TSTP Solution File: SET103-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET103-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 03:32:41 EDT 2022
% Result : Unsatisfiable 0.60s 0.77s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of clauses : 37 ( 21 unt; 2 nHn; 26 RR)
% Number of literals : 59 ( 55 equ; 24 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 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(singleton_is_null_class,axiom,
( member(X,universal_class)
| singleton(X) = null_class ) ).
cnf(prove_property_1_of_ordered_pair_1,negated_conjecture,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y) ).
cnf(prove_property_1_of_ordered_pair_2,negated_conjecture,
~ member(y,universal_class) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( unordered_pair(X,Y) != unordered_pair(Y,X)
| unordered_pair(Y,X) = unordered_pair(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(unordered_pair(X,Y))),bind(Y0,$fot(unordered_pair(Y,X)))]]) ).
cnf(refute_0_4,plain,
unordered_pair(Y,X) = unordered_pair(X,Y),
inference(resolve,[$cnf( $equal(unordered_pair(X,Y),unordered_pair(Y,X)) )],[commutativity_of_unordered_pair,refute_0_3]) ).
cnf(refute_0_5,plain,
unordered_pair(x,null_class) = unordered_pair(null_class,x),
inference(subst,[],[refute_0_4:[bind(X,$fot(null_class)),bind(Y,$fot(x))]]) ).
cnf(refute_0_6,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) = unordered_pair(singleton(x),unordered_pair(x,null_class)),
introduced(tautology,[refl,[$fot(unordered_pair(singleton(x),unordered_pair(x,null_class)))]]) ).
cnf(refute_0_7,plain,
( unordered_pair(singleton(x),unordered_pair(x,null_class)) != unordered_pair(singleton(x),unordered_pair(x,null_class))
| unordered_pair(x,null_class) != unordered_pair(null_class,x)
| unordered_pair(singleton(x),unordered_pair(x,null_class)) = unordered_pair(singleton(x),unordered_pair(null_class,x)) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,null_class)),unordered_pair(singleton(x),unordered_pair(x,null_class))) ),[1,1],$fot(unordered_pair(null_class,x))]]) ).
cnf(refute_0_8,plain,
( unordered_pair(x,null_class) != unordered_pair(null_class,x)
| unordered_pair(singleton(x),unordered_pair(x,null_class)) = unordered_pair(singleton(x),unordered_pair(null_class,x)) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,null_class)),unordered_pair(singleton(x),unordered_pair(x,null_class))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) = unordered_pair(singleton(x),unordered_pair(null_class,x)),
inference(resolve,[$cnf( $equal(unordered_pair(x,null_class),unordered_pair(null_class,x)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( unordered_pair(singleton(x),unordered_pair(null_class,x)) != ordered_pair(x,y)
| unordered_pair(singleton(x),unordered_pair(x,null_class)) != unordered_pair(singleton(x),unordered_pair(null_class,x))
| unordered_pair(singleton(x),unordered_pair(x,null_class)) = ordered_pair(x,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,null_class)),unordered_pair(singleton(x),unordered_pair(null_class,x))) ),[1],$fot(ordered_pair(x,y))]]) ).
cnf(refute_0_11,plain,
( unordered_pair(singleton(x),unordered_pair(null_class,x)) != ordered_pair(x,y)
| unordered_pair(singleton(x),unordered_pair(x,null_class)) = ordered_pair(x,y) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,null_class)),unordered_pair(singleton(x),unordered_pair(null_class,x))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
unordered_pair(singleton(x),unordered_pair(null_class,x)) != ordered_pair(x,y),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(x,null_class)),ordered_pair(x,y)) )],[refute_0_11,prove_property_1_of_ordered_pair_1]) ).
cnf(refute_0_13,plain,
unordered_pair(singleton(X_66),unordered_pair(X_66,singleton(X_67))) = ordered_pair(X_66,X_67),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_66)),bind(Y,$fot(X_67))]]) ).
cnf(refute_0_14,plain,
unordered_pair(singleton(X_67),X_66) = unordered_pair(X_66,singleton(X_67)),
inference(subst,[],[commutativity_of_unordered_pair:[bind(X,$fot(singleton(X_67))),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_15,plain,
( unordered_pair(singleton(X_67),X_66) != unordered_pair(X_66,singleton(X_67))
| unordered_pair(X_66,singleton(X_67)) = unordered_pair(singleton(X_67),X_66) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(unordered_pair(singleton(X_67),X_66))),bind(Y0,$fot(unordered_pair(X_66,singleton(X_67))))]]) ).
cnf(refute_0_16,plain,
unordered_pair(X_66,singleton(X_67)) = unordered_pair(singleton(X_67),X_66),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_67),X_66),unordered_pair(X_66,singleton(X_67))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( unordered_pair(X_66,singleton(X_67)) != unordered_pair(singleton(X_67),X_66)
| unordered_pair(singleton(X_66),unordered_pair(X_66,singleton(X_67))) != ordered_pair(X_66,X_67)
| unordered_pair(singleton(X_66),unordered_pair(singleton(X_67),X_66)) = ordered_pair(X_66,X_67) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(X_66),unordered_pair(X_66,singleton(X_67))),ordered_pair(X_66,X_67)) ),[0,1],$fot(unordered_pair(singleton(X_67),X_66))]]) ).
cnf(refute_0_18,plain,
( unordered_pair(singleton(X_66),unordered_pair(X_66,singleton(X_67))) != ordered_pair(X_66,X_67)
| unordered_pair(singleton(X_66),unordered_pair(singleton(X_67),X_66)) = ordered_pair(X_66,X_67) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_66,singleton(X_67)),unordered_pair(singleton(X_67),X_66)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
unordered_pair(singleton(X_66),unordered_pair(singleton(X_67),X_66)) = ordered_pair(X_66,X_67),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_66),unordered_pair(X_66,singleton(X_67))),ordered_pair(X_66,X_67)) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
unordered_pair(singleton(X_66),unordered_pair(singleton(y),X_66)) = ordered_pair(X_66,y),
inference(subst,[],[refute_0_19:[bind(X_67,$fot(y))]]) ).
cnf(refute_0_21,plain,
( singleton(y) = null_class
| member(y,universal_class) ),
inference(subst,[],[singleton_is_null_class:[bind(X,$fot(y))]]) ).
cnf(refute_0_22,plain,
singleton(y) = null_class,
inference(resolve,[$cnf( member(y,universal_class) )],[refute_0_21,prove_property_1_of_ordered_pair_2]) ).
cnf(refute_0_23,plain,
( singleton(y) != null_class
| unordered_pair(singleton(X_66),unordered_pair(singleton(y),X_66)) != ordered_pair(X_66,y)
| unordered_pair(singleton(X_66),unordered_pair(null_class,X_66)) = ordered_pair(X_66,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(X_66),unordered_pair(singleton(y),X_66)),ordered_pair(X_66,y)) ),[0,1,0],$fot(null_class)]]) ).
cnf(refute_0_24,plain,
( unordered_pair(singleton(X_66),unordered_pair(singleton(y),X_66)) != ordered_pair(X_66,y)
| unordered_pair(singleton(X_66),unordered_pair(null_class,X_66)) = ordered_pair(X_66,y) ),
inference(resolve,[$cnf( $equal(singleton(y),null_class) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
unordered_pair(singleton(X_66),unordered_pair(null_class,X_66)) = ordered_pair(X_66,y),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_66),unordered_pair(singleton(y),X_66)),ordered_pair(X_66,y)) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
unordered_pair(singleton(x),unordered_pair(null_class,x)) = ordered_pair(x,y),
inference(subst,[],[refute_0_25:[bind(X_66,$fot(x))]]) ).
cnf(refute_0_27,plain,
( ordered_pair(x,y) != ordered_pair(x,y)
| unordered_pair(singleton(x),unordered_pair(null_class,x)) != ordered_pair(x,y)
| unordered_pair(singleton(x),unordered_pair(null_class,x)) = ordered_pair(x,y) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(null_class,x)),ordered_pair(x,y)) ),[1],$fot(ordered_pair(x,y))]]) ).
cnf(refute_0_28,plain,
( ordered_pair(x,y) != ordered_pair(x,y)
| unordered_pair(singleton(x),unordered_pair(null_class,x)) = ordered_pair(x,y) ),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(null_class,x)),ordered_pair(x,y)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
ordered_pair(x,y) != ordered_pair(x,y),
inference(resolve,[$cnf( $equal(unordered_pair(singleton(x),unordered_pair(null_class,x)),ordered_pair(x,y)) )],[refute_0_28,refute_0_12]) ).
cnf(refute_0_30,plain,
ordered_pair(x,y) = ordered_pair(x,y),
introduced(tautology,[refl,[$fot(ordered_pair(x,y))]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( $equal(ordered_pair(x,y),ordered_pair(x,y)) )],[refute_0_30,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET103-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.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 : Mon Jul 11 09:20:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.77
% 0.60/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.77
%------------------------------------------------------------------------------