%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP144-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 : Sat Jul 16 10:37:01 EDT 2022
% Result : Unsatisfiable 0.18s 0.35s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 16 unt; 0 nHn; 17 RR)
% Number of literals : 40 ( 39 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(prove_ax_glb3a,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,b),b) != b ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_4,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(greatest_lower_bound(a,b),b) = least_upper_bound(b,greatest_lower_bound(a,b)),
inference(subst,[],[refute_0_4:[bind(X,$fot(b)),bind(Y,$fot(greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_6,plain,
( least_upper_bound(b,greatest_lower_bound(a,b)) != b
| least_upper_bound(greatest_lower_bound(a,b),b) != least_upper_bound(b,greatest_lower_bound(a,b))
| least_upper_bound(greatest_lower_bound(a,b),b) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),b),least_upper_bound(b,greatest_lower_bound(a,b))) ),[1],$fot(b)]]) ).
cnf(refute_0_7,plain,
( least_upper_bound(b,greatest_lower_bound(a,b)) != b
| least_upper_bound(greatest_lower_bound(a,b),b) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),b),least_upper_bound(b,greatest_lower_bound(a,b))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) != b,
inference(resolve,[$cnf( $equal(least_upper_bound(greatest_lower_bound(a,b),b),b) )],[refute_0_7,prove_ax_glb3a]) ).
cnf(refute_0_9,plain,
least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) = X_8,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(X_9,X_8) = greatest_lower_bound(X_8,X_9),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_11,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_12,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) ),[0,1],$fot(greatest_lower_bound(X_9,X_8))]]) ).
cnf(refute_0_14,plain,
( least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) = b,
inference(subst,[],[refute_0_15:[bind(X_8,$fot(b)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_17,plain,
( b != b
| least_upper_bound(b,greatest_lower_bound(a,b)) != b
| least_upper_bound(b,greatest_lower_bound(a,b)) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) ),[0,0],$fot(b)]]) ).
cnf(refute_0_18,plain,
( b != b
| least_upper_bound(b,greatest_lower_bound(a,b)) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
b != b,
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(a,b)),b) )],[refute_0_18,refute_0_8]) ).
cnf(refute_0_20,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_20,refute_0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP144-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.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 Jun 13 05:26:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35
% 0.18/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.35
%------------------------------------------------------------------------------