pair(x,X_64) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),singleton(singleton(X_64))),ordered_pair(x,X_64)) ),[0],$fot(unordered_pair(null_class,singleton(singleton(X_64))))]]) ).
cnf(refute_0_38,plain,
( unordered_pair(singleton(x),singleton(singleton(X_64))) != ordered_pair(x,X_64)
| unordered_pair(null_class,singleton(singleton(X_64))) = ordered_pair(x,X_64) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),singleton(singleton(X_64))),unordered_pair(null_class,singleton(singleton(X_64)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
unordered_pair(null_class,singleton(singleton(X_64))) = ordered_pair(x,X_64),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),singleton(singleton(X_64))),ordered_pair(x,X_64)) )],[refute_0_32,refute_0_38]) ).
cnf(refute_0_40,plain,
unordered_pair(null_class,singleton(singleton(y))) = ordered_pair(x,y),
inference(subst,[],[refute_0_39:[bind(X_64,$fot(y))]]) ).
cnf(refute_0_41,plain,
( ordered_pair(x,y) != ordered_pair(x,y)
| unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y)
| unordered_pair(null_class,singleton(singleton(y))) = ordered_pair(x,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,singleton(singleton(y))),ordered_pair(x,y)) ),[1],$fot(ordered_pair(x,y))]]) ).
cnf(refute_0_42,plain,
( ordered_pair(x,y) != ordered_pair(x,y)
| unordered_pair(null_class,singleton(singleton(y))) = ordered_pair(x,y) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,singleton(singleton(y))),ordered_pair(x,y)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
ordered_pair(x,y) != ordered_pair(x,y),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,singleton(singleton(y))),ordered_pair(x,y)) )],[refute_0_42,prove_property_2_of_ordered_pair_2]) ).
cnf(refute_0_44,plain,
ordered_pair(x,y) = ordered_pair(x,y),
introduced(tautology,[refl,[$fot(ordered_pair(x,y))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( $equal(ordered_pair(x,y),ordered_pair(x,y)) )],[refute_0_44,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET104-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 18:18:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 20.38/20.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.38/20.56
% 20.38/20.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.38/20.56
%------------------------------------------------------------------------------