TSTP Solution File: SET025-9 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET025-9 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 03:31:27 EDT 2022
% Result : Unsatisfiable 4.19s 4.36s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 14 unt; 0 nHn; 17 RR)
% Number of literals : 37 ( 19 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X,Y)) ).
cnf(ordered_pair,axiom,
ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ).
cnf(ordered_pair_predicate3,axiom,
( ~ ordered_pair_predicate(X)
| X = ordered_pair(f2(X),f3(X)) ) ).
cnf(an_ordered_pair_predicate,hypothesis,
ordered_pair_predicate(a) ).
cnf(prove_predicate_is_small,negated_conjecture,
~ little_set(a) ).
cnf(refute_0_0,plain,
little_set(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110))),
inference(subst,[],[non_ordered_pair4:[bind(X,$fot(singleton_set(X_109))),bind(Y,$fot(non_ordered_pair(X_109,X_110)))]]) ).
cnf(refute_0_1,plain,
ordered_pair(X_109,X_110) = non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_109)),bind(Y,$fot(X_110))]]) ).
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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ordered_pair(X_109,X_110) != non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110))
| non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)) = ordered_pair(X_109,X_110) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(ordered_pair(X_109,X_110))),bind(Y0,$fot(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110))))]]) ).
cnf(refute_0_6,plain,
non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)) = ordered_pair(X_109,X_110),
inference(resolve,[$cnf( $equal(ordered_pair(X_109,X_110),non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)) != ordered_pair(X_109,X_110)
| ~ little_set(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)))
| little_set(ordered_pair(X_109,X_110)) ),
introduced(tautology,[equality,[$cnf( little_set(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110))) ),[0],$fot(ordered_pair(X_109,X_110))]]) ).
cnf(refute_0_8,plain,
( ~ little_set(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)))
| little_set(ordered_pair(X_109,X_110)) ),
inference(resolve,[$cnf( $equal(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110)),ordered_pair(X_109,X_110)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
little_set(ordered_pair(X_109,X_110)),
inference(resolve,[$cnf( little_set(non_ordered_pair(singleton_set(X_109),non_ordered_pair(X_109,X_110))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
little_set(ordered_pair(f2(a),f3(a))),
inference(subst,[],[refute_0_9:[bind(X_109,$fot(f2(a))),bind(X_110,$fot(f3(a)))]]) ).
cnf(refute_0_11,plain,
( ~ ordered_pair_predicate(a)
| a = ordered_pair(f2(a),f3(a)) ),
inference(subst,[],[ordered_pair_predicate3:[bind(X,$fot(a))]]) ).
cnf(refute_0_12,plain,
a = ordered_pair(f2(a),f3(a)),
inference(resolve,[$cnf( ordered_pair_predicate(a) )],[an_ordered_pair_predicate,refute_0_11]) ).
cnf(refute_0_13,plain,
( a != ordered_pair(f2(a),f3(a))
| ordered_pair(f2(a),f3(a)) = a ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(a)),bind(Y0,$fot(ordered_pair(f2(a),f3(a))))]]) ).
cnf(refute_0_14,plain,
ordered_pair(f2(a),f3(a)) = a,
inference(resolve,[$cnf( $equal(a,ordered_pair(f2(a),f3(a))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ordered_pair(f2(a),f3(a)) != a
| ~ little_set(ordered_pair(f2(a),f3(a)))
| little_set(a) ),
introduced(tautology,[equality,[$cnf( little_set(ordered_pair(f2(a),f3(a))) ),[0],$fot(a)]]) ).
cnf(refute_0_16,plain,
( ~ little_set(ordered_pair(f2(a),f3(a)))
| little_set(a) ),
inference(resolve,[$cnf( $equal(ordered_pair(f2(a),f3(a)),a) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
little_set(a),
inference(resolve,[$cnf( little_set(ordered_pair(f2(a),f3(a))) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( little_set(a) )],[refute_0_17,prove_predicate_is_small]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET025-9 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n019.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 17:12:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.19/4.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.19/4.36
% 4.19/4.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.19/4.37
%------------------------------------------------------------------------------