%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET084-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 03:32:23 EDT 2022
% Result : Unsatisfiable 0.93s 1.10s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 20 ( 10 unt; 0 nHn; 19 RR)
% Number of literals : 32 ( 18 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_in_its_singleton,axiom,
( ~ member(X,universal_class)
| member(X,singleton(X)) ) ).
cnf(only_member_in_singleton,axiom,
( ~ member(Y,singleton(X))
| Y = X ) ).
cnf(prove_singleton_identified_by_element2_1,negated_conjecture,
singleton(x) = singleton(y) ).
cnf(prove_singleton_identified_by_element2_2,negated_conjecture,
member(y,universal_class) ).
cnf(prove_singleton_identified_by_element2_3,negated_conjecture,
x != y ).
cnf(refute_0_0,plain,
( ~ member(y,universal_class)
| member(y,singleton(y)) ),
inference(subst,[],[set_in_its_singleton:[bind(X,$fot(y))]]) ).
cnf(refute_0_1,plain,
member(y,singleton(y)),
inference(resolve,[$cnf( member(y,universal_class) )],[prove_singleton_identified_by_element2_2,refute_0_0]) ).
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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( singleton(x) != singleton(y)
| singleton(y) = singleton(x) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(singleton(x))),bind(Y0,$fot(singleton(y)))]]) ).
cnf(refute_0_6,plain,
singleton(y) = singleton(x),
inference(resolve,[$cnf( $equal(singleton(x),singleton(y)) )],[prove_singleton_identified_by_element2_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( singleton(y) != singleton(x)
| ~ member(y,singleton(y))
| member(y,singleton(x)) ),
introduced(tautology,[equality,[$cnf( member(y,singleton(y)) ),[1],$fot(singleton(x))]]) ).
cnf(refute_0_8,plain,
( ~ member(y,singleton(y))
| member(y,singleton(x)) ),
inference(resolve,[$cnf( $equal(singleton(y),singleton(x)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
member(y,singleton(x)),
inference(resolve,[$cnf( member(y,singleton(y)) )],[refute_0_1,refute_0_8]) ).
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,
y = x,
inference(resolve,[$cnf( member(y,singleton(x)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( y != x
| x = y ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(y)),bind(Y0,$fot(x))]]) ).
cnf(refute_0_13,plain,
y != x,
inference(resolve,[$cnf( $equal(x,y) )],[refute_0_12,prove_singleton_identified_by_element2_3]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( $equal(y,x) )],[refute_0_11,refute_0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET084-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n011.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 09:50:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.93/1.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.10
% 0.93/1.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.93/1.11
%------------------------------------------------------------------------------