TSTP Solution File: SET105-7 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET105-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:32:43 EDT 2022
% Result : Unsatisfiable 22.56s 22.72s
% Output : CNFRefutation 22.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 43
% Syntax : Number of clauses : 139 ( 64 unt; 7 nHn; 105 RR)
% Number of literals : 247 ( 237 equ; 106 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ).
cnf(successor,axiom,
union(X,singleton(X)) = successor(X) ).
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_3_of_ordered_pair_1,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y) ).
cnf(prove_property_3_of_ordered_pair_2,negated_conjecture,
~ member(x,universal_class) ).
cnf(prove_property_3_of_ordered_pair_3,negated_conjecture,
~ member(y,universal_class) ).
cnf(refute_0_0,plain,
unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(x))) = ordered_pair(X_177,x),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_177)),bind(Y,$fot(x))]]) ).
cnf(refute_0_1,plain,
( singleton(x) = null_class
| member(x,universal_class) ),
inference(subst,[],[singleton_is_null_class:[bind(X,$fot(x))]]) ).
cnf(refute_0_2,plain,
singleton(x) = null_class,
inference(resolve,[$cnf( member(x,universal_class) )],[refute_0_1,prove_property_3_of_ordered_pair_2]) ).
cnf(refute_0_3,plain,
( singleton(x) != null_class
| unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(x))) != ordered_pair(X_177,x)
| unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) = ordered_pair(X_177,x) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(x))),ordered_pair(X_177,x)) ),[0,1,1],$fot(null_class)]]) ).
cnf(refute_0_4,plain,
( unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(x))) != ordered_pair(X_177,x)
| unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) = ordered_pair(X_177,x) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) = ordered_pair(X_177,x),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(x))),ordered_pair(X_177,x)) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
unordered_pair(singleton(y),unordered_pair(y,null_class)) = ordered_pair(y,x),
inference(subst,[],[refute_0_5:[bind(X_177,$fot(y))]]) ).
cnf(refute_0_7,plain,
unordered_pair(y,Y) = union(singleton(y),singleton(Y)),
inference(subst,[],[unordered_pairs_and_singletons:[bind(X,$fot(y))]]) ).
cnf(refute_0_8,plain,
( singleton(y) = null_class
| member(y,universal_class) ),
inference(subst,[],[singleton_is_null_class:[bind(X,$fot(y))]]) ).
cnf(refute_0_9,plain,
singleton(y) = null_class,
inference(resolve,[$cnf( member(y,universal_class) )],[refute_0_8,prove_property_3_of_ordered_pair_3]) ).
cnf(refute_0_10,plain,
( singleton(y) != null_class
| unordered_pair(y,Y) != union(singleton(y),singleton(Y))
| unordered_pair(y,Y) = union(null_class,singleton(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(y,Y),union(singleton(y),singleton(Y))) ),[1,0],$fot(null_class)]]) ).
cnf(refute_0_11,plain,
( unordered_pair(y,Y) != union(singleton(y),singleton(Y))
| unordered_pair(y,Y) = union(null_class,singleton(Y)) ),
inference(resolve,[$cnf( $equal(singleton(y),null_class) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
unordered_pair(y,Y) = union(null_class,singleton(Y)),
inference(resolve,[$cnf( $equal(unordered_pair(y,Y),union(singleton(y),singleton(Y))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
unordered_pair(x,Y) = union(singleton(x),singleton(Y)),
inference(subst,[],[unordered_pairs_and_singletons:[bind(X,$fot(x))]]) ).
cnf(refute_0_14,plain,
( singleton(x) != null_class
| unordered_pair(x,Y) != union(singleton(x),singleton(Y))
| unordered_pair(x,Y) = union(null_class,singleton(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(x,Y),union(singleton(x),singleton(Y))) ),[1,0],$fot(null_class)]]) ).
cnf(refute_0_15,plain,
( unordered_pair(x,Y) != union(singleton(x),singleton(Y))
| unordered_pair(x,Y) = union(null_class,singleton(Y)) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_2,refute_0_14]) ).
cnf(refute_0_16,plain,
unordered_pair(x,Y) = union(null_class,singleton(Y)),
inference(resolve,[$cnf( $equal(unordered_pair(x,Y),union(singleton(x),singleton(Y))) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( unordered_pair(x,Y) != union(null_class,singleton(Y))
| union(null_class,singleton(Y)) = unordered_pair(x,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(unordered_pair(x,Y))),bind(Y0,$fot(union(null_class,singleton(Y))))]]) ).
cnf(refute_0_21,plain,
union(null_class,singleton(Y)) = unordered_pair(x,Y),
inference(resolve,[$cnf( $equal(unordered_pair(x,Y),union(null_class,singleton(Y))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( union(null_class,singleton(Y)) != unordered_pair(x,Y)
| unordered_pair(y,Y) != union(null_class,singleton(Y))
| unordered_pair(y,Y) = unordered_pair(x,Y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(y,Y),union(null_class,singleton(Y))) ),[1],$fot(unordered_pair(x,Y))]]) ).
cnf(refute_0_23,plain,
( unordered_pair(y,Y) != union(null_class,singleton(Y))
| unordered_pair(y,Y) = unordered_pair(x,Y) ),
inference(resolve,[$cnf( $equal(union(null_class,singleton(Y)),unordered_pair(x,Y)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
unordered_pair(y,Y) = unordered_pair(x,Y),
inference(resolve,[$cnf( $equal(unordered_pair(y,Y),union(null_class,singleton(Y))) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
unordered_pair(y,null_class) = unordered_pair(x,null_class),
inference(subst,[],[refute_0_24:[bind(Y,$fot(null_class))]]) ).
cnf(refute_0_26,plain,
( unordered_pair(singleton(y),unordered_pair(y,null_class)) != ordered_pair(y,x)
| unordered_pair(y,null_class) != unordered_pair(x,null_class)
| unordered_pair(singleton(y),unordered_pair(x,null_class)) = ordered_pair(y,x) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(y,null_class)),ordered_pair(y,x)) ),[0,1],$fot(unordered_pair(x,null_class))]]) ).
cnf(refute_0_27,plain,
( unordered_pair(singleton(y),unordered_pair(y,null_class)) != ordered_pair(y,x)
| unordered_pair(singleton(y),unordered_pair(x,null_class)) = ordered_pair(y,x) ),
inference(resolve,[$cnf( $equal(unordered_pair(y,null_class),unordered_pair(x,null_class)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
unordered_pair(singleton(y),unordered_pair(x,null_class)) = ordered_pair(y,x),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(y,null_class)),ordered_pair(y,x)) )],[refute_0_6,refute_0_27]) ).
cnf(refute_0_29,plain,
union(singleton(X_60),singleton(singleton(X_60))) = successor(singleton(X_60)),
inference(subst,[],[successor:[bind(X,$fot(singleton(X_60)))]]) ).
cnf(refute_0_30,plain,
unordered_pair(X_60,singleton(X_60)) = union(singleton(X_60),singleton(singleton(X_60))),
inference(subst,[],[unordered_pairs_and_singletons:[bind(X,$fot(X_60)),bind(Y,$fot(singleton(X_60)))]]) ).
cnf(refute_0_31,plain,
( unordered_pair(X_60,singleton(X_60)) != union(singleton(X_60),singleton(singleton(X_60)))
| union(singleton(X_60),singleton(singleton(X_60))) = unordered_pair(X_60,singleton(X_60)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(unordered_pair(X_60,singleton(X_60)))),bind(Y0,$fot(union(singleton(X_60),singleton(singleton(X_60)))))]]) ).
cnf(refute_0_32,plain,
union(singleton(X_60),singleton(singleton(X_60))) = unordered_pair(X_60,singleton(X_60)),
inference(resolve,[$cnf( $equal(unordered_pair(X_60,singleton(X_60)),union(singleton(X_60),singleton(singleton(X_60)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( union(singleton(X_60),singleton(singleton(X_60))) != successor(singleton(X_60))
| union(singleton(X_60),singleton(singleton(X_60))) != unordered_pair(X_60,singleton(X_60))
| unordered_pair(X_60,singleton(X_60)) = successor(singleton(X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(union(singleton(X_60),singleton(singleton(X_60))),successor(singleton(X_60))) ),[0],$fot(unordered_pair(X_60,singleton(X_60)))]]) ).
cnf(refute_0_34,plain,
( union(singleton(X_60),singleton(singleton(X_60))) != successor(singleton(X_60))
| unordered_pair(X_60,singleton(X_60)) = successor(singleton(X_60)) ),
inference(resolve,[$cnf( $equal(union(singleton(X_60),singleton(singleton(X_60))),unordered_pair(X_60,singleton(X_60))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
unordered_pair(X_60,singleton(X_60)) = successor(singleton(X_60)),
inference(resolve,[$cnf( $equal(union(singleton(X_60),singleton(singleton(X_60))),successor(singleton(X_60))) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
unordered_pair(x,singleton(x)) = successor(singleton(x)),
inference(subst,[],[refute_0_35:[bind(X_60,$fot(x))]]) ).
cnf(refute_0_37,plain,
( singleton(x) != null_class
| unordered_pair(x,singleton(x)) != successor(singleton(x))
| unordered_pair(x,null_class) = successor(singleton(x)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(x,singleton(x)),successor(singleton(x))) ),[0,1],$fot(null_class)]]) ).
cnf(refute_0_38,plain,
( unordered_pair(x,singleton(x)) != successor(singleton(x))
| unordered_pair(x,null_class) = successor(singleton(x)) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_2,refute_0_37]) ).
cnf(refute_0_39,plain,
unordered_pair(x,null_class) = successor(singleton(x)),
inference(resolve,[$cnf( $equal(unordered_pair(x,singleton(x)),successor(singleton(x))) )],[refute_0_36,refute_0_38]) ).
cnf(refute_0_40,plain,
( unordered_pair(X,Y) != unordered_pair(Y,X)
| unordered_pair(Y,X) = unordered_pair(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(unordered_pair(X,Y))),bind(Y0,$fot(unordered_pair(Y,X)))]]) ).
cnf(refute_0_41,plain,
unordered_pair(Y,X) = unordered_pair(X,Y),
inference(resolve,[$cnf( $equal(unordered_pair(X,Y),unordered_pair(Y,X)) )],[commutativity_of_unordered_pair,refute_0_40]) ).
cnf(refute_0_42,plain,
unordered_pair(x,null_class) = unordered_pair(null_class,x),
inference(subst,[],[refute_0_41:[bind(X,$fot(null_class)),bind(Y,$fot(x))]]) ).
cnf(refute_0_43,plain,
( unordered_pair(x,null_class) != successor(singleton(x))
| unordered_pair(x,null_class) != unordered_pair(null_class,x)
| unordered_pair(null_class,x) = successor(singleton(x)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(x,null_class),successor(singleton(x))) ),[0],$fot(unordered_pair(null_class,x))]]) ).
cnf(refute_0_44,plain,
( unordered_pair(x,null_class) != successor(singleton(x))
| unordered_pair(null_class,x) = successor(singleton(x)) ),
inference(resolve,[$cnf( $equal(unordered_pair(x,null_class),unordered_pair(null_class,x)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
successor(singleton(x)) = successor(singleton(x)),
introduced(tautology,[refl,[$fot(successor(singleton(x)))]]) ).
cnf(refute_0_46,plain,
( singleton(x) != null_class
| successor(singleton(x)) != successor(singleton(x))
| successor(singleton(x)) = successor(null_class) ),
introduced(tautology,[equality,[$cnf( $equal(successor(singleton(x)),successor(singleton(x))) ),[1,0],$fot(null_class)]]) ).
cnf(refute_0_47,plain,
( singleton(x) != null_class
| successor(singleton(x)) = successor(null_class) ),
inference(resolve,[$cnf( $equal(successor(singleton(x)),successor(singleton(x))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
successor(singleton(x)) = successor(null_class),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_2,refute_0_47]) ).
cnf(refute_0_49,plain,
( successor(singleton(x)) != successor(null_class)
| unordered_pair(null_class,x) != successor(singleton(x))
| unordered_pair(null_class,x) = successor(null_class) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,x),successor(singleton(x))) ),[1],$fot(successor(null_class))]]) ).
cnf(refute_0_50,plain,
( unordered_pair(null_class,x) != successor(singleton(x))
| unordered_pair(null_class,x) = successor(null_class) ),
inference(resolve,[$cnf( $equal(successor(singleton(x)),successor(null_class)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( unordered_pair(x,null_class) != successor(singleton(x))
| unordered_pair(null_class,x) = successor(null_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,x),successor(singleton(x))) )],[refute_0_44,refute_0_50]) ).
cnf(refute_0_52,plain,
unordered_pair(null_class,x) = successor(null_class),
inference(resolve,[$cnf( $equal(unordered_pair(x,null_class),successor(singleton(x))) )],[refute_0_39,refute_0_51]) ).
cnf(refute_0_53,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_53]) ).
cnf(refute_0_55,plain,
( unordered_pair(null_class,x) != successor(null_class)
| unordered_pair(x,null_class) != unordered_pair(null_class,x)
| unordered_pair(x,null_class) = successor(null_class) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(unordered_pair(x,null_class))),bind(Y0,$fot(unordered_pair(null_class,x))),bind(Z,$fot(successor(null_class)))]]) ).
cnf(refute_0_56,plain,
( unordered_pair(null_class,x) != successor(null_class)
| unordered_pair(x,null_class) = successor(null_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(x,null_class),unordered_pair(null_class,x)) )],[refute_0_42,refute_0_55]) ).
cnf(refute_0_57,plain,
unordered_pair(x,null_class) = successor(null_class),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,x),successor(null_class)) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
unordered_pair(null_class,unordered_pair(x,null_class)) = unordered_pair(null_class,unordered_pair(x,null_class)),
introduced(tautology,[refl,[$fot(unordered_pair(null_class,unordered_pair(x,null_class)))]]) ).
cnf(refute_0_59,plain,
( unordered_pair(null_class,unordered_pair(x,null_class)) != unordered_pair(null_class,unordered_pair(x,null_class))
| unordered_pair(x,null_class) != successor(null_class)
| unordered_pair(null_class,unordered_pair(x,null_class)) = unordered_pair(null_class,successor(null_class)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,unordered_pair(x,null_class)),unordered_pair(null_class,unordered_pair(x,null_class))) ),[1,1],$fot(successor(null_class))]]) ).
cnf(refute_0_60,plain,
( unordered_pair(x,null_class) != successor(null_class)
| unordered_pair(null_class,unordered_pair(x,null_class)) = unordered_pair(null_class,successor(null_class)) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,unordered_pair(x,null_class)),unordered_pair(null_class,unordered_pair(x,null_class))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
unordered_pair(null_class,unordered_pair(x,null_class)) = unordered_pair(null_class,successor(null_class)),
inference(resolve,[$cnf( $equal(unordered_pair(x,null_class),successor(null_class)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(singleton(y),unordered_pair(x,null_class)),
introduced(tautology,[refl,[$fot(unordered_pair(singleton(y),unordered_pair(x,null_class)))]]) ).
cnf(refute_0_63,plain,
( singleton(y) != null_class
| unordered_pair(singleton(y),unordered_pair(x,null_class)) != unordered_pair(singleton(y),unordered_pair(x,null_class))
| unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(null_class,unordered_pair(x,null_class)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,null_class)),unordered_pair(singleton(y),unordered_pair(x,null_class))) ),[1,0],$fot(null_class)]]) ).
cnf(refute_0_64,plain,
( singleton(y) != null_class
| unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(null_class,unordered_pair(x,null_class)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,null_class)),unordered_pair(singleton(y),unordered_pair(x,null_class))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(null_class,unordered_pair(x,null_class)),
inference(resolve,[$cnf( $equal(singleton(y),null_class) )],[refute_0_9,refute_0_64]) ).
cnf(refute_0_66,plain,
( unordered_pair(null_class,unordered_pair(x,null_class)) != unordered_pair(null_class,successor(null_class))
| unordered_pair(singleton(y),unordered_pair(x,null_class)) != unordered_pair(null_class,unordered_pair(x,null_class))
| unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(null_class,successor(null_class)) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(unordered_pair(singleton(y),unordered_pair(x,null_class)))),bind(Y0,$fot(unordered_pair(null_class,unordered_pair(x,null_class)))),bind(Z,$fot(unordered_pair(null_class,successor(null_class))))]]) ).
cnf(refute_0_67,plain,
( unordered_pair(null_class,unordered_pair(x,null_class)) != unordered_pair(null_class,successor(null_class))
| unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(null_class,successor(null_class)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,null_class)),unordered_pair(null_class,unordered_pair(x,null_class))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
unordered_pair(singleton(y),unordered_pair(x,null_class)) = unordered_pair(null_class,successor(null_class)),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,unordered_pair(x,null_class)),unordered_pair(null_class,successor(null_class))) )],[refute_0_61,refute_0_67]) ).
cnf(refute_0_69,plain,
( unordered_pair(singleton(y),unordered_pair(x,null_class)) != ordered_pair(y,x)
| unordered_pair(singleton(y),unordered_pair(x,null_class)) != unordered_pair(null_class,successor(null_class))
| unordered_pair(null_class,successor(null_class)) = ordered_pair(y,x) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,null_class)),ordered_pair(y,x)) ),[0],$fot(unordered_pair(null_class,successor(null_class)))]]) ).
cnf(refute_0_70,plain,
( unordered_pair(singleton(y),unordered_pair(x,null_class)) != ordered_pair(y,x)
| unordered_pair(null_class,successor(null_class)) = ordered_pair(y,x) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,null_class)),unordered_pair(null_class,successor(null_class))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
unordered_pair(singleton(x),unordered_pair(x,singleton(X_178))) = ordered_pair(x,X_178),
inference(subst,[],[ordered_pair:[bind(X,$fot(x)),bind(Y,$fot(X_178))]]) ).
cnf(refute_0_72,plain,
( singleton(x) != null_class
| unordered_pair(singleton(x),unordered_pair(x,singleton(X_178))) != ordered_pair(x,X_178)
| unordered_pair(null_class,unordered_pair(x,singleton(X_178))) = ordered_pair(x,X_178) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,singleton(X_178))),ordered_pair(x,X_178)) ),[0,0],$fot(null_class)]]) ).
cnf(refute_0_73,plain,
( unordered_pair(singleton(x),unordered_pair(x,singleton(X_178))) != ordered_pair(x,X_178)
| unordered_pair(null_class,unordered_pair(x,singleton(X_178))) = ordered_pair(x,X_178) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_2,refute_0_72]) ).
cnf(refute_0_74,plain,
unordered_pair(null_class,unordered_pair(x,singleton(X_178))) = ordered_pair(x,X_178),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,singleton(X_178))),ordered_pair(x,X_178)) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
unordered_pair(singleton(y),unordered_pair(y,singleton(X_178))) = ordered_pair(y,X_178),
inference(subst,[],[ordered_pair:[bind(X,$fot(y)),bind(Y,$fot(X_178))]]) ).
cnf(refute_0_76,plain,
unordered_pair(y,singleton(X_178)) = unordered_pair(x,singleton(X_178)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(singleton(X_178)))]]) ).
cnf(refute_0_77,plain,
( unordered_pair(singleton(y),unordered_pair(y,singleton(X_178))) != ordered_pair(y,X_178)
| unordered_pair(y,singleton(X_178)) != unordered_pair(x,singleton(X_178))
| unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = ordered_pair(y,X_178) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(y,singleton(X_178))),ordered_pair(y,X_178)) ),[0,1],$fot(unordered_pair(x,singleton(X_178)))]]) ).
cnf(refute_0_78,plain,
( unordered_pair(singleton(y),unordered_pair(y,singleton(X_178))) != ordered_pair(y,X_178)
| unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = ordered_pair(y,X_178) ),
inference(resolve,[$cnf( $equal(unordered_pair(y,singleton(X_178)),unordered_pair(x,singleton(X_178))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = ordered_pair(y,X_178),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(y,singleton(X_178))),ordered_pair(y,X_178)) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))),
introduced(tautology,[refl,[$fot(unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))))]]) ).
cnf(refute_0_81,plain,
( singleton(y) != null_class
| unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) != unordered_pair(singleton(y),unordered_pair(x,singleton(X_178)))
| unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = unordered_pair(null_class,unordered_pair(x,singleton(X_178))) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))),unordered_pair(singleton(y),unordered_pair(x,singleton(X_178)))) ),[1,0],$fot(null_class)]]) ).
cnf(refute_0_82,plain,
( singleton(y) != null_class
| unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = unordered_pair(null_class,unordered_pair(x,singleton(X_178))) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))),unordered_pair(singleton(y),unordered_pair(x,singleton(X_178)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) = unordered_pair(null_class,unordered_pair(x,singleton(X_178))),
inference(resolve,[$cnf( $equal(singleton(y),null_class) )],[refute_0_9,refute_0_82]) ).
cnf(refute_0_84,plain,
( unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) != ordered_pair(y,X_178)
| unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) != unordered_pair(null_class,unordered_pair(x,singleton(X_178)))
| unordered_pair(null_class,unordered_pair(x,singleton(X_178))) = ordered_pair(y,X_178) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))),ordered_pair(y,X_178)) ),[0],$fot(unordered_pair(null_class,unordered_pair(x,singleton(X_178))))]]) ).
cnf(refute_0_85,plain,
( unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))) != ordered_pair(y,X_178)
| unordered_pair(null_class,unordered_pair(x,singleton(X_178))) = ordered_pair(y,X_178) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))),unordered_pair(null_class,unordered_pair(x,singleton(X_178)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
unordered_pair(null_class,unordered_pair(x,singleton(X_178))) = ordered_pair(y,X_178),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,singleton(X_178))),ordered_pair(y,X_178)) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
( unordered_pair(null_class,unordered_pair(x,singleton(X_178))) != ordered_pair(x,X_178)
| unordered_pair(null_class,unordered_pair(x,singleton(X_178))) != ordered_pair(y,X_178)
| ordered_pair(y,X_178) = ordered_pair(x,X_178) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,unordered_pair(x,singleton(X_178))),ordered_pair(x,X_178)) ),[0],$fot(ordered_pair(y,X_178))]]) ).
cnf(refute_0_88,plain,
( unordered_pair(null_class,unordered_pair(x,singleton(X_178))) != ordered_pair(x,X_178)
| ordered_pair(y,X_178) = ordered_pair(x,X_178) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,unordered_pair(x,singleton(X_178))),ordered_pair(y,X_178)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
ordered_pair(y,X_178) = ordered_pair(x,X_178),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,unordered_pair(x,singleton(X_178))),ordered_pair(x,X_178)) )],[refute_0_74,refute_0_88]) ).
cnf(refute_0_90,plain,
ordered_pair(y,x) = ordered_pair(x,x),
inference(subst,[],[refute_0_89:[bind(X_178,$fot(x))]]) ).
cnf(refute_0_91,plain,
( ordered_pair(y,x) != ordered_pair(x,x)
| unordered_pair(null_class,successor(null_class)) != ordered_pair(y,x)
| unordered_pair(null_class,successor(null_class)) = ordered_pair(x,x) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),ordered_pair(y,x)) ),[1],$fot(ordered_pair(x,x))]]) ).
cnf(refute_0_92,plain,
( unordered_pair(null_class,successor(null_class)) != ordered_pair(y,x)
| unordered_pair(null_class,successor(null_class)) = ordered_pair(x,x) ),
inference(resolve,[$cnf( $equal(ordered_pair(y,x),ordered_pair(x,x)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( unordered_pair(singleton(y),unordered_pair(x,null_class)) != ordered_pair(y,x)
| unordered_pair(null_class,successor(null_class)) = ordered_pair(x,x) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),ordered_pair(y,x)) )],[refute_0_70,refute_0_92]) ).
cnf(refute_0_94,plain,
unordered_pair(null_class,successor(null_class)) = ordered_pair(x,x),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(y),unordered_pair(x,null_class)),ordered_pair(y,x)) )],[refute_0_28,refute_0_93]) ).
cnf(refute_0_95,plain,
unordered_pair(null_class,singleton(null_class)) = successor(singleton(null_class)),
inference(subst,[],[refute_0_35:[bind(X_60,$fot(null_class))]]) ).
cnf(refute_0_96,plain,
( unordered_pair(null_class,x) = singleton(null_class)
| member(x,universal_class) ),
inference(subst,[],[unordered_pair_equals_singleton1:[bind(X,$fot(null_class)),bind(Y,$fot(x))]]) ).
cnf(refute_0_97,plain,
( unordered_pair(null_class,x) != singleton(null_class)
| unordered_pair(null_class,x) != successor(null_class)
| singleton(null_class) = successor(null_class) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,x),successor(null_class)) ),[0],$fot(singleton(null_class))]]) ).
cnf(refute_0_98,plain,
( unordered_pair(null_class,x) != successor(null_class)
| singleton(null_class) = successor(null_class)
| member(x,universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,x),singleton(null_class)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( singleton(null_class) = successor(null_class)
| member(x,universal_class) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,x),successor(null_class)) )],[refute_0_52,refute_0_98]) ).
cnf(refute_0_100,plain,
singleton(null_class) = successor(null_class),
inference(resolve,[$cnf( member(x,universal_class) )],[refute_0_99,prove_property_3_of_ordered_pair_2]) ).
cnf(refute_0_101,plain,
( singleton(null_class) != successor(null_class)
| successor(null_class) = singleton(null_class) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(singleton(null_class))),bind(Y0,$fot(successor(null_class)))]]) ).
cnf(refute_0_102,plain,
successor(null_class) = singleton(null_class),
inference(resolve,[$cnf( $equal(singleton(null_class),successor(null_class)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
unordered_pair(null_class,successor(null_class)) = unordered_pair(null_class,successor(null_class)),
introduced(tautology,[refl,[$fot(unordered_pair(null_class,successor(null_class)))]]) ).
cnf(refute_0_104,plain,
( successor(null_class) != singleton(null_class)
| unordered_pair(null_class,successor(null_class)) != unordered_pair(null_class,successor(null_class))
| unordered_pair(null_class,successor(null_class)) = unordered_pair(null_class,singleton(null_class)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),unordered_pair(null_class,successor(null_class))) ),[1,1],$fot(singleton(null_class))]]) ).
cnf(refute_0_105,plain,
( successor(null_class) != singleton(null_class)
| unordered_pair(null_class,successor(null_class)) = unordered_pair(null_class,singleton(null_class)) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),unordered_pair(null_class,successor(null_class))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
unordered_pair(null_class,successor(null_class)) = unordered_pair(null_class,singleton(null_class)),
inference(resolve,[$cnf( $equal(successor(null_class),singleton(null_class)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( unordered_pair(null_class,singleton(null_class)) != successor(singleton(null_class))
| unordered_pair(null_class,successor(null_class)) != unordered_pair(null_class,singleton(null_class))
| unordered_pair(null_class,successor(null_class)) = successor(singleton(null_class)) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(unordered_pair(null_class,successor(null_class)))),bind(Y0,$fot(unordered_pair(null_class,singleton(null_class)))),bind(Z,$fot(successor(singleton(null_class))))]]) ).
cnf(refute_0_108,plain,
( unordered_pair(null_class,singleton(null_class)) != successor(singleton(null_class))
| unordered_pair(null_class,successor(null_class)) = successor(singleton(null_class)) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),unordered_pair(null_class,singleton(null_class))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
unordered_pair(null_class,successor(null_class)) = successor(singleton(null_class)),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,singleton(null_class)),successor(singleton(null_class))) )],[refute_0_95,refute_0_108]) ).
cnf(refute_0_110,plain,
( unordered_pair(null_class,successor(null_class)) != ordered_pair(x,x)
| unordered_pair(null_class,successor(null_class)) != successor(singleton(null_class))
| successor(singleton(null_class)) = ordered_pair(x,x) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),ordered_pair(x,x)) ),[0],$fot(successor(singleton(null_class)))]]) ).
cnf(refute_0_111,plain,
( unordered_pair(null_class,successor(null_class)) != ordered_pair(x,x)
| successor(singleton(null_class)) = ordered_pair(x,x) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),successor(singleton(null_class))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
successor(singleton(null_class)) = ordered_pair(x,x),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,successor(null_class)),ordered_pair(x,x)) )],[refute_0_94,refute_0_111]) ).
cnf(refute_0_113,plain,
( successor(singleton(null_class)) != ordered_pair(x,y)
| unordered_pair(null_class,singleton(null_class)) != successor(singleton(null_class))
| unordered_pair(null_class,singleton(null_class)) = ordered_pair(x,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(null_class,singleton(null_class)),successor(singleton(null_class))) ),[1],$fot(ordered_pair(x,y))]]) ).
cnf(refute_0_114,plain,
( successor(singleton(null_class)) != ordered_pair(x,y)
| unordered_pair(null_class,singleton(null_class)) = ordered_pair(x,y) ),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,singleton(null_class)),successor(singleton(null_class))) )],[refute_0_95,refute_0_113]) ).
cnf(refute_0_115,plain,
successor(singleton(null_class)) != ordered_pair(x,y),
inference(resolve,[$cnf( $equal(unordered_pair(null_class,singleton(null_class)),ordered_pair(x,y)) )],[refute_0_114,prove_property_3_of_ordered_pair_1]) ).
cnf(refute_0_116,plain,
unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(y))) = ordered_pair(X_177,y),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_177)),bind(Y,$fot(y))]]) ).
cnf(refute_0_117,plain,
( singleton(y) != null_class
| unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(y))) != ordered_pair(X_177,y)
| unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) = ordered_pair(X_177,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(y))),ordered_pair(X_177,y)) ),[0,1,1],$fot(null_class)]]) ).
cnf(refute_0_118,plain,
( unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(y))) != ordered_pair(X_177,y)
| unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) = ordered_pair(X_177,y) ),
inference(resolve,[$cnf( $equal(singleton(y),null_class) )],[refute_0_9,refute_0_117]) ).
cnf(refute_0_119,plain,
unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) = ordered_pair(X_177,y),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,singleton(y))),ordered_pair(X_177,y)) )],[refute_0_116,refute_0_118]) ).
cnf(refute_0_120,plain,
( unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) != ordered_pair(X_177,x)
| unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) != ordered_pair(X_177,y)
| ordered_pair(X_177,x) = ordered_pair(X_177,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)),ordered_pair(X_177,y)) ),[0],$fot(ordered_pair(X_177,x))]]) ).
cnf(refute_0_121,plain,
( unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)) != ordered_pair(X_177,y)
| ordered_pair(X_177,x) = ordered_pair(X_177,y) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)),ordered_pair(X_177,x)) )],[refute_0_5,refute_0_120]) ).
cnf(refute_0_122,plain,
ordered_pair(X_177,x) = ordered_pair(X_177,y),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_177),unordered_pair(X_177,null_class)),ordered_pair(X_177,y)) )],[refute_0_119,refute_0_121]) ).
cnf(refute_0_123,plain,
( ordered_pair(X_177,x) != ordered_pair(X_177,y)
| ordered_pair(X_177,y) = ordered_pair(X_177,x) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(ordered_pair(X_177,x))),bind(Y0,$fot(ordered_pair(X_177,y)))]]) ).
cnf(refute_0_124,plain,
ordered_pair(X_177,y) = ordered_pair(X_177,x),
inference(resolve,[$cnf( $equal(ordered_pair(X_177,x),ordered_pair(X_177,y)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
ordered_pair(x,y) = ordered_pair(x,x),
inference(subst,[],[refute_0_124:[bind(X_177,$fot(x))]]) ).
cnf(refute_0_126,plain,
( ordered_pair(x,y) != ordered_pair(x,x)
| successor(singleton(null_class)) != ordered_pair(x,x)
| successor(singleton(null_class)) = ordered_pair(x,y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(successor(singleton(null_class)),ordered_pair(x,y)) ),[1],$fot(ordered_pair(x,x))]]) ).
cnf(refute_0_127,plain,
( successor(singleton(null_class)) != ordered_pair(x,x)
| successor(singleton(null_class)) = ordered_pair(x,y) ),
inference(resolve,[$cnf( $equal(ordered_pair(x,y),ordered_pair(x,x)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
successor(singleton(null_class)) != ordered_pair(x,x),
inference(resolve,[$cnf( $equal(successor(singleton(null_class)),ordered_pair(x,y)) )],[refute_0_127,refute_0_115]) ).
cnf(refute_0_129,plain,
$false,
inference(resolve,[$cnf( $equal(successor(singleton(null_class)),ordered_pair(x,x)) )],[refute_0_112,refute_0_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET105-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 11 09:28:03 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 22.56/22.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.56/22.72
% 22.56/22.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.56/22.72
%------------------------------------------------------------------------------