TSTP Solution File: GRP191-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 10:37:56 EDT 2022
% Result : Unsatisfiable 1.60s 1.78s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 55
% Syntax : Number of clauses : 230 ( 127 unt; 0 nHn; 116 RR)
% Number of literals : 378 ( 377 equ; 149 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 350 ( 10 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_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(idempotence_of_lub,axiom,
least_upper_bound(X,X) = X ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_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(p39d_1,hypothesis,
greatest_lower_bound(a,b) = b ).
cnf(prove_p39d,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b) ).
cnf(refute_0_0,plain,
least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))) = inverse(inverse(X_69)),
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(inverse(inverse(X_69))))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(inverse(X_61),X_61),X_62) = multiply(inverse(X_61),multiply(X_61,X_62)),
inference(subst,[],[associativity:[bind(X,$fot(inverse(X_61))),bind(Y,$fot(X_61)),bind(Z,$fot(X_62))]]) ).
cnf(refute_0_2,plain,
multiply(inverse(X_61),X_61) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(inverse(X_61),X_61),X_62) != multiply(inverse(X_61),multiply(X_61,X_62))
| multiply(inverse(X_61),X_61) != identity
| multiply(identity,X_62) = multiply(inverse(X_61),multiply(X_61,X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_61),X_61),X_62),multiply(inverse(X_61),multiply(X_61,X_62))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_4,plain,
( multiply(multiply(inverse(X_61),X_61),X_62) != multiply(inverse(X_61),multiply(X_61,X_62))
| multiply(identity,X_62) = multiply(inverse(X_61),multiply(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_61),X_61),identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(identity,X_62) = multiply(inverse(X_61),multiply(X_61,X_62)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_61),X_61),X_62),multiply(inverse(X_61),multiply(X_61,X_62))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(identity,X_62) = X_62,
inference(subst,[],[left_identity:[bind(X,$fot(X_62))]]) ).
cnf(refute_0_7,plain,
( multiply(identity,X_62) != X_62
| multiply(identity,X_62) != multiply(inverse(X_61),multiply(X_61,X_62))
| X_62 = multiply(inverse(X_61),multiply(X_61,X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_62),multiply(inverse(X_61),multiply(X_61,X_62))) ),[0],$fot(X_62)]]) ).
cnf(refute_0_8,plain,
( multiply(identity,X_62) != multiply(inverse(X_61),multiply(X_61,X_62))
| X_62 = multiply(inverse(X_61),multiply(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_62),X_62) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
X_62 = multiply(inverse(X_61),multiply(X_61,X_62)),
inference(resolve,[$cnf( $equal(multiply(identity,X_62),multiply(inverse(X_61),multiply(X_61,X_62))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_26)),multiply(inverse(X_26),least_upper_bound(X_25,X_26))),
inference(subst,[],[refute_0_9:[bind(X_61,$fot(inverse(X_26))),bind(X_62,$fot(least_upper_bound(X_25,X_26)))]]) ).
cnf(refute_0_11,plain,
multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(multiply(inverse(X_26),X_25),multiply(inverse(X_26),X_26)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_26))),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_12,plain,
multiply(inverse(X_26),X_26) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_13,plain,
( multiply(inverse(X_26),X_26) != identity
| multiply(inverse(X_26),least_upper_bound(X_25,X_26)) != least_upper_bound(multiply(inverse(X_26),X_25),multiply(inverse(X_26),X_26))
| multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(multiply(inverse(X_26),X_25),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_26),least_upper_bound(X_25,X_26)),least_upper_bound(multiply(inverse(X_26),X_25),multiply(inverse(X_26),X_26))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_14,plain,
( multiply(inverse(X_26),least_upper_bound(X_25,X_26)) != least_upper_bound(multiply(inverse(X_26),X_25),multiply(inverse(X_26),X_26))
| multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(multiply(inverse(X_26),X_25),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),X_26),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(multiply(inverse(X_26),X_25),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),least_upper_bound(X_25,X_26)),least_upper_bound(multiply(inverse(X_26),X_25),multiply(inverse(X_26),X_26))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_17,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_18,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_20,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_19]) ).
cnf(refute_0_21,plain,
least_upper_bound(multiply(inverse(X_26),X_25),identity) = least_upper_bound(identity,multiply(inverse(X_26),X_25)),
inference(subst,[],[refute_0_20:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_26),X_25)))]]) ).
cnf(refute_0_22,plain,
( multiply(inverse(X_26),least_upper_bound(X_25,X_26)) != least_upper_bound(multiply(inverse(X_26),X_25),identity)
| least_upper_bound(multiply(inverse(X_26),X_25),identity) != least_upper_bound(identity,multiply(inverse(X_26),X_25))
| multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(identity,multiply(inverse(X_26),X_25)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_26),least_upper_bound(X_25,X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) ),[0],$fot(least_upper_bound(multiply(inverse(X_26),X_25),identity))]]) ).
cnf(refute_0_23,plain,
( multiply(inverse(X_26),least_upper_bound(X_25,X_26)) != least_upper_bound(multiply(inverse(X_26),X_25),identity)
| multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(identity,multiply(inverse(X_26),X_25)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_26),X_25),identity),least_upper_bound(identity,multiply(inverse(X_26),X_25))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(inverse(X_26),least_upper_bound(X_25,X_26)) = least_upper_bound(identity,multiply(inverse(X_26),X_25)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),least_upper_bound(X_25,X_26)),least_upper_bound(multiply(inverse(X_26),X_25),identity)) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(inverse(X_26),least_upper_bound(X_25,X_26)) != least_upper_bound(identity,multiply(inverse(X_26),X_25))
| least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_26)),multiply(inverse(X_26),least_upper_bound(X_25,X_26)))
| least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_26)),multiply(inverse(X_26),least_upper_bound(X_25,X_26)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_26),X_25)))]]) ).
cnf(refute_0_26,plain,
( least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_26)),multiply(inverse(X_26),least_upper_bound(X_25,X_26)))
| least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_26),least_upper_bound(X_25,X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_26)),multiply(inverse(X_26),least_upper_bound(X_25,X_26)))) )],[refute_0_10,refute_0_26]) ).
cnf(refute_0_28,plain,
least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_25)),multiply(inverse(X_25),least_upper_bound(X_25,X_26))),
inference(subst,[],[refute_0_9:[bind(X_61,$fot(inverse(X_25))),bind(X_62,$fot(least_upper_bound(X_25,X_26)))]]) ).
cnf(refute_0_29,plain,
multiply(inverse(X_25),least_upper_bound(X_25,X_26)) = least_upper_bound(multiply(inverse(X_25),X_25),multiply(inverse(X_25),X_26)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_25))),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_30,plain,
multiply(inverse(X_25),X_25) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_31,plain,
( multiply(inverse(X_25),X_25) != identity
| multiply(inverse(X_25),least_upper_bound(X_25,X_26)) != least_upper_bound(multiply(inverse(X_25),X_25),multiply(inverse(X_25),X_26))
| multiply(inverse(X_25),least_upper_bound(X_25,X_26)) = least_upper_bound(identity,multiply(inverse(X_25),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_25),least_upper_bound(X_25,X_26)),least_upper_bound(multiply(inverse(X_25),X_25),multiply(inverse(X_25),X_26))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_32,plain,
( multiply(inverse(X_25),least_upper_bound(X_25,X_26)) != least_upper_bound(multiply(inverse(X_25),X_25),multiply(inverse(X_25),X_26))
| multiply(inverse(X_25),least_upper_bound(X_25,X_26)) = least_upper_bound(identity,multiply(inverse(X_25),X_26)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),X_25),identity) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(inverse(X_25),least_upper_bound(X_25,X_26)) = least_upper_bound(identity,multiply(inverse(X_25),X_26)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),least_upper_bound(X_25,X_26)),least_upper_bound(multiply(inverse(X_25),X_25),multiply(inverse(X_25),X_26))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( multiply(inverse(X_25),least_upper_bound(X_25,X_26)) != least_upper_bound(identity,multiply(inverse(X_25),X_26))
| least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_25)),multiply(inverse(X_25),least_upper_bound(X_25,X_26)))
| least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_25)),multiply(inverse(X_25),least_upper_bound(X_25,X_26)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_25),X_26)))]]) ).
cnf(refute_0_35,plain,
( least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_25)),multiply(inverse(X_25),least_upper_bound(X_25,X_26)))
| least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),least_upper_bound(X_25,X_26)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
least_upper_bound(X_25,X_26) = multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_25)),multiply(inverse(X_25),least_upper_bound(X_25,X_26)))) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(X_65,X_66) = multiply(inverse(inverse(X_65)),multiply(inverse(X_65),multiply(X_65,X_66))),
inference(subst,[],[refute_0_9:[bind(X_61,$fot(inverse(X_65))),bind(X_62,$fot(multiply(X_65,X_66)))]]) ).
cnf(refute_0_38,plain,
X_66 = multiply(inverse(X_65),multiply(X_65,X_66)),
inference(subst,[],[refute_0_9:[bind(X_61,$fot(X_65)),bind(X_62,$fot(X_66))]]) ).
cnf(refute_0_39,plain,
( X_66 != multiply(inverse(X_65),multiply(X_65,X_66))
| multiply(inverse(X_65),multiply(X_65,X_66)) = X_66 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_66)),bind(Y0,$fot(multiply(inverse(X_65),multiply(X_65,X_66))))]]) ).
cnf(refute_0_40,plain,
multiply(inverse(X_65),multiply(X_65,X_66)) = X_66,
inference(resolve,[$cnf( $equal(X_66,multiply(inverse(X_65),multiply(X_65,X_66))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(X_65,X_66) != multiply(inverse(inverse(X_65)),multiply(inverse(X_65),multiply(X_65,X_66)))
| multiply(inverse(X_65),multiply(X_65,X_66)) != X_66
| multiply(X_65,X_66) = multiply(inverse(inverse(X_65)),X_66) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_65,X_66),multiply(inverse(inverse(X_65)),multiply(inverse(X_65),multiply(X_65,X_66)))) ),[1,1],$fot(X_66)]]) ).
cnf(refute_0_42,plain,
( multiply(X_65,X_66) != multiply(inverse(inverse(X_65)),multiply(inverse(X_65),multiply(X_65,X_66)))
| multiply(X_65,X_66) = multiply(inverse(inverse(X_65)),X_66) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),multiply(X_65,X_66)),X_66) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(X_65,X_66) = multiply(inverse(inverse(X_65)),X_66),
inference(resolve,[$cnf( $equal(multiply(X_65,X_66),multiply(inverse(inverse(X_65)),multiply(inverse(X_65),multiply(X_65,X_66)))) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
( multiply(X_65,X_66) != multiply(inverse(inverse(X_65)),X_66)
| multiply(inverse(inverse(X_65)),X_66) = multiply(X_65,X_66) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(X_65,X_66))),bind(Y0,$fot(multiply(inverse(inverse(X_65)),X_66)))]]) ).
cnf(refute_0_45,plain,
multiply(inverse(inverse(X_65)),X_66) = multiply(X_65,X_66),
inference(resolve,[$cnf( $equal(multiply(X_65,X_66),multiply(inverse(inverse(X_65)),X_66)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(inverse(X_25)),identity) = multiply(X_25,identity),
inference(subst,[],[refute_0_45:[bind(X_65,$fot(X_25)),bind(X_66,$fot(identity))]]) ).
cnf(refute_0_47,plain,
least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) = least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26),
introduced(tautology,[refl,[$fot(least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26))]]) ).
cnf(refute_0_48,plain,
( multiply(inverse(inverse(X_25)),identity) != multiply(X_25,identity)
| least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) != least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26)
| least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) = least_upper_bound(multiply(X_25,identity),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26),least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26)) ),[1,0],$fot(multiply(X_25,identity))]]) ).
cnf(refute_0_49,plain,
( multiply(inverse(inverse(X_25)),identity) != multiply(X_25,identity)
| least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) = least_upper_bound(multiply(X_25,identity),X_26) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26),least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) = least_upper_bound(multiply(X_25,identity),X_26),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_25)),identity),multiply(X_25,identity)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))) = least_upper_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),multiply(X_65,X_66))),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_65))),bind(Z,$fot(multiply(X_65,X_66)))]]) ).
cnf(refute_0_52,plain,
( multiply(inverse(X_65),multiply(X_65,X_66)) != X_66
| multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))) != least_upper_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),multiply(X_65,X_66)))
| multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))) = least_upper_bound(multiply(inverse(X_65),Y),X_66) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))),least_upper_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),multiply(X_65,X_66)))) ),[1,1],$fot(X_66)]]) ).
cnf(refute_0_53,plain,
( multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))) != least_upper_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),multiply(X_65,X_66)))
| multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))) = least_upper_bound(multiply(inverse(X_65),Y),X_66) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),multiply(X_65,X_66)),X_66) )],[refute_0_40,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))) = least_upper_bound(multiply(inverse(X_65),Y),X_66),
inference(resolve,[$cnf( $equal(multiply(inverse(X_65),least_upper_bound(Y,multiply(X_65,X_66))),least_upper_bound(multiply(inverse(X_65),Y),multiply(inverse(X_65),multiply(X_65,X_66)))) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) = least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26),
inference(subst,[],[refute_0_54:[bind(Y,$fot(identity)),bind(X_65,$fot(inverse(X_25))),bind(X_66,$fot(X_26))]]) ).
cnf(refute_0_56,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_57,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_18,refute_0_56]) ).
cnf(refute_0_58,plain,
( multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) != least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26)
| least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) != least_upper_bound(multiply(X_25,identity),X_26)
| multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) = least_upper_bound(multiply(X_25,identity),X_26) ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26))),bind(Z0,$fot(least_upper_bound(multiply(X_25,identity),X_26)))]]) ).
cnf(refute_0_59,plain,
( least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26) != least_upper_bound(multiply(X_25,identity),X_26)
| multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) = least_upper_bound(multiply(X_25,identity),X_26) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))),least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) = least_upper_bound(multiply(X_25,identity),X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_25)),identity),X_26),least_upper_bound(multiply(X_25,identity),X_26)) )],[refute_0_50,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))) != least_upper_bound(multiply(X_25,identity),X_26)
| least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26)))
| least_upper_bound(X_25,X_26) = least_upper_bound(multiply(X_25,identity),X_26) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26)))) ),[1],$fot(least_upper_bound(multiply(X_25,identity),X_26))]]) ).
cnf(refute_0_62,plain,
( least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26)))
| least_upper_bound(X_25,X_26) = least_upper_bound(multiply(X_25,identity),X_26) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26))),least_upper_bound(multiply(X_25,identity),X_26)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
least_upper_bound(X_25,X_26) = least_upper_bound(multiply(X_25,identity),X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_25)),least_upper_bound(identity,multiply(inverse(X_25),X_26)))) )],[refute_0_36,refute_0_62]) ).
cnf(refute_0_64,plain,
( least_upper_bound(X_25,X_26) != least_upper_bound(multiply(X_25,identity),X_26)
| least_upper_bound(multiply(X_25,identity),X_26) = least_upper_bound(X_25,X_26) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_25,X_26))),bind(Y0,$fot(least_upper_bound(multiply(X_25,identity),X_26)))]]) ).
cnf(refute_0_65,plain,
least_upper_bound(multiply(X_25,identity),X_26) = least_upper_bound(X_25,X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),least_upper_bound(multiply(X_25,identity),X_26)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25) = least_upper_bound(inverse(inverse(X_26)),X_25),
inference(subst,[],[refute_0_65:[bind(X_25,$fot(inverse(inverse(X_26)))),bind(X_26,$fot(X_25))]]) ).
cnf(refute_0_67,plain,
multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) = least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25),
inference(subst,[],[refute_0_54:[bind(Y,$fot(identity)),bind(X_65,$fot(inverse(X_26))),bind(X_66,$fot(X_25))]]) ).
cnf(refute_0_68,plain,
( multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) != least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25)
| least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25) != least_upper_bound(inverse(inverse(X_26)),X_25)
| multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) = least_upper_bound(inverse(inverse(X_26)),X_25) ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))))),bind(Y0,$fot(least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25))),bind(Z0,$fot(least_upper_bound(inverse(inverse(X_26)),X_25)))]]) ).
cnf(refute_0_69,plain,
( least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25) != least_upper_bound(inverse(inverse(X_26)),X_25)
| multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) = least_upper_bound(inverse(inverse(X_26)),X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))),least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) = least_upper_bound(inverse(inverse(X_26)),X_25),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(inverse(X_26)),identity),X_25),least_upper_bound(inverse(inverse(X_26)),X_25)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))) != least_upper_bound(inverse(inverse(X_26)),X_25)
| least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25)))
| least_upper_bound(X_25,X_26) = least_upper_bound(inverse(inverse(X_26)),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25)))) ),[1],$fot(least_upper_bound(inverse(inverse(X_26)),X_25))]]) ).
cnf(refute_0_72,plain,
( least_upper_bound(X_25,X_26) != multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25)))
| least_upper_bound(X_25,X_26) = least_upper_bound(inverse(inverse(X_26)),X_25) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25))),least_upper_bound(inverse(inverse(X_26)),X_25)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
least_upper_bound(X_25,X_26) = least_upper_bound(inverse(inverse(X_26)),X_25),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),multiply(inverse(inverse(X_26)),least_upper_bound(identity,multiply(inverse(X_26),X_25)))) )],[refute_0_27,refute_0_72]) ).
cnf(refute_0_74,plain,
least_upper_bound(inverse(inverse(X_69)),X_69) = least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))),
inference(subst,[],[refute_0_73:[bind(X_25,$fot(inverse(inverse(X_69)))),bind(X_26,$fot(X_69))]]) ).
cnf(refute_0_75,plain,
( least_upper_bound(inverse(inverse(X_69)),X_69) != least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69)))
| least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))) = least_upper_bound(inverse(inverse(X_69)),X_69) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(inverse(inverse(X_69)),X_69))),bind(Y0,$fot(least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69)))))]]) ).
cnf(refute_0_76,plain,
least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))) = least_upper_bound(inverse(inverse(X_69)),X_69),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),X_69),least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))) != inverse(inverse(X_69))
| least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))) != least_upper_bound(inverse(inverse(X_69)),X_69)
| least_upper_bound(inverse(inverse(X_69)),X_69) = inverse(inverse(X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))),inverse(inverse(X_69))) ),[0],$fot(least_upper_bound(inverse(inverse(X_69)),X_69))]]) ).
cnf(refute_0_78,plain,
( least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))) != inverse(inverse(X_69))
| least_upper_bound(inverse(inverse(X_69)),X_69) = inverse(inverse(X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))),least_upper_bound(inverse(inverse(X_69)),X_69)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
least_upper_bound(inverse(inverse(X_69)),X_69) = inverse(inverse(X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),inverse(inverse(X_69))),inverse(inverse(X_69))) )],[refute_0_0,refute_0_78]) ).
cnf(refute_0_80,plain,
least_upper_bound(X_69,X_69) = X_69,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_69))]]) ).
cnf(refute_0_81,plain,
( least_upper_bound(X_25,X_26) != least_upper_bound(inverse(inverse(X_26)),X_25)
| least_upper_bound(inverse(inverse(X_26)),X_25) = least_upper_bound(X_25,X_26) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_25,X_26))),bind(Y0,$fot(least_upper_bound(inverse(inverse(X_26)),X_25)))]]) ).
cnf(refute_0_82,plain,
least_upper_bound(inverse(inverse(X_26)),X_25) = least_upper_bound(X_25,X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),least_upper_bound(inverse(inverse(X_26)),X_25)) )],[refute_0_73,refute_0_81]) ).
cnf(refute_0_83,plain,
least_upper_bound(inverse(inverse(X_69)),X_69) = least_upper_bound(X_69,X_69),
inference(subst,[],[refute_0_82:[bind(X_25,$fot(X_69)),bind(X_26,$fot(X_69))]]) ).
cnf(refute_0_84,plain,
( least_upper_bound(X_69,X_69) != X_69
| least_upper_bound(inverse(inverse(X_69)),X_69) != least_upper_bound(X_69,X_69)
| least_upper_bound(inverse(inverse(X_69)),X_69) = X_69 ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(least_upper_bound(inverse(inverse(X_69)),X_69))),bind(Y0,$fot(least_upper_bound(X_69,X_69))),bind(Z0,$fot(X_69))]]) ).
cnf(refute_0_85,plain,
( least_upper_bound(X_69,X_69) != X_69
| least_upper_bound(inverse(inverse(X_69)),X_69) = X_69 ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),X_69),least_upper_bound(X_69,X_69)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
least_upper_bound(inverse(inverse(X_69)),X_69) = X_69,
inference(resolve,[$cnf( $equal(least_upper_bound(X_69,X_69),X_69) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
( least_upper_bound(inverse(inverse(X_69)),X_69) != X_69
| least_upper_bound(inverse(inverse(X_69)),X_69) != inverse(inverse(X_69))
| X_69 = inverse(inverse(X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),X_69),inverse(inverse(X_69))) ),[0],$fot(X_69)]]) ).
cnf(refute_0_88,plain,
( least_upper_bound(inverse(inverse(X_69)),X_69) != inverse(inverse(X_69))
| X_69 = inverse(inverse(X_69)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),X_69),X_69) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
X_69 = inverse(inverse(X_69)),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_69)),X_69),inverse(inverse(X_69))) )],[refute_0_79,refute_0_88]) ).
cnf(refute_0_90,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(inverse(least_upper_bound(inverse(a),inverse(b)))),
inference(subst,[],[refute_0_89:[bind(X_69,$fot(least_upper_bound(inverse(a),inverse(b))))]]) ).
cnf(refute_0_91,plain,
X_66 = multiply(inverse(least_upper_bound(inverse(X_66),X_29)),multiply(least_upper_bound(inverse(X_66),X_29),X_66)),
inference(subst,[],[refute_0_9:[bind(X_61,$fot(least_upper_bound(inverse(X_66),X_29))),bind(X_62,$fot(X_66))]]) ).
cnf(refute_0_92,plain,
multiply(least_upper_bound(inverse(X_27),X_29),X_27) = least_upper_bound(multiply(inverse(X_27),X_27),multiply(X_29,X_27)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_27)),bind(Y,$fot(inverse(X_27))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_93,plain,
multiply(inverse(X_27),X_27) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_94,plain,
( multiply(inverse(X_27),X_27) != identity
| multiply(least_upper_bound(inverse(X_27),X_29),X_27) != least_upper_bound(multiply(inverse(X_27),X_27),multiply(X_29,X_27))
| multiply(least_upper_bound(inverse(X_27),X_29),X_27) = least_upper_bound(identity,multiply(X_29,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(inverse(X_27),X_29),X_27),least_upper_bound(multiply(inverse(X_27),X_27),multiply(X_29,X_27))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_95,plain,
( multiply(least_upper_bound(inverse(X_27),X_29),X_27) != least_upper_bound(multiply(inverse(X_27),X_27),multiply(X_29,X_27))
| multiply(least_upper_bound(inverse(X_27),X_29),X_27) = least_upper_bound(identity,multiply(X_29,X_27)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_27),X_27),identity) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(least_upper_bound(inverse(X_27),X_29),X_27) = least_upper_bound(identity,multiply(X_29,X_27)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_27),X_29),X_27),least_upper_bound(multiply(inverse(X_27),X_27),multiply(X_29,X_27))) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(least_upper_bound(inverse(X_66),X_29),X_66) = least_upper_bound(identity,multiply(X_29,X_66)),
inference(subst,[],[refute_0_96:[bind(X_27,$fot(X_66))]]) ).
cnf(refute_0_98,plain,
( X_66 != multiply(inverse(least_upper_bound(inverse(X_66),X_29)),multiply(least_upper_bound(inverse(X_66),X_29),X_66))
| multiply(least_upper_bound(inverse(X_66),X_29),X_66) != least_upper_bound(identity,multiply(X_29,X_66))
| X_66 = multiply(inverse(least_upper_bound(inverse(X_66),X_29)),least_upper_bound(identity,multiply(X_29,X_66))) ),
introduced(tautology,[equality,[$cnf( $equal(X_66,multiply(inverse(least_upper_bound(inverse(X_66),X_29)),multiply(least_upper_bound(inverse(X_66),X_29),X_66))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_29,X_66)))]]) ).
cnf(refute_0_99,plain,
( X_66 != multiply(inverse(least_upper_bound(inverse(X_66),X_29)),multiply(least_upper_bound(inverse(X_66),X_29),X_66))
| X_66 = multiply(inverse(least_upper_bound(inverse(X_66),X_29)),least_upper_bound(identity,multiply(X_29,X_66))) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(inverse(X_66),X_29),X_66),least_upper_bound(identity,multiply(X_29,X_66))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
X_66 = multiply(inverse(least_upper_bound(inverse(X_66),X_29)),least_upper_bound(identity,multiply(X_29,X_66))),
inference(resolve,[$cnf( $equal(X_66,multiply(inverse(least_upper_bound(inverse(X_66),X_29)),multiply(least_upper_bound(inverse(X_66),X_29),X_66))) )],[refute_0_91,refute_0_99]) ).
cnf(refute_0_101,plain,
b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b))),
inference(subst,[],[refute_0_100:[bind(X_29,$fot(inverse(least_upper_bound(X_148,a)))),bind(X_66,$fot(b))]]) ).
cnf(refute_0_102,plain,
multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,least_upper_bound(X_25,X_136))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)),
inference(subst,[],[refute_0_24:[bind(X_26,$fot(least_upper_bound(X_25,X_136)))]]) ).
cnf(refute_0_103,plain,
least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(least_upper_bound(X_15,X_15),X_16),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_15)),bind(Y,$fot(X_15)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_104,plain,
least_upper_bound(X_15,X_15) = X_15,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_105,plain,
( least_upper_bound(X_15,X_15) != X_15
| least_upper_bound(X_15,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_15,X_15),X_16)
| least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_15,X_15),X_16)) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_106,plain,
( least_upper_bound(X_15,least_upper_bound(X_15,X_16)) != least_upper_bound(least_upper_bound(X_15,X_15),X_16)
| least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,X_15),X_15) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
least_upper_bound(X_15,least_upper_bound(X_15,X_16)) = least_upper_bound(X_15,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(X_15,least_upper_bound(X_15,X_16)),least_upper_bound(least_upper_bound(X_15,X_15),X_16)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
least_upper_bound(X_25,least_upper_bound(X_25,X_136)) = least_upper_bound(X_25,X_136),
inference(subst,[],[refute_0_107:[bind(X_15,$fot(X_25)),bind(X_16,$fot(X_136))]]) ).
cnf(refute_0_109,plain,
( multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,least_upper_bound(X_25,X_136))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))
| least_upper_bound(X_25,least_upper_bound(X_25,X_136)) != least_upper_bound(X_25,X_136)
| multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,least_upper_bound(X_25,X_136))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))) ),[0,1],$fot(least_upper_bound(X_25,X_136))]]) ).
cnf(refute_0_110,plain,
( multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,least_upper_bound(X_25,X_136))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))
| multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,least_upper_bound(X_25,X_136))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))) )],[refute_0_102,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(least_upper_bound(X_25,X_136)))]]) ).
cnf(refute_0_113,plain,
( multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) != identity
| multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))) ),[0],$fot(identity)]]) ).
cnf(refute_0_114,plain,
( multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)) != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)),identity) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25)),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(X_25,X_136)),least_upper_bound(X_25,X_136)),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_25,X_136)),X_25))) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_141,X_140)),X_141)),
inference(subst,[],[refute_0_115:[bind(X_136,$fot(X_140)),bind(X_25,$fot(X_141))]]) ).
cnf(refute_0_117,plain,
least_upper_bound(X_140,X_141) = least_upper_bound(X_141,X_140),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_140)),bind(Y,$fot(X_141))]]) ).
cnf(refute_0_118,plain,
( least_upper_bound(X_140,X_141) != least_upper_bound(X_141,X_140)
| least_upper_bound(X_141,X_140) = least_upper_bound(X_140,X_141) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_140,X_141))),bind(Y0,$fot(least_upper_bound(X_141,X_140)))]]) ).
cnf(refute_0_119,plain,
least_upper_bound(X_141,X_140) = least_upper_bound(X_140,X_141),
inference(resolve,[$cnf( $equal(least_upper_bound(X_140,X_141),least_upper_bound(X_141,X_140)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_141,X_140)),X_141))
| least_upper_bound(X_141,X_140) != least_upper_bound(X_140,X_141)
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_140,X_141)),X_141)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_141,X_140)),X_141))) ),[1,1,0,0],$fot(least_upper_bound(X_140,X_141))]]) ).
cnf(refute_0_121,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_141,X_140)),X_141))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_140,X_141)),X_141)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(X_141,X_140),least_upper_bound(X_140,X_141)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_140,X_141)),X_141)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_141,X_140)),X_141))) )],[refute_0_116,refute_0_121]) ).
cnf(refute_0_123,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_16))),least_upper_bound(b,X_16))),
inference(subst,[],[refute_0_122:[bind(X_140,$fot(a)),bind(X_141,$fot(least_upper_bound(b,X_16)))]]) ).
cnf(refute_0_124,plain,
least_upper_bound(a,least_upper_bound(b,X_16)) = least_upper_bound(least_upper_bound(a,b),X_16),
inference(subst,[],[associativity_of_lub:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_125,plain,
least_upper_bound(a,greatest_lower_bound(a,b)) = a,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_126,plain,
( greatest_lower_bound(a,b) != b
| least_upper_bound(a,greatest_lower_bound(a,b)) != a
| least_upper_bound(a,b) = a ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,b)),a) ),[0,1],$fot(b)]]) ).
cnf(refute_0_127,plain,
( least_upper_bound(a,greatest_lower_bound(a,b)) != a
| least_upper_bound(a,b) = a ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(a,b),b) )],[p39d_1,refute_0_126]) ).
cnf(refute_0_128,plain,
least_upper_bound(a,b) = a,
inference(resolve,[$cnf( $equal(least_upper_bound(a,greatest_lower_bound(a,b)),a) )],[refute_0_125,refute_0_127]) ).
cnf(refute_0_129,plain,
( least_upper_bound(a,b) != a
| least_upper_bound(a,least_upper_bound(b,X_16)) != least_upper_bound(least_upper_bound(a,b),X_16)
| least_upper_bound(a,least_upper_bound(b,X_16)) = least_upper_bound(a,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_16)),least_upper_bound(least_upper_bound(a,b),X_16)) ),[1,0],$fot(a)]]) ).
cnf(refute_0_130,plain,
( least_upper_bound(a,least_upper_bound(b,X_16)) != least_upper_bound(least_upper_bound(a,b),X_16)
| least_upper_bound(a,least_upper_bound(b,X_16)) = least_upper_bound(a,X_16) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,b),a) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
least_upper_bound(a,least_upper_bound(b,X_16)) = least_upper_bound(a,X_16),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_16)),least_upper_bound(least_upper_bound(a,b),X_16)) )],[refute_0_124,refute_0_130]) ).
cnf(refute_0_132,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_16))),least_upper_bound(b,X_16)))
| least_upper_bound(a,least_upper_bound(b,X_16)) != least_upper_bound(a,X_16)
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_16))),least_upper_bound(b,X_16)))) ),[1,1,0,0],$fot(least_upper_bound(a,X_16))]]) ).
cnf(refute_0_133,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_16))),least_upper_bound(b,X_16)))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,X_16))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(b,X_16)),least_upper_bound(a,X_16)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,X_16))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(b,X_16))),least_upper_bound(b,X_16)))) )],[refute_0_123,refute_0_133]) ).
cnf(refute_0_135,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(a,X_16))),least_upper_bound(b,least_upper_bound(a,X_16)))),
inference(subst,[],[refute_0_134:[bind(X_16,$fot(least_upper_bound(a,X_16)))]]) ).
cnf(refute_0_136,plain,
least_upper_bound(a,least_upper_bound(a,X_16)) = least_upper_bound(a,X_16),
inference(subst,[],[refute_0_107:[bind(X_15,$fot(a))]]) ).
cnf(refute_0_137,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(a,X_16))),least_upper_bound(b,least_upper_bound(a,X_16))))
| least_upper_bound(a,least_upper_bound(a,X_16)) != least_upper_bound(a,X_16)
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(a,X_16))),least_upper_bound(b,least_upper_bound(a,X_16))))) ),[1,1,0,0],$fot(least_upper_bound(a,X_16))]]) ).
cnf(refute_0_138,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(a,X_16))),least_upper_bound(b,least_upper_bound(a,X_16))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(a,X_16)),least_upper_bound(a,X_16)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,least_upper_bound(a,X_16))),least_upper_bound(b,least_upper_bound(a,X_16))))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)),
inference(subst,[],[refute_0_107:[bind(X_15,$fot(identity)),bind(X_16,$fot(multiply(inverse(least_upper_bound(a,X_16)),b)))]]) ).
cnf(refute_0_141,plain,
least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))) = least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)),
inference(subst,[],[associativity_of_lub:[bind(Y,$fot(identity)),bind(Z,$fot(multiply(inverse(X_55),X_54)))]]) ).
cnf(refute_0_142,plain,
multiply(inverse(X_55),least_upper_bound(X_54,X_55)) = least_upper_bound(identity,multiply(inverse(X_55),X_54)),
inference(subst,[],[refute_0_24:[bind(X_25,$fot(X_54)),bind(X_26,$fot(X_55))]]) ).
cnf(refute_0_143,plain,
( multiply(inverse(X_55),least_upper_bound(X_54,X_55)) != least_upper_bound(identity,multiply(inverse(X_55),X_54))
| least_upper_bound(identity,multiply(inverse(X_55),X_54)) = multiply(inverse(X_55),least_upper_bound(X_54,X_55)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(multiply(inverse(X_55),least_upper_bound(X_54,X_55)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_55),X_54))))]]) ).
cnf(refute_0_144,plain,
least_upper_bound(identity,multiply(inverse(X_55),X_54)) = multiply(inverse(X_55),least_upper_bound(X_54,X_55)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_55),least_upper_bound(X_54,X_55)),least_upper_bound(identity,multiply(inverse(X_55),X_54))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
( least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))) != least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))
| least_upper_bound(identity,multiply(inverse(X_55),X_54)) != multiply(inverse(X_55),least_upper_bound(X_54,X_55))
| least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) = least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))),least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))) ),[0,1],$fot(multiply(inverse(X_55),least_upper_bound(X_54,X_55)))]]) ).
cnf(refute_0_146,plain,
( least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))) != least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))
| least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) = least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_55),X_54)),multiply(inverse(X_55),least_upper_bound(X_54,X_55))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) = least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))),least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))) )],[refute_0_141,refute_0_146]) ).
cnf(refute_0_148,plain,
( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
| least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).
cnf(refute_0_149,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_148]) ).
cnf(refute_0_150,plain,
least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)) = least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))),
inference(subst,[],[refute_0_149:[bind(Y,$fot(identity)),bind(Z,$fot(multiply(inverse(X_55),X_54)))]]) ).
cnf(refute_0_151,plain,
( least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) != least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))
| least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)) != least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54)))
| least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) = least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))),least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54)))) ),[0],$fot(least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)))]]) ).
cnf(refute_0_152,plain,
( least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) != least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))
| least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) = least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54)),least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))) = least_upper_bound(X,least_upper_bound(identity,multiply(inverse(X_55),X_54))),
inference(resolve,[$cnf( $equal(least_upper_bound(X,multiply(inverse(X_55),least_upper_bound(X_54,X_55))),least_upper_bound(least_upper_bound(X,identity),multiply(inverse(X_55),X_54))) )],[refute_0_147,refute_0_152]) ).
cnf(refute_0_154,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) = least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))),
inference(subst,[],[refute_0_153:[bind(X,$fot(identity)),bind(X_54,$fot(b)),bind(X_55,$fot(least_upper_bound(a,X_16)))]]) ).
cnf(refute_0_155,plain,
( least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) != least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)))
| least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)) ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))))]]) ).
cnf(refute_0_156,plain,
( least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))),least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))) )],[refute_0_140,refute_0_156]) ).
cnf(refute_0_158,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16))))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))) != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))))]]) ).
cnf(refute_0_159,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16))))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),b)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_16)),least_upper_bound(b,least_upper_bound(a,X_16))))) )],[refute_0_139,refute_0_159]) ).
cnf(refute_0_161,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_148)),b)),
inference(subst,[],[refute_0_160:[bind(X_16,$fot(X_148))]]) ).
cnf(refute_0_162,plain,
least_upper_bound(X_148,a) = least_upper_bound(a,X_148),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_148)),bind(Y,$fot(a))]]) ).
cnf(refute_0_163,plain,
( least_upper_bound(X_148,a) != least_upper_bound(a,X_148)
| least_upper_bound(a,X_148) = least_upper_bound(X_148,a) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_148,a))),bind(Y0,$fot(least_upper_bound(a,X_148)))]]) ).
cnf(refute_0_164,plain,
least_upper_bound(a,X_148) = least_upper_bound(X_148,a),
inference(resolve,[$cnf( $equal(least_upper_bound(X_148,a),least_upper_bound(a,X_148)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_148)),b))
| least_upper_bound(a,X_148) != least_upper_bound(X_148,a)
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_148)),b))) ),[1,1,0,0],$fot(least_upper_bound(X_148,a))]]) ).
cnf(refute_0_166,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_148)),b))
| identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,X_148),least_upper_bound(X_148,a)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)),
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(a,X_148)),b))) )],[refute_0_161,refute_0_166]) ).
cnf(refute_0_168,plain,
( identity != least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)) = identity ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(identity)),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b))))]]) ).
cnf(refute_0_169,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)) = identity,
inference(resolve,[$cnf( $equal(identity,least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)))
| least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)) != identity
| b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_171,plain,
( b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)))
| b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)),identity) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
b = multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),least_upper_bound(identity,multiply(inverse(least_upper_bound(X_148,a)),b)))) )],[refute_0_101,refute_0_171]) ).
cnf(refute_0_173,plain,
X_66 = multiply(inverse(inverse(X_66)),multiply(inverse(X_66),X_66)),
inference(subst,[],[refute_0_9:[bind(X_61,$fot(inverse(X_66))),bind(X_62,$fot(X_66))]]) ).
cnf(refute_0_174,plain,
multiply(inverse(X_66),X_66) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_175,plain,
( X_66 != multiply(inverse(inverse(X_66)),multiply(inverse(X_66),X_66))
| multiply(inverse(X_66),X_66) != identity
| X_66 = multiply(inverse(inverse(X_66)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(X_66,multiply(inverse(inverse(X_66)),multiply(inverse(X_66),X_66))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_176,plain,
( X_66 != multiply(inverse(inverse(X_66)),multiply(inverse(X_66),X_66))
| X_66 = multiply(inverse(inverse(X_66)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),X_66),identity) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
X_66 = multiply(inverse(inverse(X_66)),identity),
inference(resolve,[$cnf( $equal(X_66,multiply(inverse(inverse(X_66)),multiply(inverse(X_66),X_66))) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
multiply(inverse(inverse(X_66)),identity) = multiply(X_66,identity),
inference(subst,[],[refute_0_45:[bind(X_65,$fot(X_66)),bind(X_66,$fot(identity))]]) ).
cnf(refute_0_179,plain,
( X_66 != multiply(inverse(inverse(X_66)),identity)
| multiply(inverse(inverse(X_66)),identity) != multiply(X_66,identity)
| X_66 = multiply(X_66,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_66,multiply(X_66,identity)) ),[0],$fot(multiply(inverse(inverse(X_66)),identity))]]) ).
cnf(refute_0_180,plain,
( X_66 != multiply(inverse(inverse(X_66)),identity)
| X_66 = multiply(X_66,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_66)),identity),multiply(X_66,identity)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
X_66 = multiply(X_66,identity),
inference(resolve,[$cnf( $equal(X_66,multiply(inverse(inverse(X_66)),identity)) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
( X_66 != multiply(X_66,identity)
| multiply(X_66,identity) = X_66 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_66)),bind(Y0,$fot(multiply(X_66,identity)))]]) ).
cnf(refute_0_183,plain,
multiply(X_66,identity) = X_66,
inference(resolve,[$cnf( $equal(X_66,multiply(X_66,identity)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity) = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),
inference(subst,[],[refute_0_183:[bind(X_66,$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a))))))]]) ).
cnf(refute_0_185,plain,
( multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity) != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a))))
| b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity)) ),[1],$fot(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))))]]) ).
cnf(refute_0_186,plain,
( b != multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity)
| b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity),inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a))))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),
inference(resolve,[$cnf( $equal(b,multiply(inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(X_148,a)))),identity)) )],[refute_0_172,refute_0_186]) ).
cnf(refute_0_188,plain,
b = inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a)))),
inference(subst,[],[refute_0_187:[bind(X_148,$fot(a))]]) ).
cnf(refute_0_189,plain,
least_upper_bound(a,a) = a,
inference(subst,[],[idempotence_of_lub:[bind(X,$fot(a))]]) ).
cnf(refute_0_190,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))
| least_upper_bound(a,a) != a
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
introduced(tautology,[equality,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))) ),[1,0,1,0],$fot(a)]]) ).
cnf(refute_0_191,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))
| b = inverse(least_upper_bound(inverse(b),inverse(a))) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,a),a) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
b = inverse(least_upper_bound(inverse(b),inverse(a))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(least_upper_bound(a,a))))) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
( X_69 != inverse(inverse(X_69))
| inverse(inverse(X_69)) = X_69 ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(X_69)),bind(Y0,$fot(inverse(inverse(X_69))))]]) ).
cnf(refute_0_194,plain,
inverse(inverse(X_69)) = X_69,
inference(resolve,[$cnf( $equal(X_69,inverse(inverse(X_69))) )],[refute_0_89,refute_0_193]) ).
cnf(refute_0_195,plain,
inverse(inverse(X_26)) = X_26,
inference(subst,[],[refute_0_194:[bind(X_69,$fot(X_26))]]) ).
cnf(refute_0_196,plain,
least_upper_bound(inverse(inverse(X_26)),X_25) = least_upper_bound(inverse(inverse(X_26)),X_25),
introduced(tautology,[refl,[$fot(least_upper_bound(inverse(inverse(X_26)),X_25))]]) ).
cnf(refute_0_197,plain,
( inverse(inverse(X_26)) != X_26
| least_upper_bound(inverse(inverse(X_26)),X_25) != least_upper_bound(inverse(inverse(X_26)),X_25)
| least_upper_bound(inverse(inverse(X_26)),X_25) = least_upper_bound(X_26,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(inverse(X_26)),X_25),least_upper_bound(inverse(inverse(X_26)),X_25)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_198,plain,
( inverse(inverse(X_26)) != X_26
| least_upper_bound(inverse(inverse(X_26)),X_25) = least_upper_bound(X_26,X_25) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_26)),X_25),least_upper_bound(inverse(inverse(X_26)),X_25)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
least_upper_bound(inverse(inverse(X_26)),X_25) = least_upper_bound(X_26,X_25),
inference(resolve,[$cnf( $equal(inverse(inverse(X_26)),X_26) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
( least_upper_bound(X_25,X_26) != least_upper_bound(inverse(inverse(X_26)),X_25)
| least_upper_bound(inverse(inverse(X_26)),X_25) != least_upper_bound(X_26,X_25)
| least_upper_bound(X_25,X_26) = least_upper_bound(X_26,X_25) ),
introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_25,X_26),least_upper_bound(X_26,X_25)) ),[0],$fot(least_upper_bound(inverse(inverse(X_26)),X_25))]]) ).
cnf(refute_0_201,plain,
( least_upper_bound(X_25,X_26) != least_upper_bound(inverse(inverse(X_26)),X_25)
| least_upper_bound(X_25,X_26) = least_upper_bound(X_26,X_25) ),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(inverse(X_26)),X_25),least_upper_bound(X_26,X_25)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
least_upper_bound(X_25,X_26) = least_upper_bound(X_26,X_25),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),least_upper_bound(inverse(inverse(X_26)),X_25)) )],[refute_0_73,refute_0_201]) ).
cnf(refute_0_203,plain,
( least_upper_bound(X_25,X_26) != least_upper_bound(X_26,X_25)
| least_upper_bound(X_26,X_25) = least_upper_bound(X_25,X_26) ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(least_upper_bound(X_25,X_26))),bind(Y0,$fot(least_upper_bound(X_26,X_25)))]]) ).
cnf(refute_0_204,plain,
least_upper_bound(X_26,X_25) = least_upper_bound(X_25,X_26),
inference(resolve,[$cnf( $equal(least_upper_bound(X_25,X_26),least_upper_bound(X_26,X_25)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
least_upper_bound(inverse(b),inverse(a)) = least_upper_bound(inverse(a),inverse(b)),
inference(subst,[],[refute_0_204:[bind(X_25,$fot(inverse(a))),bind(X_26,$fot(inverse(b)))]]) ).
cnf(refute_0_206,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(b),inverse(a))),
introduced(tautology,[refl,[$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_207,plain,
( inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(b),inverse(a)))
| least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(b),inverse(a)))) ),[1,0],$fot(least_upper_bound(inverse(a),inverse(b)))]]) ).
cnf(refute_0_208,plain,
( least_upper_bound(inverse(b),inverse(a)) != least_upper_bound(inverse(a),inverse(b))
| inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
inverse(least_upper_bound(inverse(b),inverse(a))) = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(b),inverse(a)),least_upper_bound(inverse(a),inverse(b))) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| inverse(least_upper_bound(inverse(b),inverse(a))) != inverse(least_upper_bound(inverse(a),inverse(b)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) ),[0],$fot(inverse(least_upper_bound(inverse(b),inverse(a))))]]) ).
cnf(refute_0_211,plain,
( b != inverse(least_upper_bound(inverse(b),inverse(a)))
| b = inverse(least_upper_bound(inverse(a),inverse(b))) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(b),inverse(a))),inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
b = inverse(least_upper_bound(inverse(a),inverse(b))),
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(b),inverse(a)))) )],[refute_0_192,refute_0_211]) ).
cnf(refute_0_213,plain,
( b != inverse(least_upper_bound(inverse(a),inverse(b)))
| inverse(least_upper_bound(inverse(a),inverse(b))) = b ),
inference(subst,[],[refute_0_18:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(least_upper_bound(inverse(a),inverse(b)))))]]) ).
cnf(refute_0_214,plain,
inverse(least_upper_bound(inverse(a),inverse(b))) = b,
inference(resolve,[$cnf( $equal(b,inverse(least_upper_bound(inverse(a),inverse(b)))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
( inverse(least_upper_bound(inverse(a),inverse(b))) != b
| least_upper_bound(inverse(a),inverse(b)) != inverse(inverse(least_upper_bound(inverse(a),inverse(b))))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(inverse(least_upper_bound(inverse(a),inverse(b))))) ),[1,0],$fot(b)]]) ).
cnf(refute_0_216,plain,
( least_upper_bound(inverse(a),inverse(b)) != inverse(inverse(least_upper_bound(inverse(a),inverse(b))))
| least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
inference(resolve,[$cnf( $equal(inverse(least_upper_bound(inverse(a),inverse(b))),b) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(inverse(least_upper_bound(inverse(a),inverse(b))))) )],[refute_0_90,refute_0_216]) ).
cnf(refute_0_218,plain,
$false,
inference(resolve,[$cnf( $equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)) )],[refute_0_217,prove_p39d]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.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 23:59:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.60/1.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.60/1.78
% 1.60/1.78 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.60/1.80
%------------------------------------------------------------------------------