TSTP Solution File: SET083-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET083-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 03:32:22 EDT 2022
% Result : Unsatisfiable 1.05s 1.22s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 10 unt; 8 nHn; 28 RR)
% Number of literals : 58 ( 50 equ; 23 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 : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(regularity1,axiom,
( X = null_class
| member(regular(X),X) ) ).
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_identified_by_element1_1,negated_conjecture,
singleton(x) = singleton(y) ).
cnf(prove_singleton_identified_by_element1_2,negated_conjecture,
member(x,universal_class) ).
cnf(prove_singleton_identified_by_element1_3,negated_conjecture,
x != y ).
cnf(refute_0_0,plain,
( singleton(X_102) = null_class
| member(regular(singleton(X_102)),singleton(X_102)) ),
inference(subst,[],[regularity1:[bind(X,$fot(singleton(X_102)))]]) ).
cnf(refute_0_1,plain,
( ~ member(regular(singleton(X_102)),singleton(X_102))
| regular(singleton(X_102)) = X_102 ),
inference(subst,[],[only_member_in_singleton:[bind(X,$fot(X_102)),bind(Y,$fot(regular(singleton(X_102))))]]) ).
cnf(refute_0_2,plain,
( regular(singleton(X_102)) = X_102
| singleton(X_102) = null_class ),
inference(resolve,[$cnf( member(regular(singleton(X_102)),singleton(X_102)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( regular(singleton(x)) = x
| singleton(x) = null_class ),
inference(subst,[],[refute_0_2:[bind(X_102,$fot(x))]]) ).
cnf(refute_0_4,plain,
( regular(singleton(y)) = y
| singleton(y) = null_class ),
inference(subst,[],[refute_0_2:[bind(X_102,$fot(y))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( singleton(x) != singleton(y)
| singleton(y) = singleton(x) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(singleton(x))),bind(Y0,$fot(singleton(y)))]]) ).
cnf(refute_0_9,plain,
singleton(y) = singleton(x),
inference(resolve,[$cnf( $equal(singleton(x),singleton(y)) )],[prove_singleton_identified_by_element1_1,refute_0_8]) ).
cnf(refute_0_10,plain,
( regular(singleton(y)) != y
| singleton(y) != singleton(x)
| regular(singleton(x)) = y ),
introduced(tautology,[equality,[$cnf( $equal(regular(singleton(y)),y) ),[0,0],$fot(singleton(x))]]) ).
cnf(refute_0_11,plain,
( regular(singleton(y)) != y
| regular(singleton(x)) = y ),
inference(resolve,[$cnf( $equal(singleton(y),singleton(x)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( regular(singleton(x)) = y
| singleton(y) = null_class ),
inference(resolve,[$cnf( $equal(regular(singleton(y)),y) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
( singleton(y) != null_class
| singleton(y) != singleton(x)
| singleton(x) = null_class ),
introduced(tautology,[equality,[$cnf( $equal(singleton(y),null_class) ),[0],$fot(singleton(x))]]) ).
cnf(refute_0_14,plain,
( singleton(y) != null_class
| singleton(x) = null_class ),
inference(resolve,[$cnf( $equal(singleton(y),singleton(x)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( regular(singleton(x)) = y
| singleton(x) = null_class ),
inference(resolve,[$cnf( $equal(singleton(y),null_class) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( singleton(x) != null_class
| ~ member(x,universal_class) ),
inference(subst,[],[corollary_to_set_in_its_singleton:[bind(X,$fot(x))]]) ).
cnf(refute_0_17,plain,
singleton(x) != null_class,
inference(resolve,[$cnf( member(x,universal_class) )],[prove_singleton_identified_by_element1_2,refute_0_16]) ).
cnf(refute_0_18,plain,
regular(singleton(x)) = y,
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( regular(singleton(x)) != x
| regular(singleton(x)) != y
| y = x ),
introduced(tautology,[equality,[$cnf( $equal(regular(singleton(x)),x) ),[0],$fot(y)]]) ).
cnf(refute_0_20,plain,
( regular(singleton(x)) != x
| y = x ),
inference(resolve,[$cnf( $equal(regular(singleton(x)),y) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( singleton(x) = null_class
| y = x ),
inference(resolve,[$cnf( $equal(regular(singleton(x)),x) )],[refute_0_3,refute_0_20]) ).
cnf(refute_0_22,plain,
y = x,
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
( y != x
| x = y ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(y)),bind(Y0,$fot(x))]]) ).
cnf(refute_0_24,plain,
y != x,
inference(resolve,[$cnf( $equal(x,y) )],[refute_0_23,prove_singleton_identified_by_element1_3]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_22,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET083-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n004.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 : Sun Jul 10 16:29:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.05/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/1.22
% 1.05/1.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.05/1.22
%------------------------------------------------------------------------------