TSTP Solution File: SET025-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET025-4 : 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 03:31:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 10 unt; 0 nHn; 8 RR)
% Number of literals : 22 ( 12 equ; 8 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 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(prove_ordered_pairs_are_small,negated_conjecture,
~ little_set(ordered_pair(a,b)) ).
cnf(refute_0_0,plain,
little_set(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8))),
inference(subst,[],[non_ordered_pair4:[bind(X,$fot(singleton_set(X_7))),bind(Y,$fot(non_ordered_pair(X_7,X_8)))]]) ).
cnf(refute_0_1,plain,
ordered_pair(X_7,X_8) = non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)),
inference(subst,[],[ordered_pair:[bind(X,$fot(X_7)),bind(Y,$fot(X_8))]]) ).
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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ordered_pair(X_7,X_8) != non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8))
| non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)) = ordered_pair(X_7,X_8) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(ordered_pair(X_7,X_8))),bind(Y0,$fot(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8))))]]) ).
cnf(refute_0_6,plain,
non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)) = ordered_pair(X_7,X_8),
inference(resolve,[$cnf( $equal(ordered_pair(X_7,X_8),non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)) != ordered_pair(X_7,X_8)
| ~ little_set(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)))
| little_set(ordered_pair(X_7,X_8)) ),
introduced(tautology,[equality,[$cnf( little_set(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8))) ),[0],$fot(ordered_pair(X_7,X_8))]]) ).
cnf(refute_0_8,plain,
( ~ little_set(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)))
| little_set(ordered_pair(X_7,X_8)) ),
inference(resolve,[$cnf( $equal(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8)),ordered_pair(X_7,X_8)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
little_set(ordered_pair(X_7,X_8)),
inference(resolve,[$cnf( little_set(non_ordered_pair(singleton_set(X_7),non_ordered_pair(X_7,X_8))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
little_set(ordered_pair(a,b)),
inference(subst,[],[refute_0_9:[bind(X_7,$fot(a)),bind(X_8,$fot(b))]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( little_set(ordered_pair(a,b)) )],[refute_0_10,prove_ordered_pairs_are_small]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 00:22:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.40
%------------------------------------------------------------------------------