%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP145-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 10:37:02 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 20 RR)
% Number of literals : 41 ( 40 equ; 19 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X,X) = X ).
cnf(prove_ax_glb3b,negated_conjecture,
greatest_lower_bound(greatest_lower_bound(a,b),b) != greatest_lower_bound(a,b) ).
cnf(refute_0_0,plain,
greatest_lower_bound(b,b) = b,
inference(subst,[],[idempotence_of_gld:[bind(X,$fot(b))]]) ).
cnf(refute_0_1,plain,
greatest_lower_bound(a,greatest_lower_bound(b,b)) = greatest_lower_bound(a,greatest_lower_bound(b,b)),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,greatest_lower_bound(b,b)))]]) ).
cnf(refute_0_2,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,b)) != greatest_lower_bound(a,greatest_lower_bound(b,b))
| greatest_lower_bound(b,b) != b
| greatest_lower_bound(a,greatest_lower_bound(b,b)) = greatest_lower_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,b)),greatest_lower_bound(a,greatest_lower_bound(b,b))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_3,plain,
( greatest_lower_bound(b,b) != b
| greatest_lower_bound(a,greatest_lower_bound(b,b)) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,b)),greatest_lower_bound(a,greatest_lower_bound(b,b))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
greatest_lower_bound(a,greatest_lower_bound(b,b)) = greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,b),b) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
| greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,greatest_lower_bound(b,b)),
inference(subst,[],[refute_0_9:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(b))]]) ).
cnf(refute_0_11,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,b)) != greatest_lower_bound(a,b)
| greatest_lower_bound(greatest_lower_bound(a,b),b) != greatest_lower_bound(a,greatest_lower_bound(b,b))
| greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,b) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(greatest_lower_bound(greatest_lower_bound(a,b),b))),bind(Y0,$fot(greatest_lower_bound(a,greatest_lower_bound(b,b)))),bind(Z0,$fot(greatest_lower_bound(a,b)))]]) ).
cnf(refute_0_14,plain,
( greatest_lower_bound(a,greatest_lower_bound(b,b)) != greatest_lower_bound(a,b)
| greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(a,greatest_lower_bound(b,b))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,greatest_lower_bound(b,b)),greatest_lower_bound(a,b)) )],[refute_0_4,refute_0_14]) ).
cnf(refute_0_16,plain,
( greatest_lower_bound(a,b) != greatest_lower_bound(a,b)
| greatest_lower_bound(greatest_lower_bound(a,b),b) != greatest_lower_bound(a,b)
| greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(a,b)) ),[0,0],$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_17,plain,
( greatest_lower_bound(a,b) != greatest_lower_bound(a,b)
| greatest_lower_bound(greatest_lower_bound(a,b),b) = greatest_lower_bound(a,b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(a,b)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
greatest_lower_bound(a,b) != greatest_lower_bound(a,b),
inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(a,b)) )],[refute_0_17,prove_ax_glb3b]) ).
cnf(refute_0_19,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(a,b),
introduced(tautology,[refl,[$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),greatest_lower_bound(a,b)) )],[refute_0_19,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP145-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.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 : Tue Jun 14 14:27:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------