TSTP Solution File: GRP150-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP150-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 10:37:03 EDT 2022
% Result : Unsatisfiable 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 40 ( 25 unt; 0 nHn; 20 RR)
% Number of literals : 61 ( 60 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 68 ( 5 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(associativity_of_lub,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(prove_ax_lub2a,negated_conjecture,
least_upper_bound(a,least_upper_bound(a,b)) != least_upper_bound(a,b) ).
cnf(refute_0_0,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_1,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_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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( greatest_lower_bound(X_9,X_8) != greatest_lower_bound(X_8,X_9)
| greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X_9,X_8))),bind(Y0,$fot(greatest_lower_bound(X_8,X_9)))]]) ).
cnf(refute_0_6,plain,
greatest_lower_bound(X_8,X_9) = greatest_lower_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_9,X_8),greatest_lower_bound(X_8,X_9)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(X_8,X_9) != greatest_lower_bound(X_9,X_8)
| least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$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_8,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( $equal(greatest_lower_bound(X_8,X_9),greatest_lower_bound(X_9,X_8)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
least_upper_bound(X_8,greatest_lower_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,greatest_lower_bound(X_8,X_9)),X_8) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) = least_upper_bound(X_13,Y),
inference(subst,[],[refute_0_9:[bind(X_8,$fot(least_upper_bound(X_13,Y))),bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_11,plain,
greatest_lower_bound(X_13,least_upper_bound(X_13,Y)) = X_13,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_12,plain,
( greatest_lower_bound(X_13,least_upper_bound(X_13,Y)) != X_13
| least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))),least_upper_bound(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_13,plain,
( least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_13,least_upper_bound(X_13,Y)),X_13) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),greatest_lower_bound(X_13,least_upper_bound(X_13,Y))),least_upper_bound(X_13,Y)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_16,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_15]) ).
cnf(refute_0_17,plain,
least_upper_bound(least_upper_bound(X_13,Y),X_13) = least_upper_bound(X_13,least_upper_bound(Y,X_13)),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_18,plain,
( least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,Y)
| least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,least_upper_bound(Y,X_13))
| least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,Y)) ),[0],$fot(least_upper_bound(X_13,least_upper_bound(Y,X_13)))]]) ).
cnf(refute_0_19,plain,
( least_upper_bound(least_upper_bound(X_13,Y),X_13) != least_upper_bound(X_13,Y)
| least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,least_upper_bound(Y,X_13))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
least_upper_bound(X_13,least_upper_bound(Y,X_13)) = least_upper_bound(X_13,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_13,Y),X_13),least_upper_bound(X_13,Y)) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
least_upper_bound(X_15,least_upper_bound(X_14,X_15)) = least_upper_bound(X_15,X_14),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_14)),bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_22,plain,
least_upper_bound(X_15,X_14) = least_upper_bound(X_14,X_15),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_15)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_23,plain,
( least_upper_bound(X_15,X_14) != least_upper_bound(X_14,X_15)
| least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_15,X_14))),bind(Y0,$fot(least_upper_bound(X_14,X_15)))]]) ).
cnf(refute_0_24,plain,
least_upper_bound(X_14,X_15) = least_upper_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_14),least_upper_bound(X_14,X_15)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( least_upper_bound(X_14,X_15) != least_upper_bound(X_15,X_14)
| least_upper_bound(X_15,least_upper_bound(X_14,X_15)) != least_upper_bound(X_15,X_14)
| least_upper_bound(X_15,least_upper_bound(X_15,X_14)) = least_upper_bound(X_15,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_14,X_15)),least_upper_bound(X_15,X_14)) ),[0,1],$fot(least_upper_bound(X_15,X_14))]]) ).
cnf(refute_0_26,plain,
( least_upper_bound(X_15,least_upper_bound(X_14,X_15)) != least_upper_bound(X_15,X_14)
| least_upper_bound(X_15,least_upper_bound(X_15,X_14)) = least_upper_bound(X_15,X_14) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_14,X_15),least_upper_bound(X_15,X_14)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
least_upper_bound(X_15,least_upper_bound(X_15,X_14)) = least_upper_bound(X_15,X_14),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_14,X_15)),least_upper_bound(X_15,X_14)) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
least_upper_bound(a,least_upper_bound(a,b)) = least_upper_bound(a,b),
inference(subst,[],[refute_0_27:[bind(X_14,$fot(b)),bind(X_15,$fot(a))]]) ).
cnf(refute_0_29,plain,
( least_upper_bound(a,b) != least_upper_bound(a,b)
| least_upper_bound(a,least_upper_bound(a,b)) != least_upper_bound(a,b)
| least_upper_bound(a,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,b)),least_upper_bound(a,b)) ),[0,1],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_30,plain,
( least_upper_bound(a,b) != least_upper_bound(a,b)
| least_upper_bound(a,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,b)),least_upper_bound(a,b)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
least_upper_bound(a,b) != least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,b)),least_upper_bound(a,b)) )],[refute_0_30,prove_ax_lub2a]) ).
cnf(refute_0_32,plain,
least_upper_bound(a,b) = least_upper_bound(a,b),
introduced(tautology,[refl,[$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),least_upper_bound(a,b)) )],[refute_0_32,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP150-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 06:09:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------