TSTP Solution File: GRP169-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP169-2 : 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 10:37:15 EDT 2022
% Result : Unsatisfiable 0.91s 1.08s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 37
% Syntax : Number of clauses : 142 ( 80 unt; 0 nHn; 90 RR)
% Number of literals : 229 ( 228 equ; 88 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
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(glb_absorbtion,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p02b_1,hypothesis,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a) ).
cnf(prove_p02b,negated_conjecture,
greatest_lower_bound(a,b) != b ).
cnf(refute_0_0,plain,
greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) = X_8,
inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_1,plain,
least_upper_bound(X_9,X_8) = least_upper_bound(X_8,X_9),
inference(subst,[],[symmetry_of_lub:[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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( least_upper_bound(X_9,X_8) != least_upper_bound(X_8,X_9)
| least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X_9,X_8))),bind(Y0,$fot(least_upper_bound(X_8,X_9)))]]) ).
cnf(refute_0_6,plain,
least_upper_bound(X_8,X_9) = least_upper_bound(X_9,X_8),
inference(resolve,[$cnf( $equal(least_upper_bound(X_9,X_8),least_upper_bound(X_8,X_9)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| least_upper_bound(X_8,X_9) != least_upper_bound(X_9,X_8)
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) ),[0,1],$fot(least_upper_bound(X_9,X_8))]]) ).
cnf(refute_0_8,plain,
( greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)) != X_8
| greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8 ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_8,X_9),least_upper_bound(X_9,X_8)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
greatest_lower_bound(X_8,least_upper_bound(X_9,X_8)) = X_8,
inference(resolve,[$cnf( $equal(greatest_lower_bound(X_8,least_upper_bound(X_8,X_9)),X_8) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
greatest_lower_bound(b,least_upper_bound(a,b)) = b,
inference(subst,[],[refute_0_9:[bind(X_8,$fot(b)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(inverse(X_33),X_33),X_34) = multiply(inverse(X_33),multiply(X_33,X_34)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_33))),bind(Y,$fot(X_33)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_12,plain,
multiply(inverse(X_33),X_33) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_13,plain,
( multiply(multiply(inverse(X_33),X_33),X_34) != multiply(inverse(X_33),multiply(X_33,X_34))
| multiply(inverse(X_33),X_33) != identity
| multiply(identity,X_34) = multiply(inverse(X_33),multiply(X_33,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_33),X_33),X_34),multiply(inverse(X_33),multiply(X_33,X_34))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_14,plain,
( multiply(multiply(inverse(X_33),X_33),X_34) != multiply(inverse(X_33),multiply(X_33,X_34))
| multiply(identity,X_34) = multiply(inverse(X_33),multiply(X_33,X_34)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_33),X_33),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(identity,X_34) = multiply(inverse(X_33),multiply(X_33,X_34)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_33),X_33),X_34),multiply(inverse(X_33),multiply(X_33,X_34))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(identity,X_34) = X_34,
inference(subst,[],[left_identity:[bind(X,$fot(X_34))]]) ).
cnf(refute_0_17,plain,
( multiply(identity,X_34) != X_34
| multiply(identity,X_34) != multiply(inverse(X_33),multiply(X_33,X_34))
| X_34 = multiply(inverse(X_33),multiply(X_33,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_34),multiply(inverse(X_33),multiply(X_33,X_34))) ),[0],$fot(X_34)]]) ).
cnf(refute_0_18,plain,
( multiply(identity,X_34) != multiply(inverse(X_33),multiply(X_33,X_34))
| X_34 = multiply(inverse(X_33),multiply(X_33,X_34)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_34),X_34) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
X_34 = multiply(inverse(X_33),multiply(X_33,X_34)),
inference(resolve,[$cnf( $equal(multiply(identity,X_34),multiply(inverse(X_33),multiply(X_33,X_34))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
X_36 = multiply(inverse(inverse(X_36)),multiply(inverse(X_36),X_36)),
inference(subst,[],[refute_0_19:[bind(X_33,$fot(inverse(X_36))),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_21,plain,
multiply(inverse(X_36),X_36) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_22,plain,
( X_36 != multiply(inverse(inverse(X_36)),multiply(inverse(X_36),X_36))
| multiply(inverse(X_36),X_36) != identity
| X_36 = multiply(inverse(inverse(X_36)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_36,multiply(inverse(inverse(X_36)),multiply(inverse(X_36),X_36))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_23,plain,
( X_36 != multiply(inverse(inverse(X_36)),multiply(inverse(X_36),X_36))
| X_36 = multiply(inverse(inverse(X_36)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_36),X_36),identity) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
X_36 = multiply(inverse(inverse(X_36)),identity),
inference(resolve,[$cnf( $equal(X_36,multiply(inverse(inverse(X_36)),multiply(inverse(X_36),X_36))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(X_35,X_36) = multiply(inverse(inverse(X_35)),multiply(inverse(X_35),multiply(X_35,X_36))),
inference(subst,[],[refute_0_19:[bind(X_33,$fot(inverse(X_35))),bind(X_34,$fot(multiply(X_35,X_36)))]]) ).
cnf(refute_0_26,plain,
X_36 = multiply(inverse(X_35),multiply(X_35,X_36)),
inference(subst,[],[refute_0_19:[bind(X_33,$fot(X_35)),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_27,plain,
( X_36 != multiply(inverse(X_35),multiply(X_35,X_36))
| multiply(inverse(X_35),multiply(X_35,X_36)) = X_36 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_36)),bind(Y0,$fot(multiply(inverse(X_35),multiply(X_35,X_36))))]]) ).
cnf(refute_0_28,plain,
multiply(inverse(X_35),multiply(X_35,X_36)) = X_36,
inference(resolve,[$cnf( $equal(X_36,multiply(inverse(X_35),multiply(X_35,X_36))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( multiply(X_35,X_36) != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),multiply(X_35,X_36)))
| multiply(inverse(X_35),multiply(X_35,X_36)) != X_36
| multiply(X_35,X_36) = multiply(inverse(inverse(X_35)),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_35,X_36),multiply(inverse(inverse(X_35)),multiply(inverse(X_35),multiply(X_35,X_36)))) ),[1,1],$fot(X_36)]]) ).
cnf(refute_0_30,plain,
( multiply(X_35,X_36) != multiply(inverse(inverse(X_35)),multiply(inverse(X_35),multiply(X_35,X_36)))
| multiply(X_35,X_36) = multiply(inverse(inverse(X_35)),X_36) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),multiply(X_35,X_36)),X_36) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(X_35,X_36) = multiply(inverse(inverse(X_35)),X_36),
inference(resolve,[$cnf( $equal(multiply(X_35,X_36),multiply(inverse(inverse(X_35)),multiply(inverse(X_35),multiply(X_35,X_36)))) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
( multiply(X_35,X_36) != multiply(inverse(inverse(X_35)),X_36)
| multiply(inverse(inverse(X_35)),X_36) = multiply(X_35,X_36) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(X_35,X_36))),bind(Y0,$fot(multiply(inverse(inverse(X_35)),X_36)))]]) ).
cnf(refute_0_33,plain,
multiply(inverse(inverse(X_35)),X_36) = multiply(X_35,X_36),
inference(resolve,[$cnf( $equal(multiply(X_35,X_36),multiply(inverse(inverse(X_35)),X_36)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(inverse(inverse(X_36)),identity) = multiply(X_36,identity),
inference(subst,[],[refute_0_33:[bind(X_35,$fot(X_36)),bind(X_36,$fot(identity))]]) ).
cnf(refute_0_35,plain,
( X_36 != multiply(inverse(inverse(X_36)),identity)
| multiply(inverse(inverse(X_36)),identity) != multiply(X_36,identity)
| X_36 = multiply(X_36,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_36,multiply(X_36,identity)) ),[0],$fot(multiply(inverse(inverse(X_36)),identity))]]) ).
cnf(refute_0_36,plain,
( X_36 != multiply(inverse(inverse(X_36)),identity)
| X_36 = multiply(X_36,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_36)),identity),multiply(X_36,identity)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
X_36 = multiply(X_36,identity),
inference(resolve,[$cnf( $equal(X_36,multiply(inverse(inverse(X_36)),identity)) )],[refute_0_24,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(inverse(X_38)) = multiply(inverse(inverse(X_38)),identity),
inference(subst,[],[refute_0_37:[bind(X_36,$fot(inverse(inverse(X_38))))]]) ).
cnf(refute_0_39,plain,
multiply(X_38,identity) = multiply(inverse(inverse(X_38)),identity),
inference(subst,[],[refute_0_31:[bind(X_35,$fot(X_38)),bind(X_36,$fot(identity))]]) ).
cnf(refute_0_40,plain,
( multiply(X_38,identity) != multiply(inverse(inverse(X_38)),identity)
| multiply(inverse(inverse(X_38)),identity) = multiply(X_38,identity) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(X_38,identity))),bind(Y0,$fot(multiply(inverse(inverse(X_38)),identity)))]]) ).
cnf(refute_0_41,plain,
multiply(inverse(inverse(X_38)),identity) = multiply(X_38,identity),
inference(resolve,[$cnf( $equal(multiply(X_38,identity),multiply(inverse(inverse(X_38)),identity)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiply(inverse(inverse(X_38)),identity) != multiply(X_38,identity)
| inverse(inverse(X_38)) != multiply(inverse(inverse(X_38)),identity)
| inverse(inverse(X_38)) = multiply(X_38,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_38)),multiply(inverse(inverse(X_38)),identity)) ),[1],$fot(multiply(X_38,identity))]]) ).
cnf(refute_0_43,plain,
( inverse(inverse(X_38)) != multiply(inverse(inverse(X_38)),identity)
| inverse(inverse(X_38)) = multiply(X_38,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_38)),identity),multiply(X_38,identity)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(inverse(X_38)) = multiply(X_38,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_38)),multiply(inverse(inverse(X_38)),identity)) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( X_36 != multiply(X_36,identity)
| multiply(X_36,identity) = X_36 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(X_36)),bind(Y0,$fot(multiply(X_36,identity)))]]) ).
cnf(refute_0_46,plain,
multiply(X_36,identity) = X_36,
inference(resolve,[$cnf( $equal(X_36,multiply(X_36,identity)) )],[refute_0_37,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(X_38,identity) = X_38,
inference(subst,[],[refute_0_46:[bind(X_36,$fot(X_38))]]) ).
cnf(refute_0_48,plain,
( multiply(X_38,identity) != X_38
| inverse(inverse(X_38)) != multiply(X_38,identity)
| inverse(inverse(X_38)) = X_38 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_38)),multiply(X_38,identity)) ),[1],$fot(X_38)]]) ).
cnf(refute_0_49,plain,
( inverse(inverse(X_38)) != multiply(X_38,identity)
| inverse(inverse(X_38)) = X_38 ),
inference(resolve,[$cnf( $equal(multiply(X_38,identity),X_38) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
inverse(inverse(X_38)) = X_38,
inference(resolve,[$cnf( $equal(inverse(inverse(X_38)),multiply(X_38,identity)) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
inverse(inverse(least_upper_bound(a,b))) = least_upper_bound(a,b),
inference(subst,[],[refute_0_50:[bind(X_38,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_52,plain,
inverse(a) = multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a))),
inference(subst,[],[refute_0_19:[bind(X_33,$fot(least_upper_bound(a,b))),bind(X_34,$fot(inverse(a)))]]) ).
cnf(refute_0_53,plain,
multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(multiply(X_69,X_70),multiply(X_69,inverse(X_69))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(X_69)),bind(Y,$fot(X_70)),bind(Z,$fot(inverse(X_69)))]]) ).
cnf(refute_0_54,plain,
multiply(inverse(inverse(X_38)),inverse(X_38)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_38)))]]) ).
cnf(refute_0_55,plain,
multiply(X_38,inverse(X_38)) = multiply(inverse(inverse(X_38)),inverse(X_38)),
inference(subst,[],[refute_0_31:[bind(X_35,$fot(X_38)),bind(X_36,$fot(inverse(X_38)))]]) ).
cnf(refute_0_56,plain,
( multiply(X_38,inverse(X_38)) != multiply(inverse(inverse(X_38)),inverse(X_38))
| multiply(inverse(inverse(X_38)),inverse(X_38)) = multiply(X_38,inverse(X_38)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(X_38,inverse(X_38)))),bind(Y0,$fot(multiply(inverse(inverse(X_38)),inverse(X_38))))]]) ).
cnf(refute_0_57,plain,
multiply(inverse(inverse(X_38)),inverse(X_38)) = multiply(X_38,inverse(X_38)),
inference(resolve,[$cnf( $equal(multiply(X_38,inverse(X_38)),multiply(inverse(inverse(X_38)),inverse(X_38))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(inverse(inverse(X_38)),inverse(X_38)) != multiply(X_38,inverse(X_38))
| multiply(inverse(inverse(X_38)),inverse(X_38)) != identity
| multiply(X_38,inverse(X_38)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_38)),inverse(X_38)),identity) ),[0],$fot(multiply(X_38,inverse(X_38)))]]) ).
cnf(refute_0_59,plain,
( multiply(inverse(inverse(X_38)),inverse(X_38)) != identity
| multiply(X_38,inverse(X_38)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_38)),inverse(X_38)),multiply(X_38,inverse(X_38))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(X_38,inverse(X_38)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_38)),inverse(X_38)),identity) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(X_69,inverse(X_69)) = identity,
inference(subst,[],[refute_0_60:[bind(X_38,$fot(X_69))]]) ).
cnf(refute_0_62,plain,
( multiply(X_69,inverse(X_69)) != identity
| multiply(X_69,least_upper_bound(X_70,inverse(X_69))) != least_upper_bound(multiply(X_69,X_70),multiply(X_69,inverse(X_69)))
| multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(multiply(X_69,X_70),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_69,least_upper_bound(X_70,inverse(X_69))),least_upper_bound(multiply(X_69,X_70),multiply(X_69,inverse(X_69)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_63,plain,
( multiply(X_69,least_upper_bound(X_70,inverse(X_69))) != least_upper_bound(multiply(X_69,X_70),multiply(X_69,inverse(X_69)))
| multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(multiply(X_69,X_70),identity) ),
inference(resolve,[$cnf( $equal(multiply(X_69,inverse(X_69)),identity) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(multiply(X_69,X_70),identity),
inference(resolve,[$cnf( $equal(multiply(X_69,least_upper_bound(X_70,inverse(X_69))),least_upper_bound(multiply(X_69,X_70),multiply(X_69,inverse(X_69)))) )],[refute_0_53,refute_0_63]) ).
cnf(refute_0_65,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_66,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_65]) ).
cnf(refute_0_67,plain,
least_upper_bound(multiply(X_69,X_70),identity) = least_upper_bound(identity,multiply(X_69,X_70)),
inference(subst,[],[refute_0_66:[bind(X,$fot(identity)),bind(Y,$fot(multiply(X_69,X_70)))]]) ).
cnf(refute_0_68,plain,
( multiply(X_69,least_upper_bound(X_70,inverse(X_69))) != least_upper_bound(multiply(X_69,X_70),identity)
| least_upper_bound(multiply(X_69,X_70),identity) != least_upper_bound(identity,multiply(X_69,X_70))
| multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(identity,multiply(X_69,X_70)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_69,least_upper_bound(X_70,inverse(X_69))),least_upper_bound(identity,multiply(X_69,X_70))) ),[0],$fot(least_upper_bound(multiply(X_69,X_70),identity))]]) ).
cnf(refute_0_69,plain,
( multiply(X_69,least_upper_bound(X_70,inverse(X_69))) != least_upper_bound(multiply(X_69,X_70),identity)
| multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(identity,multiply(X_69,X_70)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_69,X_70),identity),least_upper_bound(identity,multiply(X_69,X_70))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(X_69,least_upper_bound(X_70,inverse(X_69))) = least_upper_bound(identity,multiply(X_69,X_70)),
inference(resolve,[$cnf( $equal(multiply(X_69,least_upper_bound(X_70,inverse(X_69))),least_upper_bound(multiply(X_69,X_70),identity)) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(b,least_upper_bound(inverse(a),inverse(b))) = least_upper_bound(identity,multiply(b,inverse(a))),
inference(subst,[],[refute_0_70:[bind(X_69,$fot(b)),bind(X_70,$fot(inverse(a)))]]) ).
cnf(refute_0_72,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| least_upper_bound(X,greatest_lower_bound(X,Y)) != X
| least_upper_bound(X,greatest_lower_bound(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X) ),[0,1],$fot(greatest_lower_bound(Y,X))]]) ).
cnf(refute_0_73,plain,
( least_upper_bound(X,greatest_lower_bound(X,Y)) != X
| least_upper_bound(X,greatest_lower_bound(Y,X)) = X ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_72]) ).
cnf(refute_0_74,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(resolve,[$cnf( $equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X) )],[lub_absorbtion,refute_0_73]) ).
cnf(refute_0_75,plain,
least_upper_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(b))) = inverse(b),
inference(subst,[],[refute_0_74:[bind(X,$fot(inverse(b))),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_76,plain,
( greatest_lower_bound(inverse(a),inverse(b)) != inverse(a)
| least_upper_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(b))) != inverse(b)
| least_upper_bound(inverse(b),inverse(a)) = inverse(b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(b))),inverse(b)) ),[0,1],$fot(inverse(a))]]) ).
cnf(refute_0_77,plain,
( least_upper_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(b))) != inverse(b)
| least_upper_bound(inverse(b),inverse(a)) = inverse(b) ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)) )],[p02b_1,refute_0_76]) ).
cnf(refute_0_78,plain,
least_upper_bound(inverse(b),inverse(a)) = inverse(b),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),greatest_lower_bound(inverse(a),inverse(b))),inverse(b)) )],[refute_0_75,refute_0_77]) ).
cnf(refute_0_79,plain,
least_upper_bound(inverse(b),inverse(a)) = least_upper_bound(inverse(a),inverse(b)),
inference(subst,[],[refute_0_66:[bind(X,$fot(inverse(a))),bind(Y,$fot(inverse(b)))]]) ).
cnf(refute_0_80,plain,
( least_upper_bound(inverse(b),inverse(a)) != inverse(b)
| least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(b),inverse(a)),inverse(b)) ),[0],$fot(least_upper_bound(inverse(a),inverse(b)))]]) ).
cnf(refute_0_81,plain,
( least_upper_bound(inverse(b),inverse(a)) != inverse(b)
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(a)),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(a)),inverse(b)) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( multiply(b,least_upper_bound(inverse(a),inverse(b))) != least_upper_bound(identity,multiply(b,inverse(a)))
| least_upper_bound(inverse(a),inverse(b)) != inverse(b)
| multiply(b,inverse(b)) = least_upper_bound(identity,multiply(b,inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,least_upper_bound(inverse(a),inverse(b))),least_upper_bound(identity,multiply(b,inverse(a)))) ),[0,1],$fot(inverse(b))]]) ).
cnf(refute_0_84,plain,
( multiply(b,least_upper_bound(inverse(a),inverse(b))) != least_upper_bound(identity,multiply(b,inverse(a)))
| multiply(b,inverse(b)) = least_upper_bound(identity,multiply(b,inverse(a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(b,inverse(b)) = least_upper_bound(identity,multiply(b,inverse(a))),
inference(resolve,[$cnf( $equal(multiply(b,least_upper_bound(inverse(a),inverse(b))),least_upper_bound(identity,multiply(b,inverse(a)))) )],[refute_0_71,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(b,inverse(b)) = identity,
inference(subst,[],[refute_0_60:[bind(X_38,$fot(b))]]) ).
cnf(refute_0_87,plain,
( multiply(b,inverse(b)) != identity
| multiply(b,inverse(b)) != least_upper_bound(identity,multiply(b,inverse(a)))
| identity = least_upper_bound(identity,multiply(b,inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(b)),least_upper_bound(identity,multiply(b,inverse(a)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_88,plain,
( multiply(b,inverse(b)) != least_upper_bound(identity,multiply(b,inverse(a)))
| identity = least_upper_bound(identity,multiply(b,inverse(a))) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(b)),identity) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
identity = least_upper_bound(identity,multiply(b,inverse(a))),
inference(resolve,[$cnf( $equal(multiply(b,inverse(b)),least_upper_bound(identity,multiply(b,inverse(a)))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(least_upper_bound(X_108,X_109),inverse(X_108)) = least_upper_bound(multiply(X_108,inverse(X_108)),multiply(X_109,inverse(X_108))),
inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_108))),bind(Y,$fot(X_108)),bind(Z,$fot(X_109))]]) ).
cnf(refute_0_91,plain,
multiply(X_108,inverse(X_108)) = identity,
inference(subst,[],[refute_0_60:[bind(X_38,$fot(X_108))]]) ).
cnf(refute_0_92,plain,
( multiply(X_108,inverse(X_108)) != identity
| multiply(least_upper_bound(X_108,X_109),inverse(X_108)) != least_upper_bound(multiply(X_108,inverse(X_108)),multiply(X_109,inverse(X_108)))
| multiply(least_upper_bound(X_108,X_109),inverse(X_108)) = least_upper_bound(identity,multiply(X_109,inverse(X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_108,X_109),inverse(X_108)),least_upper_bound(multiply(X_108,inverse(X_108)),multiply(X_109,inverse(X_108)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_93,plain,
( multiply(least_upper_bound(X_108,X_109),inverse(X_108)) != least_upper_bound(multiply(X_108,inverse(X_108)),multiply(X_109,inverse(X_108)))
| multiply(least_upper_bound(X_108,X_109),inverse(X_108)) = least_upper_bound(identity,multiply(X_109,inverse(X_108))) ),
inference(resolve,[$cnf( $equal(multiply(X_108,inverse(X_108)),identity) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(least_upper_bound(X_108,X_109),inverse(X_108)) = least_upper_bound(identity,multiply(X_109,inverse(X_108))),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,X_109),inverse(X_108)),least_upper_bound(multiply(X_108,inverse(X_108)),multiply(X_109,inverse(X_108)))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(least_upper_bound(X_108,X_109),inverse(X_108)) != least_upper_bound(identity,multiply(X_109,inverse(X_108)))
| least_upper_bound(identity,multiply(X_109,inverse(X_108))) = multiply(least_upper_bound(X_108,X_109),inverse(X_108)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(multiply(least_upper_bound(X_108,X_109),inverse(X_108)))),bind(Y0,$fot(least_upper_bound(identity,multiply(X_109,inverse(X_108)))))]]) ).
cnf(refute_0_96,plain,
least_upper_bound(identity,multiply(X_109,inverse(X_108))) = multiply(least_upper_bound(X_108,X_109),inverse(X_108)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_108,X_109),inverse(X_108)),least_upper_bound(identity,multiply(X_109,inverse(X_108)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
least_upper_bound(identity,multiply(b,inverse(a))) = multiply(least_upper_bound(a,b),inverse(a)),
inference(subst,[],[refute_0_96:[bind(X_108,$fot(a)),bind(X_109,$fot(b))]]) ).
cnf(refute_0_98,plain,
( identity != least_upper_bound(identity,multiply(b,inverse(a)))
| least_upper_bound(identity,multiply(b,inverse(a))) != multiply(least_upper_bound(a,b),inverse(a))
| identity = multiply(least_upper_bound(a,b),inverse(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,multiply(least_upper_bound(a,b),inverse(a))) ),[0],$fot(least_upper_bound(identity,multiply(b,inverse(a))))]]) ).
cnf(refute_0_99,plain,
( identity != least_upper_bound(identity,multiply(b,inverse(a)))
| identity = multiply(least_upper_bound(a,b),inverse(a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(b,inverse(a))),multiply(least_upper_bound(a,b),inverse(a))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
identity = multiply(least_upper_bound(a,b),inverse(a)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(b,inverse(a)))) )],[refute_0_89,refute_0_99]) ).
cnf(refute_0_101,plain,
( identity != multiply(least_upper_bound(a,b),inverse(a))
| multiply(least_upper_bound(a,b),inverse(a)) = identity ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(identity)),bind(Y0,$fot(multiply(least_upper_bound(a,b),inverse(a))))]]) ).
cnf(refute_0_102,plain,
multiply(least_upper_bound(a,b),inverse(a)) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(least_upper_bound(a,b),inverse(a))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( multiply(least_upper_bound(a,b),inverse(a)) != identity
| inverse(a) != multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a)))
| inverse(a) = multiply(inverse(least_upper_bound(a,b)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(a),multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_104,plain,
( inverse(a) != multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a)))
| inverse(a) = multiply(inverse(least_upper_bound(a,b)),identity) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,b),inverse(a)),identity) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
inverse(a) = multiply(inverse(least_upper_bound(a,b)),identity),
inference(resolve,[$cnf( $equal(inverse(a),multiply(inverse(least_upper_bound(a,b)),multiply(least_upper_bound(a,b),inverse(a)))) )],[refute_0_52,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(inverse(least_upper_bound(a,b)),identity) = inverse(least_upper_bound(a,b)),
inference(subst,[],[refute_0_46:[bind(X_36,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_107,plain,
( multiply(inverse(least_upper_bound(a,b)),identity) != inverse(least_upper_bound(a,b))
| inverse(a) != multiply(inverse(least_upper_bound(a,b)),identity)
| inverse(a) = inverse(least_upper_bound(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(a),multiply(inverse(least_upper_bound(a,b)),identity)) ),[1],$fot(inverse(least_upper_bound(a,b)))]]) ).
cnf(refute_0_108,plain,
( inverse(a) != multiply(inverse(least_upper_bound(a,b)),identity)
| inverse(a) = inverse(least_upper_bound(a,b)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(a,b)),identity),inverse(least_upper_bound(a,b))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
inverse(a) = inverse(least_upper_bound(a,b)),
inference(resolve,[$cnf( $equal(inverse(a),multiply(inverse(least_upper_bound(a,b)),identity)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
( inverse(a) != inverse(least_upper_bound(a,b))
| inverse(least_upper_bound(a,b)) = inverse(a) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(inverse(a))),bind(Y0,$fot(inverse(least_upper_bound(a,b))))]]) ).
cnf(refute_0_111,plain,
inverse(least_upper_bound(a,b)) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(a),inverse(least_upper_bound(a,b))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( inverse(inverse(least_upper_bound(a,b))) != least_upper_bound(a,b)
| inverse(least_upper_bound(a,b)) != inverse(a)
| inverse(inverse(a)) = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(a,b))),least_upper_bound(a,b)) ),[0,0],$fot(inverse(a))]]) ).
cnf(refute_0_113,plain,
( inverse(inverse(least_upper_bound(a,b))) != least_upper_bound(a,b)
| inverse(inverse(a)) = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(a,b)),inverse(a)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
inverse(inverse(a)) = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(a,b))),least_upper_bound(a,b)) )],[refute_0_51,refute_0_113]) ).
cnf(refute_0_115,plain,
inverse(inverse(a)) = a,
inference(subst,[],[refute_0_50:[bind(X_38,$fot(a))]]) ).
cnf(refute_0_116,plain,
( inverse(inverse(a)) != a
| inverse(inverse(a)) != least_upper_bound(a,b)
| a = least_upper_bound(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a)),least_upper_bound(a,b)) ),[0],$fot(a)]]) ).
cnf(refute_0_117,plain,
( inverse(inverse(a)) != least_upper_bound(a,b)
| a = least_upper_bound(a,b) ),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
a = least_upper_bound(a,b),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),least_upper_bound(a,b)) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( a != least_upper_bound(a,b)
| least_upper_bound(a,b) = a ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(a)),bind(Y0,$fot(least_upper_bound(a,b)))]]) ).
cnf(refute_0_120,plain,
least_upper_bound(a,b) = a,
inference(resolve,[$cnf( $equal(a,least_upper_bound(a,b)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( greatest_lower_bound(b,least_upper_bound(a,b)) != b
| least_upper_bound(a,b) != a
| greatest_lower_bound(b,a) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,b)),b) ),[0,1],$fot(a)]]) ).
cnf(refute_0_122,plain,
( greatest_lower_bound(b,least_upper_bound(a,b)) != b
| greatest_lower_bound(b,a) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),a) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
greatest_lower_bound(b,a) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,least_upper_bound(a,b)),b) )],[refute_0_10,refute_0_122]) ).
cnf(refute_0_124,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_125,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_124]) ).
cnf(refute_0_126,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(subst,[],[refute_0_125:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_127,plain,
( greatest_lower_bound(b,a) != b
| greatest_lower_bound(b,a) != greatest_lower_bound(a,b)
| greatest_lower_bound(a,b) = b ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(b,a),b) ),[0],$fot(greatest_lower_bound(a,b))]]) ).
cnf(refute_0_128,plain,
( greatest_lower_bound(b,a) != b
| greatest_lower_bound(a,b) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,a),greatest_lower_bound(a,b)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
greatest_lower_bound(a,b) = b,
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,a),b) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
$false,
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[refute_0_129,prove_p02b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.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 : Mon Jun 13 12:11:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.91/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/1.08
% 0.91/1.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.91/1.09
%------------------------------------------------------------------------------