TSTP Solution File: GRP188-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 10:37:53 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 41 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 66 ( 65 equ; 27 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 : 64 ( 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_p38a,negated_conjecture,
least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,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( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_3]) ).
cnf(refute_0_5,plain,
least_upper_bound(b,a) = least_upper_bound(a,b),
inference(subst,[],[refute_0_4:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_6,plain,
least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) = X_10,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_7,plain,
greatest_lower_bound(X_11,X_10) = greatest_lower_bound(X_10,X_11),
inference(subst,[],[symmetry_of_glb:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(X_11,X_10) != greatest_lower_bound(X_10,X_11)
| greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(greatest_lower_bound(X_11,X_10))),bind(Y0,$fot(greatest_lower_bound(X_10,X_11)))]]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(X_10,X_11) = greatest_lower_bound(X_11,X_10),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,X_10),greatest_lower_bound(X_10,X_11)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( greatest_lower_bound(X_10,X_11) != greatest_lower_bound(X_11,X_10)
| least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) ),[0,1],$fot(greatest_lower_bound(X_11,X_10))]]) ).
cnf(refute_0_11,plain,
( least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)) != X_10
| least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,X_11),greatest_lower_bound(X_11,X_10)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
least_upper_bound(X_10,greatest_lower_bound(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(least_upper_bound(X_10,greatest_lower_bound(X_10,X_11)),X_10) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) = least_upper_bound(X_11,X_15),
inference(subst,[],[refute_0_12:[bind(X_10,$fot(least_upper_bound(X_11,X_15)))]]) ).
cnf(refute_0_14,plain,
greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)) = X_11,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_11)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_15,plain,
( greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)) != X_11
| least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) != least_upper_bound(X_11,X_15)
| least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))),least_upper_bound(X_11,X_15)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_16,plain,
( least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))) != least_upper_bound(X_11,X_15)
| least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_11,least_upper_bound(X_11,X_15)),X_11) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),greatest_lower_bound(X_11,least_upper_bound(X_11,X_15))),least_upper_bound(X_11,X_15)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_19,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_18]) ).
cnf(refute_0_20,plain,
least_upper_bound(least_upper_bound(X_11,X_15),X_11) = least_upper_bound(X_11,least_upper_bound(X_15,X_11)),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_11)),bind(Y,$fot(X_15)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_21,plain,
( least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,X_15)
| least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,least_upper_bound(X_15,X_11))
| least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,X_15)) ),[0],$fot(least_upper_bound(X_11,least_upper_bound(X_15,X_11)))]]) ).
cnf(refute_0_22,plain,
( least_upper_bound(least_upper_bound(X_11,X_15),X_11) != least_upper_bound(X_11,X_15)
| least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,least_upper_bound(X_15,X_11))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
least_upper_bound(X_11,least_upper_bound(X_15,X_11)) = least_upper_bound(X_11,X_15),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_11,X_15),X_11),least_upper_bound(X_11,X_15)) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(b,a),
inference(subst,[],[refute_0_23:[bind(X_11,$fot(b)),bind(X_15,$fot(a))]]) ).
cnf(refute_0_25,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_25]) ).
cnf(refute_0_27,plain,
( least_upper_bound(b,a) != least_upper_bound(a,b)
| least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(b,a)
| least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(least_upper_bound(b,least_upper_bound(a,b)))),bind(Y0,$fot(least_upper_bound(b,a))),bind(Z0,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_28,plain,
( least_upper_bound(b,a) != least_upper_bound(a,b)
| least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(a,b)),least_upper_bound(b,a)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(b,a),least_upper_bound(a,b)) )],[refute_0_5,refute_0_28]) ).
cnf(refute_0_30,plain,
( least_upper_bound(a,b) != least_upper_bound(a,b)
| least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b)
| least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,least_upper_bound(a,b)),least_upper_bound(a,b)) ),[0,1],$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_31,plain,
( least_upper_bound(a,b) != least_upper_bound(a,b)
| least_upper_bound(b,least_upper_bound(a,b)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(a,b)),least_upper_bound(a,b)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
least_upper_bound(a,b) != least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(least_upper_bound(b,least_upper_bound(a,b)),least_upper_bound(a,b)) )],[refute_0_31,prove_p38a]) ).
cnf(refute_0_33,plain,
least_upper_bound(a,b) = least_upper_bound(a,b),
introduced(tautology,[refl,[$fot(least_upper_bound(a,b))]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),least_upper_bound(a,b)) )],[refute_0_33,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.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 04:43:18 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
% 0.12/0.36
%------------------------------------------------------------------------------